Re: [sage-support] Re: [sage-devel] simplify_full on matrices.
On Wed, Jan 19, 2011 at 10:16 AM, kcrisman kcris...@gmail.com wrote: On Jan 19, 8:24 am, ancienthart joalheag...@gmail.com wrote: Attempting to use this on my matrix, I end up with the following results (D is my matrix): I personally wish that sage simplify functions worked as follows: simplify_rational and simplify_trig work as currently implemented. simplify was renamed simplify_basic Simplify was replaced with a new method/function that try/excepted the algorithms in simplify_full, simplify_trig, simplify_rational then simplify_basic, returning the first that succeeded. I understand the need to provide functions that control the level of detail used when simplifying complex problems. However I'd assume that most basic/mid-level users just want the expression/equation/object simplified with as little fiddly-ness as possible. Currently I tend to call simplify_full on most problems - I.e. simplify_full is my practical default rather than simplify. I feel like there is a ticket out there to refactor a lot of this kind of stuff (simplify, expand, factor, etc.). Since there is a lot of disagreement on what exactly is the best course of action, we have thus far continued our current scheme. I think that this is not the worst of the proposals I've heard. More important is the option to apply a lot of things to a matrix. Simon's got the right idea (lambda functions) for what you want to do. But we should make this easier. My guess is that even the 'magic' decorator for turning methods into functions wouldn't help here, and that is too bad. Maybe matrices need some way for that to happen - but I have no idea how one would implement something general like that, esp. if one couldn't tell ahead of time whether all the elements would have the method. sage: A = random_matrix(SR, 3) - x; A [-x -2 -2] [ 2 -x - 1 -2] [-1 -2 -x + 1] sage: A.apply_map(type(x).simplify_full) [-x -2 -2] [ 2 -x - 1 -2] [-1 -2 -x + 1] sage: A = matrix(3, 3, [(1+x)^k for k in range(9)]); A [1 x + 1 (x + 1)^2] [(x + 1)^3 (x + 1)^4 (x + 1)^5] [(x + 1)^6 (x + 1)^7 (x + 1)^8] sage: type(x) type 'sage.symbolic.expression.Expression' sage: A.apply_map(Expression.expand) [ 1 x + 1 x^2 + 2*x + 1] [ x^3 + 3*x^2 + 3*x + 1 x^4 + 4*x^3 + 6*x^2 + 4*x + 1 x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1] [ x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1 x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1 x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1] Also, +1 to renaming apply_map to map. The top-level map is a Python function, perhaps we could re-purpose it if the first argument has a map method? - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] plot problem
On Tue, Jan 18, 2011 at 2:35 PM, Daniel Harris mail.dhar...@googlemail.com wrote: Hello everybody I am just looking at sketching graphs and I came across a problem that has me stumped. The graph I am trying to sketch is (x-3) / ( (x+1) * (x-2) ) now I have plotted the graph in sage on my TI-83 and at wolfram and they all different. Now I am thinking is sage right and the others wrong? or have I made an error inputting the equation? I would certainly welcome some help on the issue What range are you plotting over? -1 x 1? -5 x 5? This could make a big difference on what the graph looks like. Likewise, what is the scale of the y-axis? I don't think Sage yet tries to remove the asymptotes at -1 and 2 from the plot. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] solving equation question --- rounding error ?
On Tuesday, January 18, 2011 10:19:58 AM UTC-7, einek wrote: Hi tvn, Am Montag, den 17.01.2011, 14:22 -0800 schrieb tvn: I try to solve for 3 variables x y z with 3 equations as below , I am expecting something like z = r1, x = -r1, y = -2*r1 but instead get x = y = z = 0 (which trivially valid though not expected). Is this because the numbers used too complex (equation 2) and have some rounding errors ? if not what's the cause and how to get around it ? Thanks sage version 4.6.1 solve([x + 0.106*y + 1.212*z == 0, 3.8759765625*x + 0.04801171875*y + 3.972*z == 0, 3.0625*x + 0.09325*y + 3.249*z == 0],[x,y,z]) [[x == 0, y == 0, z == 0]] #not expected sage: A = matrix([[1, 0.106, 1.212], [3.8759765625, 0.04801171875, 3.972], [3.0625, 0.09325, 3.249]]) sage: A.rank() 3 Thus (0,0,0) is the unique solution of your system. The problem is rounding error. Over the rationals: sage: A = matrix(3, 3, [QQ(a) for a in [1, 0.106, 1.212, 3.8759765625, 0.04801171875, 3.972, 3.0625, 0.09325, 3.249]]) sage: A [ 1 53/500 303/250] [ 3969/1024 12291/256000 993/250] [ 49/16 373/40003249/1000] sage: A.rank() 2 - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Sage compatibility in Leopard Mac OS
In fact, many sage developers use OS X as their primary system. On Dec 29, 2010 9:58 PM, Michael Welsh yom...@yomcat.geek.nz wrote: Sage runs just fine in OS X. On 30/12/2010, at 5:36 PM, DigDug_the_2nd wrote: I am trying to choose whether to use Sage a Ubuntu machine or a Mac running Leopard on a 64 bit Duo 2 Core processor. As I understand it, Sage started in the Linux world and still can't run well under Windows with out using virtualization. I am new to Macs but I thought the Mac OS was more similar to Linux than Windows is and comes loaded with python. Does this mean that Sage can run all of its features in Leopard without virtualization, or are their some limitations? Thanks in advance for putting up with a newbie Doug -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.comsage-support%2bunsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- http://yomcat.geek.nz -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.comsage-support%2bunsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: PY_TYPE_CHECK or isinstance?
On Tue, Dec 21, 2010 at 4:16 AM, Volker Braun vbraun.n...@gmail.com wrote: No, it's because your loop is over 1 rather than 1000. Sharp eyes! :) So, to summarize, with the improved Cython one should always use isinstance as it will be optimized to be at least as fast. Yes, as long as the rhs is known by the compiler to be a type (extension or built-in). I guess we should remove the PY_TYPE_CHECK macro from Sage altogether and replace every occurrence with isinstance? Exactly. However, I just found a compiler crash with isinstance(x, typet), so we should wait for the next Cython to go in before doing this. There's a lot of cruft from when Cython just wasn't as good as it is now that's still being used. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: PY_TYPE_CHECK or isinstance?
On Tue, Dec 21, 2010 at 10:29 AM, Jason Grout jason-s...@creativetrax.com wrote: On 12/21/10 11:36 AM, Robert Bradshaw wrote: On Tue, Dec 21, 2010 at 4:16 AM, Volker Braunvbraun.n...@gmail.com wrote: No, it's because your loop is over 1 rather than 1000. Sharp eyes! :) So, to summarize, with the improved Cython one should always use isinstance as it will be optimized to be at least as fast. Yes, as long as the rhs is known by the compiler to be a type (extension or built-in). I guess we should remove the PY_TYPE_CHECK macro from Sage altogether and replace every occurrence with isinstance? Exactly. However, I just found a compiler crash with isinstance(x, typet), so we should wait for the next Cython to go in before doing this. There's a lot of cruft from when Cython just wasn't as good as it is now that's still being used. Do you mean wait until Cython 0.14 goes into Sage, or wait until Cython 0.15 is released and goes into Sage? 0.14.1, which I'm thinking will be out in January (in time for 4.6.2, and I think the 4.6.1 window is almost closed anyway). - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: factor() behaving badly
On Sun, Dec 19, 2010 at 9:39 PM, John H Palmieri jhpalmier...@gmail.com wrote: On Dec 19, 7:01 pm, Alex Raichev tortoise.s...@gmail.com wrote: Hi all: I get differently formatted answers using factor() multiple times on the same polynomial. I wouldn't call it a bug, but it sure is annoying when doctesting. Alex -- | Sage Version 4.6, Release Date: 2010-10-30 | | Type notebook() for the GUI, and license() for information. | -- sage: R.x,y= PolynomialRing(QQ) sage: H= x^2*y^4 +y^6 +2*x^3*y^2 +2*x*y^4 -7*x^4 +7*x^2*y^2 +14*y^4 +6*x^3 +6*x*y^2 +47*x^2 +47*y^2 sage: for k in range(20): : print H.factor() : (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47) (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47) (x^2 + y^2) * (y^4 + 2*x*y^2 - 7*x^2 + 14*y^2 + 6*x + 47) (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47) (x^2 + y^2) * (y^4 + 2*x*y^2 - 7*x^2 + 14*y^2 + 6*x + 47) (x^2 + y^2) * (y^4 + 2*x*y^2 - 7*x^2 + 14*y^2 + 6*x + 47) (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47) (x^2 + y^2) * (y^4 + 2*x*y^2 - 7*x^2 + 14*y^2 + 6*x + 47) (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47) (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47) (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47) (x^2 + y^2) * (y^4 + 2*x*y^2 - 7*x^2 + 14*y^2 + 6*x + 47) (x^2 + y^2) * (y^4 + 2*x*y^2 - 7*x^2 + 14*y^2 + 6*x + 47) (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47) (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47) (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47) (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47) (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47) (-x^2 - y^2) * (-y^4 - 2*x*y^2 + 7*x^2 - 14*y^2 - 6*x - 47) (x^2 + y^2) * (y^4 + 2*x*y^2 - 7*x^2 + 14*y^2 + 6*x + 47) Well, you could do sage: all([H==H.factor().prod() for k in range(20)]) True to doctest it. (I'm assuming that the prod method just does basic multiplication, and so its implementation has nothing to do with that of factor, so H==H.factor().prod() actually tests something meaningful.) +1 Probably worth noting the number of factors as well, e.g. sage: factorization = H.factor() sage: len(factorization) 2 sage: prod(factorization) == H True - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: PY_TYPE_CHECK or isinstance?
The PY_TYPE_CHECK macro exists primarily because Cython didn't used to
optimize isinstance.
On Mon, Dec 20, 2010 at 12:34 PM, Volker Braun vbraun.n...@gmail.com wrote:
PY_TYPE_CHECK is just a wrapper macro around PyObject_TypeCheck which
dereferences and compares the object type fields. So that part should be
insanely fast.
If A is a cdef'd type (which is the precondition for using
PY_TYPE_CHECK), then isinstance(x, A) produces exactly the same code
as PY_TYPE_CHECK(x, A) (a single inline call to PyObject_TypeCheck).
Thus I'd say it's better to use the Pythonic isinstance. For some
builtins it can use even more specialized code.
sage: cython('cpdef t(x):\n for i in range(0,1000):\n
PY_TYPE_CHECK(x,int)'); timeit(t(5000), repeat=100)
625 loops, best of 100: 14.1 µs per loop
sage: cython('cpdef t(x):\n for i in range(0,1000):\n
PY_TYPE_CHECK(x,float)'); timeit(t(5000), repeat=100)
625 loops, best of 100: 14.1 µs per loop
sage: cython('cpdef t(x):\n for i in range(0,1000):\n
isinstance(x,int)'); timeit(t(5000), repeat=100)
625 loops, best of 100: 182 ns per loop
sage: cython('cpdef t(x):\n for i in range(0,1000):\n
isinstance(x,float)'); timeit(t(5000), repeat=100)
625 loops, best of 100: 14.1 µs per loop
It seems like isinstance and PY_TYPE_CHECK are equally fast, except that
isinstance caches the result if it was positive.
But if you really write Cython code then you probably want to type the
argument so that the compiler knows what x is. Then I get
sage: cython('cpdef t(int x):\n for i in range(0,1000):\n
PY_TYPE_CHECK(x,int)'); timeit(t(5000), repeat=100)
625 loops, best of 100: 7.72 µs per loop
sage: cython('cpdef t(int x):\n for i in range(0,1000):\n
PY_TYPE_CHECK(x,float)'); timeit(t(5000), repeat=100)
625 loops, best of 100: 12 µs per loop
sage: cython('cpdef t(int x):\n for i in range(0,1):\n
isinstance(x,int)'); timeit(t(5000), repeat=100)
625 loops, best of 100: 111 µs per loop
sage: cython('cpdef t(int x):\n for i in range(0,1):\n
isinstance(x,float)'); timeit(t(5000), repeat=100)
625 loops, best of 100: 118 µs per loop
Now isinstance is a lot slower, while PY_TYPE_CHECK got moderately faster. I
guess isinstance calls from C into Python while the PY_TYPE_CHECK stays in
C?
No, it's because your loop is over 1 rather than 1000.
- Robert
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Re: [sage-support] Re: PY_TYPE_CHECK or isinstance?
On Mon, Dec 20, 2010 at 12:27 PM, Jason Grout
jason-s...@creativetrax.com wrote:
On 12/20/10 1:42 PM, Simon King wrote:
Dear sage-support,
at #10496, David Roe gave me the advice to use PY_TYPE_CHECK rather
than isinstance in Cython files. I did so.
But actually I didn't know PY_TYPE_CHECK at all, and so I have a two
questions:
1) Apparently there are several PY_... functions. Where can I read
about them?
I see them imported in devel/sage/sage/ext/stdsage.pxi:
---
cdef extern from stdsage.h:
ctypedef void PyObject
# Global tuple -- useful optimization
void init_global_empty_tuple()
object PY_NEW(object t)
object PY_NEW_SAME_TYPE(object t)
void* PY_TYPE(object o)
bint PY_TYPE_CHECK(object o, object t)
bint PY_TYPE_CHECK_EXACT(object o, object t)
object IS_INSTANCE(object o, object t)
void PY_SET_TP_NEW(object t1, object t2)
bint HAS_DICTIONARY(object o)
bint PY_IS_NUMERIC(object o)
---
The stdsage.h file is in devel/sage/c_lib/include/stdsage.h, where we find:
---
/** Tests whether zzz_obj is of type zzz_type. The zzz_type must be a
* built-in or extension type. This is just a C++-compatible wrapper
* for PyObject_TypeCheck.
*/
#define PY_TYPE_CHECK(zzz_obj, zzz_type) \
(PyObject_TypeCheck((PyObject*)(zzz_obj), (PyTypeObject*)(zzz_type)))
---
in fact, we find later on:
---
/** This is exactly the same as isinstance (and does return a Python
* bool), but the second argument must be a C-extension type -- so it
* can't be a Python class or a list. If you just want an int return
* value, i.e., aren't going to pass this back to Python, just use
* PY_TYPE_CHECK.
*/
#define IS_INSTANCE(zzz_obj, zzz_type) \
PyBool_FromLong(PY_TYPE_CHECK(zzz_obj, zzz_type))
---
...interpret how you will
2) Is PY_TYPE_CHECK really quicker than isinstance?
It doesn't seem so, actually.
In testtype.pyx, I wrote
cpdef t1(x):
return PY_TYPE_CHECK(x,int)
cpdef t2(x):
return isinstance(x,int)
Then, I got the following timings:
{{{
sage: attach typecheck.pyx
Compiling typecheck.pyx...
sage: t1(5)
False
sage: t1(int(5))
True
sage: t2(5)
False
sage: t2(int(5))
True
sage: timeit(a=t1(5))
625 loops, best of 3: 218 ns per loop
sage: timeit(a=t2(5))
625 loops, best of 3: 205 ns per loop
sage: timeit(a=t1(int(5)))
625 loops, best of 3: 416 ns per loop
sage: timeit(a=t2(int(5)))
625 loops, best of 3: 401 ns per loop
}}}
So, actually isinstance is slightly quicker than PY_TYPE_CHECK. Or do
I misunderstand something?
I notice in the generated C code, Cython is smart and makes isinstance
actually call PyInt_Check, which presumably is faster than PY_TYPE_CHECK.
If instead, you are checking for the Integer type, I get faster numbers for
PY_TYPE_CHECK than isinstance. I also tried to lessen the effects of python
call overhead by running the call in a loop in Cython:
http://demo.sagenb.org/home/pub/65/
if you do from sage.rings.integer cimport Integer the speed
difference should go away.
- Robert
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Re: [sage-support] bool(arcsin(x) == 2*arctan(x/(1+sqrt(1-x^2)))) returns false !!!
On Fri, Nov 12, 2010 at 3:44 PM, Derrick we.sana...@gmail.com wrote: Any clue why bool(arcsin(x) == 2*arctan(x/(1+sqrt(1-x^2 returns false where the expressions are mathematically equivalent. Because an expression being equal to zero is, in general, and undecideable question. If it can't tell, it'd rather error on the side of caution (not being equal) than claim they're equal. I found that arcsin(x) - 2*arctan(x/(1+sqrt(1-x^2))) is not exactly 0 for all x in [-1,1]. True. You can't even represent arcsin(x) exactly as a floating point number for most values of x. There's rounding error and all when you combine operations as well. In sage, is there any way to compare expressions with some numerical precision? sage: expr.subs(x=1/3).n() 0.000 sage: expr.subs(x=1/3).n(100) 3.9443045261050590270586428264e-31 sage: expr.subs(x=1/3).n(1000) 0. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Display all XXXX possibilities? Problem
Sounds like you have a tab in there somewhere, it typically shouldn't be doing this. On Mon, Nov 8, 2010 at 7:27 AM, JJBWebb johnjackw...@gmail.com wrote: I'm trying to build a power series, and when I call the function to build it, sage responds Display all possiblities? (y or n). I hit n, then the same command pops up and then computes the power series correctly. Is there some way to get it so I don't have to hit n (i.e. avoid the Display all ... completely) so I can automate this process? Thanks, -John -- | Sage Version 4.2, Release Date: 2009-10-24 | | Type notebook() for the GUI, and license() for information. | -- sage: P = 79 sage: m = 2 sage: upbound= integer_floor(P^m*(P-1)/10)+10 sage: R.q = PowerSeriesRing(IntegerModRing(P^m),upbound) sage: def EEbuild(bound): : EE = 1 - q -q2 +O(q^upbound) : for i in range(2,bound+1): : EE=EE+(-1)^i*(q^((1/2)*i*(3*i+1))+q^((1/2)*i*(3*i-1))) : return EE : sage: lil = integer_floor(sqrt(upbound*4/3)) + 10 sage: sage: ee = EEbuild(lil)+O(q^upbound) Display all 1859 possibilities? (y or n) sage: ee = EEbuild(lil)+O(q^upbound) sage: -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Creating large matrix hangs
On Fri, Oct 22, 2010 at 9:34 PM, Cary Cherng cche...@gmail.com wrote: I have a sage script that ultimately creates a python list called MMv of length 35354. Each element is a list of length 55. This is in effect a 35354 by 55 matrix. Print statements show that when I run my script with load two.sage it gets stuck at taking this list and creating a matrix. I am using the following to try to create the matrix. MM = matrix(ZZ, MMv) Is there a way I can debug or understand why the matrix creation isn't returning? Can you run top() and see (1) how much CPU it's using and (2) how much memory it's using (compared to your free memory). -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Python or Sage behavior? - List - tuple and iterator
On Sat, Oct 23, 2010 at 8:07 PM, Jason Grout jason-s...@creativetrax.com wrote: A correction to my corrections inline below! On 10/23/10 9:56 PM, Jason Grout wrote: A few little corrections or explanations inline below... On 10/23/10 8:34 AM, Francois Maltey wrote: Rolandb wrote : test=((k2,k1) for k1 in xrange(2,4) for k2 in xrange(1,k1) if gcd(k1,k2)==1) print [t for t in test] print [t for t in test] [(1, 2), (1, 3), (2, 3)] [] I begun to confuse lists L with [...] we can free change : one change one term by L[1]=123, and change the length by L[3:4]=[7,6,8], or del, or L.pop(), ... And tuple with (...) as T=(12,13,14,15) it's impossible to change. A void tuple or a void list are [] and () Actually, the empty tuple is (,)---you mention why in this next sentence: You were right and I was wrong! sage: type(()) type 'tuple' sage: (,) File ipython console, line 1 (,) ^ SyntaxError: invalid syntax In most cases, it's really the comma (not the parentheses) that creates the tuple. sage: a = 123, sage: a (123,) The parentheses are often needed for grouping purposes though. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] What's easiest way to get Sage running on Windows for non-techie students?
On Sat, Oct 9, 2010 at 7:53 AM, Chris Seberino cseber...@gmail.com wrote: What's easiest way to get Sage running on Windows for non-techie students? They'll be lost if the instructions are complicated. Possible to wrap a VMWare + Ubuntu + Sage blob into one big Windows exe file that requires no set up? Depending on how technical you are, the easiest way by far is to set up a Sage server for them yourself, and then all they need on their windows boxes is a web browser and a password. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] What's easiest way to get Sage running on Windows for non-techie students?
On Mon, Oct 11, 2010 at 5:30 AM, A. Jorge Garcia calcp...@aol.com wrote: Depending on how technical you are, the easiest way by far is to set up a Sage server for them yourself, and then all they need on their windows boxes is a web browser and a password. I tried this, and I'm pretty techie, but found it was a huge hassle compared with just letting my students make an account on one of the SAGE servers online. I have a lot of other hardware/software/firmware/networking issues to deal with, this way I have one less headache! I've found pointing people to the public notebooks gives a less than ideal experience, given how overloaded those things often are. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: a sage simple server question
On Tue, Oct 5, 2010 at 7:57 AM, Francisco Botana fbot...@uvigo.es wrote: My question was (and is): is it possible to simultaneously send multiple commands to the simple server? That is, instead of setting, for instance, a to 2 and b to 3 with two distinct http requests, is it possible to send a=2;b=3 through the same request? Yes, it should be. (Been a long time since I've looked at that code.) A similar question: sending a request as if True: a=5, 5 is assigned to a. But I get nothing with if False: a=5; else: b=3 and get NameError: name 'b' is not defined when asking about b. My goal is using Sage as a remote mathematical service for adding symbolic abilities to dynamic geometry environments such as GeoGebra. Any idea? Thanks in advance Try inserting some newlines (and indentation). Newlines can be inserted into a url with if True:%0a a=5%0aelse:%0a b=3 (though typically you'd use a library call to do this). - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Global variables called in a function
On Thu, Sep 30, 2010 at 3:07 AM, Walker ebwal...@gmail.com wrote:
sage: x = this is x
sage: y = this is y
sage: z = this is z
sage: def f():
: print x
: y = new value
: print y
: global z
: z = new value
: print z
:
sage: f()
this is x
new value
new value
sage: x, y, z
('this is x', 'this is y', 'new value')
Yes it's true, that's the behavior I was referring to. My problem was
actually that I couldn't print a global variable inside a function
before I made an assignment to it; the error was something like
Cannot istantiate a local variable before assigning it. and I didn't
understand why I had to assign locally a global variable which had
already been assigned globally. Anyway the keyword global solved my
problem.
Yep, a variable is either local or global throughout the entire function.
- Robert
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Re: [sage-support] Re: Global variables called in a function
On Wed, Sep 29, 2010 at 8:18 AM, Simon King simon.k...@nuigalway.ie wrote:
Hi Walker!
On 29 Sep., 16:42, Walker ebwal...@gmail.com wrote:
... My question is: is there a way to make Sage not
creating a global variable but assigning directly the global one?
This is actually a Python question.
Yes.
It would of course be very
dangerous if variables defined outside a function would influence what
happens inside a function.
No, that's the expected and useful behavior. Otherwise you couldn't
even call other functions from your function (as they are just
variables).
So, unless you explicitly declare *inside
the function* that a variable is global, it won't be visible inside
the function.
So, you could do:
sage: def f():
: global x
: print x
:
sage: x=3
sage: f()
3
sage: x=5
sage: f()
5
Your f will have the same behavior even if x is not declared global.
It works just as it does in Python. Global variables are by default
readable but not writeable from the local scope, so if you do an
assignment and don't declare a variable to be global, then a local
shadow will be created. (Function arguments are considered assignments
as well.) In other words, variable declaration in Python is done by
assignment (as opposed to other languages where it is explicit). An
example is worth a thousand words:
sage: x = this is x
sage: y = this is y
sage: z = this is z
sage: def f():
: print x
: y = new value
: print y
: global z
: z = new value
: print z
:
sage: f()
this is x
new value
new value
sage: x, y, z
('this is x', 'this is y', 'new value')
- Robert
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Re: [sage-support] Question about polynomial rings and their fraction fields
On Fri, Sep 24, 2010 at 6:56 PM, kcrisman kcris...@gmail.com wrote: If I make a polynomial ring using sage: b = PolynomialRing(ZZ, 'x') I get some odd behavior. Namely, sage: bool(b(x)==x) True sage: b(x) x sage: type(b(x)) something about element of the ring sage: type(x) symbolic expression This isn't really that odd, but still I don't know whether it is good that one can still use x as a symbolic variable. Probably this was a design decision. There is the distinction between x the Python variable and x the symbol (aka symbolic variable). For example, in the code below x and y both store the symbol x. sage: y = x sage: y x x just happens to start out as a symbolic variable with the same name as the Python variable. In general, we try to avoid overwriting the namespace, so when you do sage: x = 3 sage: PolynomialRing(ZZ, 'x') Univariate Polynomial Ring in x over Integer Ring sage: x 3 you don't have any surprises. You can change this with inject_on() sage: inject_on() Redefining: FiniteField Frac FractionField FreeMonoid GF LaurentSeriesRing NumberField PolynomialRing quo quotient sage: PolynomialRing(ZZ, 'x') Defining x Univariate Polynomial Ring in x over Integer Ring sage: x x sage: type(x) type 'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint' (And whatever used to be in x is now gone.) Of course most people just write sage: R.x = ZZ[] which defines the ring and assigns the generator in one step. Anyway, what I really don't like is when you make sage: a = FractionField(PolynomialRing(ZZ, 'x')) sage: a(1/x) weird error that seems to imply it has not coerced x to the polynomial ring We should certainly raise a better error here (or accept it). Automatic coercion is always a compromise between convenience and surprise. For example, if we didn't have any coercions there than sage: a = ZZ['x'].gen() sage: a = ZZ['x'](2) sage: b = SR(2) sage: a 2 sage: b 2 sage: bool(a == b) False# hypothetically would be especially confusing, especially if the context weren't so clear (e.g. trying to debug something when a and b were generated by completely different functions at completely different times.) Even if one made an exception for constants sage: a x sage: b x sage: bool(a == b) False# hypothetically I think would still cause more confusion than the current behavior. Did I do something wrong, or is this a bug? Because of the initial behavior, maybe I shouldn't expect to be able to do this. Thanks, - kcrisman -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Question about polynomial rings and their fraction fields
On Sat, Sep 25, 2010 at 10:51 AM, kcrisman kcris...@gmail.com wrote:
This is the only possibility, because the var('x') command executed
by default at startup did the assignment
x = SR('x')
and you haven't bound x to any other object. Once you execute
x = b.0
[ or one of its implicit forms like b.x=PolynomialRing(ZZ,'x')] then
x is no longer referencing the symbolic expression x, but the
univariate polynomial x instead.
Okay, I knew that this would work, but it seems odd that
PolynomialRing(ZZ, 'x') doesn't actually change x, though it's
consistent. So it just represents things with x until I ask for the
Python variable x to be that x, not the var x.
I you want that, do
sage: inject_on()
Nice to see the positive review for
http://trac.sagemath.org/sage_trac/ticket/7741
:) Thanks
Thanks from me too, that's been waiting a long time.
- Robert
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Re: [sage-support] Wrapping C++
On Thu, Sep 23, 2010 at 6:57 AM, Bruce brucewestb...@gmail.com wrote: I have a C++ function I want to call from sage. I have attempted to follow the example in http://docs.cython.org/src/userguide/wrapping_CPlusPlus.html This was unsuccessful. The C++ class is not recognised. The problem seems to be that this is Cython v0.13 whereas sage 4.5.2 (which I am using) and sage 4.5.3 uses Cython v0.12. If this is correct the options seem to be to use cython v0.12 (in which case I don't have documentation) or to upgrade to cython v0.13 (which I don't know how to do). Here is how I tried to read in my C++ header file: cdef extern from /home/masdbn/planargraph/Graph.hpp namespace PlanarGraph: cdef cppclass Graph: pass Where do I go from here? Thanks You have to wrap it the old style way: http://wiki.cython.org/WrappingCPlusPlus?action=recallrev=24 Or get someone to review http://trac.sagemath.org/sage_trac/ticket/9828 so we can get 0.13 into Sage. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Is this a bug?
http://trac.sagemath.org/sage_trac/ticket/9945 needs review. On Fri, Sep 17, 2010 at 8:28 PM, Robert Bradshaw rober...@math.washington.edu wrote: Oops. I'll post a fix. On Fri, Sep 17, 2010 at 12:42 PM, kcrisman kcris...@gmail.com wrote: On Sep 17, 2:30 pm, Alex Lara lrodr...@gmail.com wrote: Hi everyone In Sage 4.5.2 and Sage 4.5.3, I get the following error using partial_fraction_decomposition() sage: R.x = GF(3)[] sage: q = (x+1)/(x^3+x+1) If you try sage: q.part[tab] you'll see that this isn't a method for this object. You are also right that this *was* a method, even as recently as Sage 4.4.4. Old: sage: type(q) type 'sage.rings.fraction_field_element.FractionFieldElement' New: sage: type(q) type 'sage.rings.fraction_field_FpT.FpTElement' Sounds like a small API change to me, though probably unintentional. Looks like ticket #9051, which added this file, was due to Robert Bradshaw. I'm sure he or someone else will have additional info for you. I would log this as a new Trac ticket, but I'm not sure whether this is related to http://trac.sagemath.org/sage_trac/ticket/8499 Thanks for the report! - kcrisman The same error I get using primes different from 2. But if I use 3^2 instead of 3, or a power of some prime, I get a right answer. I did not have the problem using Sage 4.4.1. Thanks in advance. Alex -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Is this a bug?
Oops. I'll post a fix. On Fri, Sep 17, 2010 at 12:42 PM, kcrisman kcris...@gmail.com wrote: On Sep 17, 2:30 pm, Alex Lara lrodr...@gmail.com wrote: Hi everyone In Sage 4.5.2 and Sage 4.5.3, I get the following error using partial_fraction_decomposition() sage: R.x = GF(3)[] sage: q = (x+1)/(x^3+x+1) If you try sage: q.part[tab] you'll see that this isn't a method for this object. You are also right that this *was* a method, even as recently as Sage 4.4.4. Old: sage: type(q) type 'sage.rings.fraction_field_element.FractionFieldElement' New: sage: type(q) type 'sage.rings.fraction_field_FpT.FpTElement' Sounds like a small API change to me, though probably unintentional. Looks like ticket #9051, which added this file, was due to Robert Bradshaw. I'm sure he or someone else will have additional info for you. I would log this as a new Trac ticket, but I'm not sure whether this is related to http://trac.sagemath.org/sage_trac/ticket/8499 Thanks for the report! - kcrisman The same error I get using primes different from 2. But if I use 3^2 instead of 3, or a power of some prime, I get a right answer. I did not have the problem using Sage 4.4.1. Thanks in advance. Alex -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: continued_fraction returns nothing
On Wed, Sep 15, 2010 at 3:47 AM, Håkan Granath hakan.gran...@googlemail.com wrote: On Sep 15, 3:44 am, Robert Bradshaw rober...@math.washington.edu wrote: On Tue, Sep 14, 2010 at 10:44 AM, Håkan Granath hakan.gran...@googlemail.com wrote: On Sep 14, 12:16 am, Robert Bradshaw rober...@math.washington.edu wrote: Alastair correctly deduced the issue that it can't tell if the number is less than or greater than 2, what should it do here? I do not know what it should do, but what I would have expected in this case is that continued_fraction would first compute the 53 bit approximation of the input, and then return the continued fraction of that approximation. If this is what you want, the way to get that is to give it something that has 53 bits of precision. I completely agree :-) In fact, that is what I tried to do but got unexpected results. Some background information: I compute some quantity a, which is a product of the result of some high precision (say 1000 bits) numerical computation and an exact algebraic factor. The number a is expected to be rational, so to identify it I do something like b = a.n(1000) v = continued_fraction(b) However this did not always work, because in some cases b was not a floating point number as expected but a symbolic expression (a bug in my opinion, see below). This, I found, can make the continued fraction computation fail in 2 ways: 1. Sometimes, since b is symbolic it is computed with the default 53 bit precision which is inadequate for my purposes. 2. Sometimes v would be the empty list. Of course I can work around this by doing something like b = a.n(1000).n(1000) but, although it works for my code, it is somewhat of a cludge. Hence I reported the two issues: the topic of this thread and the issue I found with the n() function: http://groups.google.com/group/sage-support/browse_thread/thread/b36c90f1490eac19 I hope this makes sense. Yes, that issue with n() is certainly the root of the problem. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: continued_fraction returns nothing
On Tue, Sep 14, 2010 at 10:44 AM, Håkan Granath hakan.gran...@googlemail.com wrote: On Sep 14, 12:16 am, Robert Bradshaw rober...@math.washington.edu wrote: Alastair correctly deduced the issue that it can't tell if the number is less than or greater than 2, what should it do here? I do not know what it should do, but what I would have expected in this case is that continued_fraction would first compute the 53 bit approximation of the input, and then return the continued fraction of that approximation. If this is what you want, the way to get that is to give it something that has 53 bits of precision. Not returning anything is quite unexpected. Nothing != the empty list. In any case, I think it's better to only give correct digits than have an arbitrary number of tail terms be spurious random stuff that may or may not stabilize as the precision goes up. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: continued_fraction returns nothing
On Tue, Sep 14, 2010 at 6:44 PM, Robert Bradshaw rober...@math.washington.edu wrote: On Tue, Sep 14, 2010 at 10:44 AM, Håkan Granath hakan.gran...@googlemail.com wrote: On Sep 14, 12:16 am, Robert Bradshaw rober...@math.washington.edu wrote: Alastair correctly deduced the issue that it can't tell if the number is less than or greater than 2, what should it do here? I do not know what it should do, but what I would have expected in this case is that continued_fraction would first compute the 53 bit approximation of the input, and then return the continued fraction of that approximation. If this is what you want, the way to get that is to give it something that has 53 bits of precision. I should add that I think some of the confusion comes in the way symbolics and numerical approximations interact. sage: sqrt(2).n() * sqrt(2) 1.41421356237310*sqrt(2) This is, in general, a hard problem, as one needs to guess what the user actually wants... - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: continued_fraction returns nothing
On Mon, Sep 13, 2010 at 1:30 PM, Marshall Hampton hampto...@gmail.com wrote: I am guessing this is an indirect effect from this patch: http://trac.sagemath.org/sage_trac/ticket/8017 but I am not sure. If you do continued_fraction(N(a)) you get the same answer as before, but I would say this is a bug that shouldn't need a workaround. Alastair correctly deduced the issue that it can't tell if the number is less than or greater than 2, what should it do here? On Sep 13, 11:31 am, Håkan Granath hakan.gran...@googlemail.com wrote: In certain cases I get nothing from the continued_fraction function in the latest Sage version: -- | Sage Version 4.5.3, Release Date: 2010-09-04 | | Type notebook() for the GUI, and license() for information. | -- sage: a=sqrt(2).n()*sqrt(2) sage: continued_fraction(a) [] In version 4.5.2 the output was [2, 2251799813685248] Which was wrong. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Arbitrary precision in Cython NumPy?
On Wed, Sep 8, 2010 at 6:39 PM, KvS keesvansch...@gmail.com wrote:
Thanks all, however I am not very successful so far :(.
I tried both options mentioned before:
- only optimize the loops in Cython and keep using symbolic
expressions/infinite precision, but this is unfortunately rather
slow;
What do you mean by symbolic? Are you actually using maxima and the
various calculus modules?
- fully optimize in Cython by turning to doubles everywhere, although
it gets very fast here happens what I was already afraid of: the
algorithm goes belly up after 15 steps :( (I would need a lot more
steps). In step 14 values like 2.51885860e-34 appear and in
combination with the numerical noise gathered this turns out to
produce very wrong values at the next step.
@Robert: I'm trying to implement an algorithm that computes a sequence
of functions v_k according to the rule v_k(x) = \max \{ K-e^x, \int
v_{k-1}(y) p(x+y) dy \}, v_0(x)=K-e^x, where p is a prob. density. The
background is an optimal stopping problem in stochastics. So at each
step I essentially first compute the integral and then determine where
the integral and x - K-e^x intersect, this just by the basic
find_root function in Sage.
It's not difficult (however very annoying...) to write down a formula
for the integral (given the specific density p I'm using) and work out
formulae for all the coefficients that appear in this formula for the
integral in terms of those appearing in v_{k-1}. The number of
coefficients (and hence computations) involved in the formula for v_k
increases very quickly with k, that explains why the algorithm gets
slow in 'symbolic mode'. However 'double mode' is not good enough as
mentioned above.
It sounds like you're trying too extreems--how about using your
double mode algorithm, but instead using elements of RealField(N)
where N 53. This should be much faster than symbolic (if I
understand you right, calling find_root and integrate) but have higher
precision than using raw doubles. This may be enough, without getting
your hands on MPFR directly yourself.
You might also consider looking at how the dickman rho function is
implemented
http://hg.sagemath.org/sage-main/file/b5dab6864f35/sage/functions/transcendental.py#l464
which sounds similar in spirit.
I will try your suggestion for using mpfr, thanks Robert and Greg!
(however it looks a bit scary to me ;)). I need to store the huge
amounts of coefficients somewhere, I guess numpy is my best guess even
though I have to declare the dtype as object then, no?
What do you mean by huge? Would a list suffice? Or if it's a
polynomial, what about a polynomial in RR? For high precision, the
per-element overhead is constant, so I don't see an advantage to using
NumPy here just as a storage divice if the dtype is object.
- Robert
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Re: [sage-support] Re: Arbitrary precision in Cython NumPy?
On Thu, Sep 9, 2010 at 9:46 AM, Jason Grout jason-s...@creativetrax.com wrote: On 9/9/10 11:27 AM, Robert Bradshaw wrote: This should be much faster than symbolic (if I understand you right, calling find_root and integrate) but have higher precision than using raw doubles. I believe the standard find_root uses scipy, which is limited to double precision. Shouldn't be too hard to follow up with Newton's method to increase the precision if desired. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Arbitrary precision in Cython NumPy?
On Thu, Sep 9, 2010 at 11:44 AM, KvS keesvansch...@gmail.com wrote:
On Sep 9, 5:27 pm, Robert Bradshaw rober...@math.washington.edu
wrote:
On Wed, Sep 8, 2010 at 6:39 PM, KvS keesvansch...@gmail.com wrote:
Thanks all, however I am not very successful so far :(.
I tried both options mentioned before:
- only optimize the loops in Cython and keep using symbolic
expressions/infinite precision, but this is unfortunately rather
slow;
What do you mean by symbolic? Are you actually using maxima and the
various calculus modules?
By symbolic/infinite precision I just mean keeping quantities like say
log(2) as they are, rather than approximating them by some finite
precision real number, sorry for the confusion. No, I am not using
Maxima or anything more advanced than the elementary operations, the
exponential function and the find_root function.
- fully optimize in Cython by turning to doubles everywhere, although
it gets very fast here happens what I was already afraid of: the
algorithm goes belly up after 15 steps :( (I would need a lot more
steps). In step 14 values like 2.51885860e-34 appear and in
combination with the numerical noise gathered this turns out to
produce very wrong values at the next step.
@Robert: I'm trying to implement an algorithm that computes a sequence
of functions v_k according to the rule v_k(x) = \max \{ K-e^x, \int
v_{k-1}(y) p(x+y) dy \}, v_0(x)=K-e^x, where p is a prob. density. The
background is an optimal stopping problem in stochastics. So at each
step I essentially first compute the integral and then determine where
the integral and x - K-e^x intersect, this just by the basic
find_root function in Sage.
It's not difficult (however very annoying...) to write down a formula
for the integral (given the specific density p I'm using) and work out
formulae for all the coefficients that appear in this formula for the
integral in terms of those appearing in v_{k-1}. The number of
coefficients (and hence computations) involved in the formula for v_k
increases very quickly with k, that explains why the algorithm gets
slow in 'symbolic mode'. However 'double mode' is not good enough as
mentioned above.
It sounds like you're trying too extreems--how about using your
double mode algorithm, but instead using elements of RealField(N)
where N 53. This should be much faster than symbolic (if I
understand you right, calling find_root and integrate) but have higher
precision than using raw doubles. This may be enough, without getting
your hands on MPFR directly yourself.
(I don't need to do any integration in the code, sorry if my previous
post seemed to suggest that, the integral that occurs there I have
worked out completely in terms of elementary operations.) Yes, I have
tried your suggestion of using RealField (without Cython though) and
this works good in the sense that the added precision in comparison
with floats makes the algorithm produce reliable output, thanks!
However, it is still too slow.
Just out of curiosity, how much did it help?
If I could further speed it up by a few
factors that would be great. I will further try if I can figure out
how to use Cython to speed up parts of the algorithm where a lot of
looping and computing is done.
That should be feasible--you probably don't need to change the whole
thing--profile to see what parts. Excessive coercion may also impact
things.
You might also consider looking at how the dickman rho function is
implementedhttp://hg.sagemath.org/sage-main/file/b5dab6864f35/sage/functions/tra...
which sounds similar in spirit.
I will try your suggestion for using mpfr, thanks Robert and Greg!
(however it looks a bit scary to me ;)). I need to store the huge
amounts of coefficients somewhere, I guess numpy is my best guess even
though I have to declare the dtype as object then, no?
What do you mean by huge? Would a list suffice? Or if it's a
polynomial, what about a polynomial in RR? For high precision, the
per-element overhead is constant, so I don't see an advantage to using
NumPy here just as a storage divice if the dtype is object.
The function v_k is not a polynomial but a piecewise function
consisting of linear combinations of terms a*x^b*exp(c*x) (*) in each
part of its domain. 'Huge' means that the number of coefficients (i.e.
all the a, b and c's in (*)) to be computed in the k-th step of the
algorithm roughly grows like k^2. These coefficients are currently
organized in 4-dimensional Numpy-arrays: the k runs along one axis and
there are three other 'counters' (one to keep track of the part of the
domain etc.). I would prefer not to give up this way of representing
the coefficients as my notes use this form as well. Would you say I
could better use 4-d Python lists rather?
No, for multi-dimensional stuff, NumPy is better, even if you're using
the object dtype.
- Robert
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Re: [sage-support] Re: Arbitrary precision in Cython NumPy?
On Wed, Sep 8, 2010 at 3:03 PM, Greg Marks gtma...@gmail.com wrote: It sounds like a C program using MPFR (http://www.mpfr.org) would do what you want. As MPFR is built into SAGE, you might perhaps find it more convenient to invoke MPFR within SAGE. This is what I would recommend. You can do something like from sage.rings.real_mpfr cimport * def square(RealNumber x): cdef RealNumber result = x._new() mpfr_mul(result.value, x.value, x.value, GMP_RNDN) return result If you really need speed, you can declare, allocate, and free mpfr_t variables themselves (declared via cdef mpfr_t var) rather than using the RealNumber Python objects as wrappers. Just out of curiosity, what multi-precision root finding tools are you using? Also, I don't think numpy supports high-precision floating point arrays (except as arrays of generic objects). - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] sticking matricies together
On Sat, Sep 4, 2010 at 8:15 AM, andrew ewart aewartma...@googlemail.com wrote: How do u stick a matrix on the bottom of antoher martix, in particular the identity matrix so if had M (l,k) how do I stick Id(k) on the bottom to produce a new matrix N=M and N is dimension (l+k,k) Id Look at M.stack() and M.augment(). - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Factoring denominator of a rational function
On Sat, Sep 4, 2010 at 3:25 AM, ma...@mendelu.cz ma...@mendelu.cz wrote: What about to use polynomial division to get polynomial q=Q/p and then return P/q ? I do not remember the command for polynomial division, but should be in the manual or help. If Q and p are polynomials, polynomial division is just Q/p (or Q//p for divide and truncate). - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Factoring denominator of a rational function
On Sat, Sep 4, 2010 at 7:00 PM, Cary Cherng cche...@gmail.com wrote: Ok i think I've resolved my problems by avoiding var for declaring variables and instead using R.g17,g19,g27,g29,g37,g38,g47,g48,g58,g59,g68,g69 = PolynomialRing(QQ) Yes, that should be orders of magnitude faster than doing things purely symbolically. I think we all assumed you were already doing this, sorry. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Number of CPUs?
On Fri, Sep 3, 2010 at 10:47 AM, Simon King simon.k...@nuigalway.ie wrote: Hi! I have a list of computations (in fact, a test suite), and I'd like to do them in parallel. Of course, I could use @parallel, but: 1) each computation uses 3 processes (Sage, GAP, Singular) 2) it is probably not nice to other users if parallel computation uses all available CPUs. Are the tests simultaneously using lots of CPU on all three processes, or (more likely) is one doing the work and the other two waiting around for most of the time. In this case, no need to divide by two or three. I'd like to restrict @parallel(ncpus=...), where ... is something like 1/2 (or 1/3?) of the available CPUs. But how can I determine this number? Besides, a while ago I asked how one can execute the sage test script on a string, *without* saving that string into a file and *without* forking a sage -t subprocess. Do you see a way? I don't know of any way to do that, but saving to a file isn't so bad. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Fixed Point arithmetic
On Tue, Aug 24, 2010 at 1:27 PM, William Stein wst...@gmail.com wrote: Did you do this once for something... Yes, see http://trac.sagemath.org/sage_trac/ticket/9180 -- Forwarded message -- From: Mike Hansen mhan...@gmail.com Date: Tue, Aug 24, 2010 at 12:21 PM Subject: Re: [sage-support] Fixed Point arithmetic To: sage-support@googlegroups.com On Tue, Aug 24, 2010 at 12:14 PM, Jeroen Demeyer jdeme...@cage.ugent.be wrote: Is there any support in Sage for fixed point arithmetic? That is, computing with real numbers with a fixed number of bits after the decimal point? Fredrik Johansson has done some work in this area -- see http://code.google.com/p/fastfunlib/. Note that there isn't really a usable library there. --Mike -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: How can I make implicit_multiplication default?
On Mon, Aug 23, 2010 at 6:54 AM, Simon King simon.k...@nuigalway.ie wrote: Hi Robin, On 23 Aug., 13:43, robin hankin hankin.ro...@gmail.com wrote: Re automatic_names(): why isn't this the default? Now I know it exists, I think I'll probably use it all the time. Who uses sage without this option? I find automatic_names horrible, to say the least! In my opinion, such thing should *never ever* be standard! 1. If you write a little program on the command line and it does something, but simply it doesn't do the right thing or you get strange error messages about missing attributes -- it would be very hard to find out that you forgot to define some object X, so that Sage worked in the wrong assumption that X is a symbolic variable. I strongly prefer to get a clear error message, namely NameError: Name 'X' is not defined or so. 2. Explicit is better than implicit is a quite common credo. I think it is unsafe to rely on implicit assumptions of the type of an object. 3. I hardly ever work with symbolic variables. So, I really don't see the point why X should default to a symbolic variable. 4. My impression is that for quite many people a symbolic variable is the first thing that comes to mind when computing in a CAS - and it takes them a long while until they find that for their particular problem a different class (like a polynomial) works much better. Making a symbolic variable the default, I am afraid that one would support the wrong belief that symbolic variables are good for *everything*. So, it is not so much that programs would break. But debugging would be more difficult, and it would teach the people the wrong lesson, IMHO. And on the other hand, I can't see how life with Sage would be any easier if automatic_names was the standard. Think about someone working through a series of calculus textbook exercises (mostly one-liners). Personally, I wouldn't every want it to be default, but can see how some people could really find it useful (especially as we're aiming to be a viable alternative to the Ma's. Also, note that Python itself has implicit variable declaration (as opposed to, say, C, etc.) which has its pros and cons (though I like it). This, and implicit multiplication, should be in the FAQ at least. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: How can I make implicit_multiplication default?
On Mon, Aug 23, 2010 at 9:08 AM, Robert Bradshaw rober...@math.washington.edu wrote: On Mon, Aug 23, 2010 at 6:54 AM, Simon King simon.k...@nuigalway.ie wrote: Hi Robin, On 23 Aug., 13:43, robin hankin hankin.ro...@gmail.com wrote: Re automatic_names(): why isn't this the default? Now I know it exists, I think I'll probably use it all the time. Who uses sage without this option? I find automatic_names horrible, to say the least! In my opinion, such thing should *never ever* be standard! 1. If you write a little program on the command line and it does something, but simply it doesn't do the right thing or you get strange error messages about missing attributes -- it would be very hard to find out that you forgot to define some object X, so that Sage worked in the wrong assumption that X is a symbolic variable. I strongly prefer to get a clear error message, namely NameError: Name 'X' is not defined or so. 2. Explicit is better than implicit is a quite common credo. I think it is unsafe to rely on implicit assumptions of the type of an object. 3. I hardly ever work with symbolic variables. So, I really don't see the point why X should default to a symbolic variable. 4. My impression is that for quite many people a symbolic variable is the first thing that comes to mind when computing in a CAS - and it takes them a long while until they find that for their particular problem a different class (like a polynomial) works much better. Making a symbolic variable the default, I am afraid that one would support the wrong belief that symbolic variables are good for *everything*. So, it is not so much that programs would break. But debugging would be more difficult, and it would teach the people the wrong lesson, IMHO. And on the other hand, I can't see how life with Sage would be any easier if automatic_names was the standard. Think about someone working through a series of calculus textbook exercises (mostly one-liners). Personally, I wouldn't every want it to be default, but can see how some people could really find it useful (especially as we're aiming to be a viable alternative to the Ma's. Also, note that Python itself has implicit variable declaration (as opposed to, say, C, etc.) which has its pros and cons (though I like it). This, and implicit multiplication, should be in the FAQ at least. One more thing--I find it really handy when I'm pasting in expressions form elsewhere, e.g. a paper or something. However, rather than enable the options in the preparser and changing the language, I do sage: SR(x^2 + 2x - 5y) x^2 + 2*x - 5*y This string-level implicit multiplication/variable binding for polynomial rings too: sage: R = QQ['x'] sage: R(3x^5 - 2x) 3*x^5 - 2*x - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Boolean operators... Implication ?
On Mon, Aug 9, 2010 at 9:40 PM, Nathann Cohen nathann.co...@gmail.com wrote: This can of course be written (not g.is_forest() and g.has_even_cycle()) Ok, ok, I know... Let's make it g.is_forest() or g.has_even_cycle() Yes, one could create an infix operator, but I think the above is much more clear than having to learn yet more notation. Explicit is better than implicit. Simple is better than complex. ... - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] regarding arrayobject.h
On Mon, Aug 9, 2010 at 1:59 AM, Rajeev rajs2...@gmail.com wrote: Hi, I was trying to work out the first example given in http://wiki.cython.org/WrappingNumpy in sage notebook, but got an error saying arrayobject.h not found. How do I get this example working? I've fixed that page so it should work, but a better tutorial (linked at the top of the page) is http://wiki.cython.org/tutorials/numpy (From the Sage notebook, you can just skip all the installation/setup stuff...) - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Cython: importing a cdef class
On Sat, Jul 31, 2010 at 1:21 AM, Simon King simon.k...@nuigalway.ie wrote: Hi Jeroen! On 31 Jul., 02:30, Robert Bradshaw rober...@math.washington.edu wrote: ... In file A.pyx, I have cdef MyClass myobj cdef class MyClass: [...] In file A.pxd, I have cdef class MyClass: [...] In file B.pyx, I would like to access myobj from A.pyx, but how? You can't access cdef members of Cython modules from other modules (yet). Here you'd probably want to make an accessors method in A. Either that our you could not declare it as a MyClass (but in that case it'd be just a normal Python object). Would this work? in A.pyx: myobj_py = MyClass(...) cdef MyClass myobj = myobj_py cdef class MyClass ... in A.pxd cdef class MyClass: [...] in B.pyx: from A import myobj_py from A cimport MyClass cdef MyClass myobj = myobj_py In that way, you have the cdef object myobj in both A and B Yep. -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Cython: importing a cdef class
On Fri, Jul 30, 2010 at 2:39 PM, Jeroen Demeyer jdeme...@cage.ugent.be wrote: Hello sage-support, I have been breaking my head all evening around the file organisation and import model with Cython. If there is any tutorial explaining this, I will gladly read it. Anyway, here is a concrete question: In file A.pyx, I have cdef MyClass myobj cdef class MyClass: [...] In file A.pxd, I have cdef class MyClass: [...] In file B.pyx, I would like to access myobj from A.pyx, but how? You can't access cdef members of Cython modules from other modules (yet). Here you'd probably want to make an accessors method in A. Either that our you could not declare it as a MyClass (but in that case it'd be just a normal Python object). - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Define an action
On Tue, Jul 27, 2010 at 12:50 AM, Simon King simon.k...@nuigalway.ie wrote:
Hi Drenwal,
On 25 Jul., 10:52, drenwal dren...@free.fr wrote:
But, I would prefer to use a more mathematical notation, like Y[k] or
y...@k or whatever non already used symbol instead of Ac(y,k).
As Johannes has pointed out, Y[k] is already used, so, this might not
be what you want. But, if it is, overwrite __getitem__ of matrices
(this is the method that Python expects if you do Y[...]).
'^' is also used; if you still want to use it, overwrite __pow__.
How is it possible to do that?
I don't know if/how '@' can be made use of. Usually, it seems that @
indicates that a so-called decorator is being used.
Talking about generators: There is a decorator that allows to define a
custom infix operator (see
http://www.sagemath.org/doc/reference/sage/misc/misc.html#sage.misc.misc.infix_operator).
This might be what you were looking for, because it allows to create
new operator names.
Example:
sage: from sage.all import infix_operator
sage: @infix_operator('multiply')
: def foo(a,b):
: return '%s acts from the right on %s'%(b,a)
:
sage: 5 *foo* 2
'2 acts from the right on 5'
Of course, in your case, it would be
return b.transpose()*a*b
This is exactly what I was going to suggest. This is how we handle the
backslash operator for linear system solving:
http://hg.sagemath.org/sage-main/file/426be7b253ad/sage/misc/preparser.py#l1310
- Robert
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Re: [sage-support] How to deal with wrapper_descriptor / slot wrapper
On Tue, Jul 27, 2010 at 9:24 AM, Simon King simon.k...@nuigalway.ie wrote: Hi! I have a Cython class COCH that inherits from RingElement. I define a method __pow__ for it, and it gets some doc string (which means tests). I thought that such method would be a class_method or whatever. Instead, I get sage: COCH.__pow__ slot wrapper '__pow__' of 'pGroupCohomology.cochain.COCH' objects sage: type(COCH.__pow__) type 'wrapper_descriptor' And what's worse, I seem to be unable to retrieve the documentation! sage: COCH.__pow__.__doc__ 'x.__pow__(y[, z]) == pow(x, y[, z])' is not the documentation that I provided. So, how can I get my docstring back? This is actually very related to http://groups.google.com/group/sage-devel/browse_thread/thread/c97d36d23131f4c5/bfa082a5ef5f153a but unfortunately, there's not a good answer (yet?). - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: How to deal with wrapper_descriptor / slot wrapper
On Tue, Jul 27, 2010 at 1:25 PM, Simon King simon.k...@nuigalway.ie wrote: On 27 Jul., 21:30, Simon King simon.k...@nuigalway.ie wrote: Is there no workaround? Say, defining the method (or slot method wrapper envelop whatever) and explicitly assign an attribute __doc__ to it? For the record: AttributeError: attribute '__doc__' of 'method-wrapper' objects is not writable Not writeable from Python space ;) I will surely be looking into trying to resolve this issue. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] complexity of computations in Z/n*Z
On Tue, Jul 27, 2010 at 1:58 PM, Luis Finotti luis.fino...@gmail.com wrote: Hi, I have an algorithm that has pieces that perform computations on Z/ p^i*Z for different values of i. I can count the operations for each piece, but to have an overall complexity, I need to know how the difference pieces compare. So, can anyone tell me how many bit operations are performed, in Sage, in a product of two elements of Z/n*Z (in terms of n and size of the input)? (I am particularly interested in cases where n=p^i for various i's, but it would be nice to know in general for future reference.) What about in Z? (A general reference would be fine too, of course.) For anything that doesn't fit inside a single word, Sage uses the mpz functions in MPIR to do arithmetic. There are a variety of algorithms used--from the classical O(n^2) to various Karatsuba/Toom-Cook ones to Schönhage–Strassen for large values. The latter, if you're interested in asymtotics, is O(n log n log log n). IIRC, The reduction (division) has similar asymptotics. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] An argument for more direct axiom integration
On Mon, Jul 5, 2010 at 4:39 AM, Dr. David Kirkby david.kir...@onetel.net wrote: On 07/ 5/10 06:18 AM, William Stein wrote: Great idea - you could add an algorithm=axiom option to sage's integrate command. Personally, and I am going to dare risk argue with a mathematician, I would not have considered Axion an algorithm, but a software package. So something like method=use_axiom would seem more logical to me. The only argument for algorithm is that it's a standard idiom in Sage (though with a greatly generalized meaning). Better still if Sage behaved like Mathematica, so seamlessly switched from one method to another, if the first one fails. As far as I know, it usually does. I'm sure that maxima tries more than one algorithm (or at least has some heuristic to figure out which way to attack the problem). Switching over to a different system is a bit different. Also, note that axiom is an optional package. In other words, automatically switch to Axiom if Maxima can't solve the integral - perhaps with a message like Unable to solve with Maxima, now trying Axiom. I would still leave the option of someone just using Axiom though. One of the annoying things with Sage, is that you often need to know what bit of software to use to do something. With Mathematica, I can request a zero of a Bessel function - I don't need to know that I should be doing this using mpmath or whatever else can be used for finding zeros of Bessel functions (see recent thread on this topic) This is certainly the goal--we're just not there yet in all areas. For, e.g. (exact) linear algebra or most of number theory it chooses and uses the right components under the hood. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Which python for sage?
On Sun, Jul 4, 2010 at 9:47 AM, Greg Kuperberg greg.kuperb...@gmail.com wrote: On Jul 3, 8:33 am, William Stein wst...@gmail.com wrote: Sage can't switch to Python 3 until every single Python package in Sage is ported to Python 3. This is far from done. It's possible that for some packages, nobody is even working on doing a port. In such cases, our only hope is to either do the port ourselves or remove the package from Sage, which may both be incredibly difficult. I've heard Twisted may be an example of such a package, but there might be others. Even numpy hasn't been ported to Python 3 yet, though at least there work is rumored to be in progress. Of course, you understand these issues better than I do. I didn't even consider that Sage has so many third-party libraries at the Python level. So yeah, I can see that it could take a long time to do such a conversion. Even so, I would suggest a more developed policy than just that you can't do it right now. Certainly at first glance, Python 3 looks a really good idea. Maybe at second glance, the conversion cost is very high for many projects and you could estimate that it will take many years for the world to switch. (But note that the same was true of a really great editor called NEdit and Unicode, and the result in the long run was that it hurt NEdit a lot.) What advantages do you see Sage getting from Python 3? I think the Sage library is probably in better shape than many of our dependancies (and the Cython files should just work), but it's hard to know 'till we get to it. In any case the all-or-nothing answer cannot be completely true. After all, you have interface support for packages written entirely in C or whatever other language. So how could it be that if you were in Python 3, then Python 2.* would be the one language that you can't support at all? What would you do if you wanted to support a Python 3 package? We'd have to ship Python 3 as a distinct spkg, and probably call it via pexpect. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Minus sign not being typeset?
This is a known bug. http://trac.sagemath.org/sage_trac/ticket/9314
On Jun 26, 2010, at 10:29 AM, Mike Witt wrote:
More info:
--
| Sage Version 4.3.1, Release Date: 2010-01-20 |
| Type notebook() for the GUI, and license() for information.|
--
sage: n=var('n')
sage: f = -n/(n-1) + 1
sage: f
-n/(n - 1) + 1
sage: latex(f)
-\frac{n}{{\left(n - 1\right)}} + 1
sage: quit
--
| Sage Version 4.3.5, Release Date: 2010-03-28 |
| Type notebook() for the GUI, and license() for information.|
--
sage: n=var('n')
sage: f = -n/(n-1) + 1
sage: f
-n/(n - 1) + 1
sage: latex(f)
\frac{-n}{{\left(n - 1\right)}} + 1
-Mike
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Re: [sage-support] Re: Sage showing its work
On Jun 26, 2010, at 7:24 PM, S. Robert James wrote: I didn't receive a response on this. If the question isn't clear, please let me know what needs to be clarified. I'm sure my request isn't unique: one of the major goals of Sage is to provide a platform that allows people to _verify_ it, which is par for the course for any mathematician. I'd like to see the steps Sage uses to convert the sum I give it (or what not) to the form it chooses. For the most part, the answer to that question is if you want to see what went on you have to read the source. It is possible that some functions (maxima?) has a verbose mode, but that may not be what you want. - Robert On Jun 25, 2:44 pm, S. Robert James srobertja...@gmail.com wrote: Hi. Checking out sage, and it's amazing. I'm a bit overwhelmed by its size, though... I intend to use it to handle some of the messy algebraic manipulations while I work on combinatorics. Can anyone help with these questions: 1) When I enter a sum in sage: h = sum(h_m, m, 1, 2*n)/2*n # h_m is already defined in terms of m and n sage gives me an answer in closed algebraic form. That's great. But I'd like to know how it simplified it. Is there anyway to have Sage show it's work? That is, show the steps it took to rewrite my sum into the closed form . (As a beginner, I'm not sure if I'm using Sage right - so it's very important for me to be able to verify what it does.) 2) Now, when I tell sage to display h, it displays it in simplified form. Great. But I'd also like to be able to print out the original definition - how can I do that? In general, both of these questions relate to the same concern: Sage is great; but I don't want to follow it blindly. I'd like to be able to query what I put in, what Sage converted it to, and how. -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Is sage 4.3.5 able to solve quadratic equations??
On Jun 21, 2010, at 10:53 PM, Matthias Meulien wrote:
I guess that the problem comes from the type of p1, not
being an Expression. So is it possible to cast this p1 to the
Expression class?
A direct conversion like the following works:
sage: p3 = 0
sage: for c in p1.coeffs():
: p3 = x*p3 + c
:
sage: p3
-3/4*pi + 7/4*pi*x
sage: type(p3)
type 'sage.symbolic.expression.Expression'
sage: p3.roots(x)
[(3/7, 1)]
You could evaluate p1 at the symbolic variable x.
sage: basering = PolynomialRing(SR, 'x')
sage: p1 = basering.lagrange_polynomial([(0,0), (1,pi), (2, pi/2)])
sage: expr = p1(var('x'))
sage: type(expr)
type 'sage.symbolic.expression.Expression'
sage: expr.roots(x)
[(7/3, 1), (0, 1)]
- Robert
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Re: [sage-support] Re: notebook control panel
On Jun 23, 2010, at 9:04 AM, William Stein wrote: On Wed, Jun 23, 2010 at 8:43 AM, Harald Schilly harald.schi...@gmail.com wrote: On Jun 23, 3:57 pm, kcrisman kcris...@gmail.com wrote: maybe because frames didn't work well or we wanted to avoid them...? I don't know the conversation but no frames please - just a floating div at a fixed position would be my wish! It would also be really easy We had a floating div at a fix position for *years*.Mike Hansen finally removed it in early 2008 (if I remember correctly), and it was a great improvement to *not* have it. I really liked not having to scroll all the way to the top to restart a worksheet...it would be nice to make this toggleable (and of course even better to finally have a full user preferences page). - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Unexact computation with roots of unity.
On Jun 22, 2010, at 1:02 PM, Nils Bruin wrote: On Jun 22, 11:13 am, cjung cjun...@gmx.de wrote: My question is now, if this is a bug or just a mistake in my code? I suspect that you create your roots of unity using exponents that are floats. If m and n are integers, m/n shouldn't be a float. In that case it may be a bug in Sage that it doesn't throw an error. +1 It may be what you are triggering: We create an approximate 6th root of unity. Of course the input data shouldn't be interpreted as an algebraic number because 0.333 can easily mean a non-rational number. This is where it might be safer if sage threw an error instead of accepting the input sage: c=QQbar(e^(I*pi*0.333)) sage: c 0.5009066253607099? + 0.865501330253019?*I As this example shows, sage has done a best guess as to interpreting the input as an algebraic number: sage: c.minpoly() x^800 - x^600 + x^400 - x^200 + 1 Indeed, its cube is close to -1, but not equal to it: sage: c^3 -0.950652018582? + 0.003141587485879564?*I QQbar clearly tries too hard to interpret symbolic expressions as algebraic numbers. More blatant non-algebraic input gets recognised: sage: QQbar(1.34) TypeError: Illegal initializer for algebraic number sage: QQbar(1.13+3.2*I) TypeError: Illegal initializer for algebraic number Since QQbar(...) is a forced coercion, perhaps this is what you should expect. You are asking the system to try to make sense of what you're asking if at all possible and in some sense it does ... but rather unexpectedly. I don't know how robust the strategies are that the system uses, but for smallish input it seems to work rather well: sage: u1=QQbar(1958*e^(pi*I*-2/5)+34/5*e^(pi*I*3/7)) sage: u2=(QQbar(1958*e^(pi*I*-2/5))+QQbar(34/5*e^(pi*I*3/7))) sage: u3=1958*QQbar.zeta(10)^(-2)+34/5*QQbar.zeta(14)^3 sage: u1 == u2 and u1 == u3 and u2 == u3 True sage: u1.minpoly() == u2.minpoly() True sage: u3.minpoly()(u2) == 0 True If it uses numerical methods somewhere along the way to recognise these symbolic expressions as algebraic numbers, I suspect you can break it by feeding it some devious input. The problem is probably the minpoly routine on symbolic expressions: sage: v=e^(I*pi*0.333) sage: v.minpoly() x^800 - x^600 + x^400 - x^200 + 1 sage: (e^(I*pi*333/1000)).minpoly() x^800 - x^600 + x^400 - x^200 + 1 sage: (e^(I*pi*1.0/3)).minpoly() x^2 - x + 1 -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Unexact computation with roots of unity.
On Jun 22, 2:13 pm, cjung cjun...@gmx.de wrote: Dear all, Here's my problem: I've written a function (the scource code below), which should compute the scalarproduct of two classfunction of a group G. But there is a little problem with that, the values of the classfunction are just given as a list of values (one entry for every conjugacy-class of G). As normal some of these values are roots of unity, given in the form e^(2*pi*I m/n); if I try to compute the valus of that function for irreducible characters of the group, then for some distinct characters the values are not zero. They are near zero but not at all zero. Here the code: def sage_ScalarProd(self,X,Y): card=self.card_conjugacyClasses() # gives us the cardinality of the conjugacy classes of G n=len(card); if len(X) != n : print X is not a Classfunction on G. return 0 if len(Y) != n: print Y is not a Classfunction on G. return 0 s=0 s=QQbar(s) for i in range(0,n): s=s+QQbar(card[i]) * QQbar(X[i] *Y[i].conjugate()); s=s/self.order() #self.order() gives us the order of that group return s Now an example C=S.irreducibleCharacters() #a list of values of the irreducible characters; and indeed these characters are irreducible for i in range(0,len(C)): print S.sage_ScalarProd(C[1],C[i]) #this gives us: 0.?e-18 + 0.?e-19*I # - should be zero 1 0.?e-18 + 0.?e-19*I # - should be zero 0.?e-18 + 0.?e-19*I # - should be zero 0.?e-18 + 0.?e-19*I # - should be zero 0 0 #we also hav C [[1, 1, 1, 1, 1, 1, 1], [1, e^(4/3*I*pi), e^(2/3*I*pi), 1, e^(2/3*I*pi), e^(4/3*I*pi), 1], [1, e^(2/3*I*pi), e^(4/3*I*pi), 1, e^(4/3*I*pi), e^(2/3*I*pi), 1], [2, 1, 1, -2, -1, -1, 0], [2, e^(2/3*I*pi), e^(4/3*I*pi), -2, -e^(4/3*I*pi), -e^(2/3*I*pi), 0], [2, e^(4/3*I*pi), e^(2/3*I*pi), -2, -e^(2/3*I*pi), -e^(4/3*I*pi), 0], [3, 0, 0, 3, 0, 0, -1]] My question is now, if this is a bug or just a mistake in my code? Note that 0.?e-18 does *not* mean that the result is not zero, it just means that it's something numerically close to zero. In generally QQbar avoids doing algebraic resolution until it needs to. (This is a feature, not a bug.) sage: a = QQbar(sqrt(2)) * QQbar(sqrt(3)) - QQbar(sqrt(6)); a 0.?e-18 sage: a == 0 True sage: a = QQbar(sqrt(-2)) * QQbar(sqrt(3)) - QQbar(sqrt(-6)); a 0.?e-18*I sage: a.exactify(); a 0 -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage/Python Startup Failing on Snow Leopard
On Jun 18, 2010, at 1:58 PM, arthur wrote: On Jun 18, 3:25 pm, kcrisman kcris...@gmail.com wrote: But sounds like, as with a big buffet, too much of a good thing is just too much. It's worth pointing out, though, that most of the optional packages are databases, packages for some very specific research use, additional graphics, or computer internals, in which case perhaps the user could download his/her own copy of Sage to use them? What sort of context are you envisioning this for? - kcrisman Well, I'm a SysAdmin, not a mathematician, hence my knowledge of what our various mathematicians might need is limited. I'm working on standardized disk images that will be distributed on a few dozen Macs. I'm trying to install the broadest, most useable version of SAGE possible, so it will be most useful for the broadest swathe of mathematicians who use those disk images. For individuals I'd be happy to install specific packages if they're not already installed, but I'd much prefer to have the needed packages already available on their installation so they don't have to figure out what they need, tell me, wait for me to have the time to install it, etc. Most of our users don't have root on their desktop machines: not being able to change system level software and configs allows me to push out new software, updates, etc. without breaking what they're used to, but it also means I have to give them what they need, hopefully anticipating it before they need it. Sounds great. Also, we have a fair number of shared public machines, so for those I can't really install individual packages since I never know which individuals will be using which public systems, they all have a common disk image. One thing to note is that Sage ships with batteries included and has a most functionality in just the standard install. I'm not trying to discourage you from installing optional package, but just note that they're not necessary to have a very versatile, useful install. Personally, the only optional packages I've ever used are the elliptic curve databases, and I've been using Sage for years. Part of why I posted was not only to get my own installation in good shape, but to help out others in the same boat by helping to improve the documentation, error messages, and installation procedures for non- specialists (like me). I suspect William would say I should help improve the documentation by not only posting reports (and should any of this sort of thing be a formal bug report?) but by fixing the source/docs... and I'd agree with him except 1) I don't know the answers to these questions (i.e. which databases go with which research purposes, etc) and 2) I'd have to properly (re)learn mercurial... though the latter I really ought to do anyway, if I only had the time. Or, as an even lower barrier, add it to the wiki. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Notebook Login and registration of users : Legacy DB or LDAP
On Jun 20, 2010, at 7:21 AM, Thierry Dumont wrote: Le 20/06/2010 16:14, Patrick ABOU BAKAR a écrit : I know that SAGE contains its own installation of pretty much of all the modules it depends on.. My assumption is that there is a table that holds the username and password of the users as they sign up.. What SGBD is used for it? (SQLite, PostreSQL, MySQL) I search but couldn't find any collaborative work on how to use a legacy database of users (username, password) to authenticate users when working on Notebook... Or maybe the usage of LDAP or anything of the sort.. Any directions or answers would be appreciated. Thanks for your help! Hello, I have a patch for the notebook which allow to use LDAP (Open Ldap, Active Directory,...). We use it in our University server ( http://sage-math.univ-lyon1.fr ). If you are intersted, I can help you installing it. Yours Sounds like something we've wanted for a long time, is your patch up on trac as well? - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Why is map using memory?
On Jun 20, 2010, at 7:50 AM, Rolandb wrote: Hi, I found a more simplified example: print get_memory_usage() for i in xrange(1): A(1,8,9) print get_memory_usage() Why is type(A) 'sage .rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingu \lar' using memory? No idea, maybe a memory leak in __call__ (or perhaps in libsingular itself)? http://trac.sagemath.org/sage_trac/ticket/9298 - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] strange behavior in matrix substitution
On Jun 12, 2010, at 17:27 , Byungchul Cha wrote: Please tell me if this is a bug, or, I'm missing something obvious... sage: a = 3 # Assign a value to a variable a sage: b = a # Create a copy of a You're not really copying a, you're just making 'b' refer to the same thing that 'a' does, i.e. '3'. sage: b = 2 # Change the value of b Now b points to a different integer (2). sage: b 2 sage: a # The value of a remains unchanged, as expected. 3 So far, it looks good to me. But, when I do a similar thing with matrices, it doesn't look to be the same. sage: v = matrix(ZZ, 3, range(9)) sage: u = v u and v point to the same thing. sage: u[2] = [0,0,0] The matrix stored in the variable u has not been reassigned, it' been mutated. sage: u [0 1 2] [3 4 5] [0 0 0] sage: v [0 1 2] [3 4 5] [0 0 0] Shouldn't the value of v remain the same? Why does the change in u (or, a row of u) affect v? On Jun 12, 2010, at 8:25 PM, Justin C. Walker wrote: On Jun 12, 2010, at 19:07 , William Stein wrote: On Saturday, June 12, 2010, Justin C. Walker jus...@mac.com wrote: On Jun 12, 2010, at 17:27 , Byungchul Cha wrote: [snip] Shouldn't the value of v remain the same? Why does the change in u (or, a row of u) affect v? [snip] For, e.g., integers, u=v means that the names u,v both refer to their own copies of the value in question. Are you sure??? I think you statement that u is a new copy is wrong. I bet u is v would still return true above. Picky picky picky. I was hoping to avoid a trip into the twisty maze of passages in language definition (all of which are subtly different :-}). But you are correct. u is v does return true and the two actually refer to the same (physical) value. And, if one variable is modified, this doesn't modify the other, or the value that both previously referred to. Actually, even in the case of integers, if you were to modify one, it would modify the other. Most object are (basically) immutable, so this doesn't come up. Assignment never copies, it only creates references. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] How to do it in cython?
On Jun 11, 2010, at 11:23 PM, Rolandb wrote: Hi, I have a small (nonsense) example of a program I would like to be able to convert to cython. But I don't know how to convert: R.A,B,C=QQ[], .factor(), .unit() and .factor(proof=False,limit=10^5). I could not find anything in the documentation about for instance handling elements of R.A,B,C=QQ[], thus sage .rings .polynomial.multi_polynomial_libsingular.MPolynomial_libsingular. R.A,B,C=QQ[] def test(trio,expr=(A,B,C)): (a,b,c)=sorted(map(lambda x: abs(x(trio)),expr)) basis=prod(expr).factor() te_ontbinden=[abs(w[0](trio)) for w in basis]+[QQ(basis.unit())] radl=abs(prod(uniq([p for g in te_ontbinden for p,_ in ZZ(g).factor(proof=False,limit=10^5)]))) return radl test((1,8,9),(A^2,C^2-A^2,C^2)) 30 Any help is appreciated! Roland Sage is preparsed. To see what comes out, do sage: preparse(3.factor()) 'Integer(3).factor()' sage: print preparse( R.A,B,C=QQ[] def test(trio,expr=(A,B,C)): (a,b,c)=sorted(map(lambda x: abs(x(trio)),expr)) basis=prod(expr).factor() te_ontbinden=[abs(w[0](trio)) for w in basis]+[QQ(basis.unit())] radl=abs(prod(uniq([p for g in te_ontbinden for p,_ in ZZ(g).factor(proof=False,limit=10^5)]))) return radl ) R = QQ['A, B, C']; (A, B, C,) = R._first_ngens(3) def test(trio,expr=(A,B,C)): (a,b,c)=sorted(map(lambda x: abs(x(trio)),expr)) basis=prod(expr).factor() te_ontbinden=[abs(w[Integer(0)](trio)) for w in basis]+ [QQ(basis.unit())] radl=abs(prod(uniq([p for g in te_ontbinden for p,_ in ZZ(g).factor(proof=False,limit=Integer(10)**Integer(5))]))) return radl - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Data list
On Jun 10, 2010, at 12:22 PM, Christian Stump wrote: m=[0.6158, 0.5893, 0.5682, 0.51510, 0.4980, 0.4750, 0.5791, 0.5570,0.5461, 0.4970, 0.4920, 0.4358, 0.422, 0.420] m.count len(m) does the job, you should probably look into the tutorial at http://www.sagemath.org/doc/tutorial/ for this kind of questions... m.count is a function returning the number of times some element appears in the list, so [1,2,3,2,2,4].count(2) returns 3 Another similar thing, i want to multiply the all the elements for 10^-6 if you want to apply a function to every element in a list, you can do that by [ f(i) for i in your_list ]. e.g., [ 2*i for i in [1,2,3] ] returns 2,4,6 Or, you might want an actual vector. sage: m = vector([0.6158, 0.5893, 0.5682, 0.51510, 0.4980, 0.4750, 0.5791, 0.5570,0.5461, 0.4970, 0.4920, 0.4358, 0.422, 0.420]) sage: len(m) 14 sage: m * 10^-6 (6.158000e-7, 5.893000e-7, 5.682000e-7, 5.151000e-7, 4.98e-7, 4.75e-7, 5.791000e-7, 5.57e-7, 5.461000e-7, 4.97e-7, 4.92e-7, 4.358000e-7, 4.22e-7, 4.20e-7) -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Building from source sage 4.4.3 under Debian lenny amd64: gcc and g++ versions do not match
On Jun 11, 2010, at 2:51 PM, orca wrote: Hi there, I am a newbie to Sage, though I have some experience with Linux and Python in general. I have tried to build the latest 4.4.3 version of Sage from source, but, after having checked that I apparently have all necessary program dependencies satisfied, and issuing the command make under my Sage root directory, the following error was reported: configure: gcc (4.3.2) and g++ (4.2.4) are not the same version configure: which they must be. Check your setting of CC and CXX configure: error: Exiting since the C and C++ compilers have different versions ERROR: You do not have all of the prerequisites needed to build Sage from source. See the errors above. make[1]: *** [installed/prereq-0.7] Error 1 So what do you recommend? As far as I could check, there are deb files for both the lower version of gcc and the higher version of g++, under Debian lenny repositories and, indeed, my machine has both 4.3.2 and 4.2.4 gcc versions installed (SIC). The point is, if I install these other versions, how do I force the use of a given version of gcc (or g+ +, for that matter) when building Sage?? If that is possible, is it advisable? I would imagine that either would work fine--chances are if you install, for example, the 4.3.2 g++ package then it will get picked up by default over what was there previously. Thanks in advance!!! PS: when is it due to appear Debian lenny i386 and amd64 official binary versions of Sage, such as there are for Ubuntu and Suse in Sage's site?? When someone is willing to consistently build and upload them. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Building from source sage 4.4.3 under Debian lenny amd64: gcc and g++ versions do not match
On Jun 11, 2010, at 4:48 PM, Dr. David Kirkby wrote: On 06/11/10 10:51 PM, orca wrote: Hi there, I am a newbie to Sage, though I have some experience with Linux and Python in general. I have tried to build the latest 4.4.3 version of Sage from source, but, after having checked that I apparently have all necessary program dependencies satisfied, and issuing the command make under my Sage root directory, the following error was reported: configure: gcc (4.3.2) and g++ (4.2.4) are not the same version configure: which they must be. Check your setting of CC and CXX configure: error: Exiting since the C and C++ compilers have different versions ERROR: You do not have all of the prerequisites needed to build Sage from source. See the errors above. make[1]: *** [installed/prereq-0.7] Error 1 So what do you recommend? As far as I could check, there are deb files for both the lower version of gcc and the higher version of g++, under Debian lenny repositories and, indeed, my machine has both 4.3.2 and 4.2.4 gcc versions installed (SIC). The point is, if I install these other versions, how do I force the use of a given version of gcc (or g+ +, for that matter) when building Sage?? If that is possible, is it advisable? Thanks in advance!!! What do the following commands give you? $ command -v gcc $ command -v g++ $ command -v gfortran $ gcc -v $ g++ -v $ gfortran -v $ echo $PATH give you? You would certainly be advised to use the same version of gcc, g++ and gfortran. I don't know what command may or may not exist in any given linux distribution, but one can often get the commands one wants by suitably setting the path. It's not possible to build g++ without building gcc, the g++ 4.2.4 must have had a gcc 4.2.4 version at some point. Whether you only have g++ installed is another matter, but it must have been built with C support. I'd personally be inclined to suggest you To be clear, you're suggesting building your own gcc and g++ from source, and then trying to configure it to use that one instead of the system default, right? To me, that sounds more complicated and error prone than just trying to use the package manager to get the latest binaries (but, of course, it's nice that you can do so). * Download the latest gmp * Download the latest mpfr * Download gcc 4.4.4 (not 4.5, as that is less well tested). * Patch mpfr to get the latest updates (just read the readme) * copy the mpfr directory under the gcc sources and rename it to mpfr * copy the gmp sources under the gcc source directory and rename it gmp so you get a diretory layout like this gcc-4.4.4 gcc-4.4.4/gmp gcc-4.4.4/mpfr $ mkdir build $ cd build $ /path/to/gcc-4.4.4/configure --prefix=/somewhere/I/can/write/to -- enable-languages=c,c++,fortran then go away and wait until you have a new gcc 4.4.4 (You should however read the gcc docs to see if there are some specific switches recommended for your distro. Do *not* make build under the gcc-4.4.4 source tree - it should be outside the source tree. Using a later gcc is probably your safest solution. If nothing else, Sage tends to be more tested with late compiler releases, except on OS X, where many people use the Apple-supplied gcc 4.0.1 Dave -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Problem finding numeric eigenvectors
On Jun 7, 2010, at 7:46 AM, Mike Witt wrote: On 06/06/2010 10:43:38 PM, Rob Beezer wrote: On Jun 6, 9:05 am, Mike Witt msg...@gmail.com wrote: This does kind of reinforce the concept, which I guess I've heard expressed before here, that you have to be prepared to update your sage build very frequently in order to keep up with things. Exactly. ;-) But with sage -upgrade at a system prompt, it couldn't be much easier. Rob Well, getting a new version is no problem (assuming it builds on one's system). But since there is no distinction between bug fix releases and releases in which the interface to some function might change (such as the change we were just discussing) you never know when downloading a new version is going to cause you some work figuring out how to update existing code. We have a deprecation policy, so at the very least your old code should work for a while (with warnings) before breaking completely. Of course that's the theory, some people are better at following it than others. Again, I may be an atypical user. I like to have a stable system. I only install every *other* fedora release :-) I have the distinct impression that most of the people here are active developers, who spend time every day reading the mailing lists, looking at the code, and keeping track of the status of bugs, etc. I'm actually the guy who is trying to use Sage as a viable free open source alternative to Magma, Maple, Mathematica and Matlab :-) But, note that I'm not asking for my money back ... In your case, what I'd do is read the release notes when it comes out, and decide to upgrade based on that. You don't have to upgrade unless it fixes bugs or adds features you need. sage -upgrade has always worked for me (and I've been using Sage since 1.x) but downloading a whole new tarball is also safer in the sense that you can try it out, and if that doesn't work just nuke it and wait for the next release. It is nice to be able to have any number of installations in parallel (assuming the necessary disk space). - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Cython and static data
On Jun 7, 2010, at 8:04 AM, Rolandb wrote: Hi, Using cython, I want to make optimal use of static data. The reason is that lookup is (often) much faster than recalulating. I now use: cdef list nice_list_name=[3 , 3 , 3 , 3 , 3 , 3 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 5 , 5 , 5 , et cetera] But this didn't increase the speed. Suggestions are appriciated! Perhaps in your case lookup isn't faster than recalculating? If it's about a tie, re-calculating is probably better, as it's less of a black box. Here you're using a Python list of ints, if you really want speed you'd want to use a int*. You could globally calculate this the first time it's used and use a lookup from then on. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Using LiE
On Jun 3, 2010, at 9:46 AM, William Stein wrote:
On Thu, Jun 3, 2010 at 9:44 AM, Bruce brucewestb...@googlemail.com
wrote:
I am just starting with sage. I type a url into firefox to start the
notebook on a local machine.
I typed: install_package('lie-2.2.2.p3')
and got along error message.
[Errno 13] Permission denied: '/usr/local/sage/sage-4.4.2/tmp/list'
I assume this is a local problem.
You are not allowed to install packages system-wide. If you can be
admin on that computer, do
sudo su
and try again. If not, contact the admin.
Alternatively, you could install and use your own personal copy of
Sage in your home directory.
- Robert
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Re: [sage-support] zeros of the Riemann zeta function
On Jun 1, 2010, at 8:13 AM, Anne Driver wrote: Hello, I am new to this list, and relatively new to Sage. I'm puzzled by the logic of one part of Sage though. Although I don't have access to Mathematica at the minute on this computer, I know if I compute the first zero, I get something like In[1] = ZetaZero[1] //N (to get a numerical value) Out[1] = 1/2 + I*14.134... Trying this in Sage, I get: sage: lcalc.zeros(1) [14.1347251] Why does Sage not do the sensible thing like Mathematica and return the complex number 0.5 + I 14.1347251 ? It would seem much more logical. Of course, it is not proven that the real part is 1/2, so how would the case be handled if a root was not found to have a real part of 1/2 ? I believe both algorithms assume the Riemann hypothesis in computing them (otherwise, for example, it would be ambiguous to talk about the n-th zero anyways). I would guess the reason that lcalc returns the imaginary part only is that otherwise the first thing one would do to actually do anything interesting with this data would be to take the imaginary part, so this just saves the effort and overhead. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] zeros of the Riemann zeta function
On Jun 1, 2010, at 11:05 AM, William Stein wrote: On Tue, Jun 1, 2010 at 10:58 AM, Robert Bradshaw rober...@math.washington.edu wrote: On Jun 1, 2010, at 8:13 AM, Anne Driver wrote: Hello, I am new to this list, and relatively new to Sage. I'm puzzled by the logic of one part of Sage though. Although I don't have access to Mathematica at the minute on this computer, I know if I compute the first zero, I get something like In[1] = ZetaZero[1] //N (to get a numerical value) Out[1] = 1/2 + I*14.134... Trying this in Sage, I get: sage: lcalc.zeros(1) [14.1347251] Why does Sage not do the sensible thing like Mathematica and return the complex number 0.5 + I 14.1347251 ? It would seem much more logical. Of course, it is not proven that the real part is 1/2, so how would the case be handled if a root was not found to have a real part of 1/2 ? I believe both algorithms assume the Riemann hypothesis in computing them (otherwise, for example, it would be ambiguous to talk about the n- th zero anyways). Often such computations actually prove the Riemann hypothesis up to a given height (see, e.g., http://numbers.computation.free.fr/Constants/Miscellaneous/zetazeros1e13-1e24.pdf I've cc'd Mike Rubinstein, so he can respond if he wants, since I'm not sure lcalc is actually doing this or not. IIRC, the broad idea is to compute sign changes and then perform a contour integral to prove that you have located all the zeros. If no, refine the grid and try again. Of course this is a huge oversimplification, but if there are zeros not on the critical line than this would simply fail to terminate, and otherwise it would prove the hypothesis. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: MemoryError
On May 28, 2010, at 9:53 PM, Rolandb wrote: Tnx Robert, I rewrote the routine somewhat to use less stored values. Still I got the following message: error: no more memory System -1596988k:2096917k Appl -1763860k/20285k Malloc 277k/0k Valloc -1743852k/20285k Pages 612613/0 Regions 5045:5045 What does this tell me? Usually this means exactly what it says, you've used up all the memory on your machine and can't allocate any more. What kind of machine are you running this on? If this is a Virtual Machine, you may be able to increase the amount of memory you give it, but otherwise you may need to rewrite your code, put more RAM in your machine, or run it on a bigger machine. Without more details it's hard to give advice on how you could rewrite your code, but 13 million real numbers should be easy to handle, 13 million large matrices not so much. Roland On 27 mei, 20:41, Robert Bradshaw rober...@math.washington.edu wrote: On May 27, 2010, at 11:31 AM, Rolandb wrote: Hi, I'm running a routine which uses a large data set (13 million elements). After a while the output is: MemoryError no mem for new parser What to do? Thanks in advance for the swift reply! Roland What are you doing with this data? Do you have a sample session? How much memory do you have? How much is it using? It might actually be out of memory. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] How can I get a PDF from a .show() acting on an expression, from within the notebook ?
On May 28, 2010, at 6:13 AM, Nicolas wrote: Hi all, I am trying to get, from within the notebook, a PDF from the show method acting on an expression, just like sage does when used on the command line. It works very nicely for graphics objects but I have not figured out either how to get a graphics object from a nicely typeset expression of just get the pdf that is produced by the command line. Has this been thought of ? Is this possible ? Oh, I didn't see that you were talking about an expression. Try sage: view(expr, viewer='pdf') - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Integer.sqrt() memory leak?
On May 27, 2010, at 9:07 AM, rickhg12hs wrote: I noticed that doing sqrt() for large integers seems to continually chew up memory. For example: sage: m = get_memory_usage() sage: while True: a = ZZ(randint(2^400,2^800)).sqrt() print get_memory_usage(m) This prints ever increasing memory usage values, but I'm not sure that it should. Looks like a memory leak to me. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] MemoryError
On May 27, 2010, at 11:31 AM, Rolandb wrote: Hi, I'm running a routine which uses a large data set (13 million elements). After a while the output is: MemoryError no mem for new parser What to do? Thanks in advance for the swift reply! Roland What are you doing with this data? Do you have a sample session? How much memory do you have? How much is it using? It might actually be out of memory. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Illegal Instruction errors when trying to run sage
On May 27, 2010, at 3:22 PM, Alex Goater wrote: Hello, I'm trying to use sage version 4.4.2 within Linux Mint 7 Gloria. I've downloaded the sage-4.4.2-linux-32bit-ubuntu_10.04_lts-i686- Linux.tar.gz from the webiste, unpacked it and tried to run sage and this came up: -- | Sage Version 4.4.2, Release Date: 2010-05-19 | | Type notebook() for the GUI, and license() for information.| -- ** WARNING! This Sage install was built on a machine that supports instructions that are not available on this computer. Sage will likely fail with ILLEGAL INSTRUCTION errors! The following processor flags were on the build machine but are not on this computer: pni Email http://groups.google.com/group/sage-support for help. To remove this warning and make Sage start, just delete /home/alex/Desktop/sage/local/lib/sage-flags.txt ** I thought perhaps I installed it wrong so I ran make within the sage directory and when I tried to run sage again the same message came up. Can I just ignore this warning or do I need to download a package perhaps for linux mint to be able to run sage? This binary was probably built on a newer machine than you have. You could try to ignore this warning, but the safest thing to do is try a different binary or build from source. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Which python for sage?
On May 26, 2010, at 3:06 PM, William Stein wrote: On Wednesday, May 26, 2010, Micha Hofri ho...@wpi.edu wrote: Dear Mr. Stein: I heard about Sage when looking for an alternative to Maple. I find it is a good idea to know Python. I take a text, and it tells me it is mostly about python 3, which is incompatible with python 2.6. Can I use sage with/within python 3? No. Sage uses python 2.6, and will for at least the next year. On the other hand, Python 3 is over 95% the same as Python 2.6, so learning Python from a text based on Python 3 is not that big of a deal. Another good resource is http://diveintopython.org/ - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Display of i vs I
On May 22, 2010, at 8:05 AM, Mike Witt wrote:
I just thought I'd try this question one more time:
On May 20, 10:59 am, Mike Witt wrote:
Is there any way to make the square root of -1 display lower case
i rather than I (at least for latex output)?
Sage complex numbers already print out that way.
sage: latex(CDF(1,1))
1.0 + 1.0i
sage: latex(CC(1,1))
1.00 + 1.00i
sage: latex(sqrt(-1))
I
The symbolic I doesn't, however, though I think that would be an easy
and worthwhile change. For now you could do something like
sage: latex(1 + sqrt(-1)).replace('I', 'i')
'i + 1'
(though of course this will replace any capital I).
- Robert
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Re: [sage-support] Re: Display of i vs I
On May 22, 2010, at 8:28 AM, Robert Bradshaw wrote:
On May 22, 2010, at 8:05 AM, Mike Witt wrote:
I just thought I'd try this question one more time:
On May 20, 10:59 am, Mike Witt wrote:
Is there any way to make the square root of -1 display lower case
i rather than I (at least for latex output)?
Sage complex numbers already print out that way.
sage: latex(CDF(1,1))
1.0 + 1.0i
sage: latex(CC(1,1))
1.00 + 1.00i
sage: latex(sqrt(-1))
I
The symbolic I doesn't, however, though I think that would be an
easy and worthwhile change. For now you could do something like
sage: latex(1 + sqrt(-1)).replace('I', 'i')
'i + 1'
(though of course this will replace any capital I).
http://trac.sagemath.org/sage_trac/ticket/9017
- Robert
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Re: [sage-support] Re: SAGE being extremely slow with multivariable poly rings - is this normal?
On May 21, 2010, at 11:35 PM, Simon King wrote: On 22 Mai, 00:12, Robert Bradshaw rober...@math.washington.edu wrote: Try working a multivariate ring rather than a tower of univariate rings, e.g. ... ... which suggests the question why Sage does not automatically transform a tower of polynomial rings into a single ring -- for efficiency, and in order to avoid weird constructions such as sage: QQ['t']['t']['t'] Univariate Polynomial Ring in t over Univariate Polynomial Ring in t over Univariate Polynomial Ring in t over Rational Field There is a difference, for example list(f) and degree(f) have different meanings if f is a Univariate ring with a polynomial basering. Also, I can safely do sage: P.x = R['x'] Of course we could possibility do this transformation under the hood, and then remember where things came from. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Display of i vs I
On May 22, 2010, at 8:49 AM, Burcin Erocal wrote: Hi Mike, On May 20, 10:59 am, Mike Witt wrote: Is there any way to make the square root of -1 display lower case i rather than I (at least for latex output)? Not in a user friendly way. The complex I is just a number field element and number fields don't support latex output with different names. This problem is tracked here: http://trac.sagemath.org/sage_trac/ticket/6405 That's the ticket I was looking for... - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] SAGE being extremely slow with multivariable poly rings - is this normal?
On May 21, 2010, at 2:53 PM, Alex P wrote: Hi all, I tried the following code in SAGE and it seems that it is taking way too long -- | Sage Version 4.3.4, Release Date: 2010-03-19 | | Type notebook() for the GUI, and license() for information.| -- sage: q = 5 sage: F = FiniteField(q) sage: P.T = PolynomialRing(F) sage: PP.z = PolynomialRing(P) sage: UU.X = PolynomialRing(PP) sage: pro = X - 1/z sage: for p in P.monics(of_degree = 1): ...: time pro = pro*(X - p^q/(z + z^q)) ...: CPU times: user 0.05 s, sys: 0.00 s, total: 0.05 s Wall time: 0.15 s CPU times: user 0.39 s, sys: 0.00 s, total: 0.39 s Wall time: 0.39 s CPU times: user 2.56 s, sys: 0.00 s, total: 2.56 s Wall time: 2.57 s CPU times: user 16.53 s, sys: 0.02 s, total: 16.55 s Wall time: 16.58 s CPU times: user 139.67 s, sys: 0.32 s, total: 139.99 s Wall time: 141.16 s Even worse if I try to continue the calculations in degree 2 it is already taking over 10 min (and counting). Is this normal? And if so is there a way to avoid this? Try working a multivariate ring rather than a tower of univariate rings, e.g. sage: q = 5 sage: F = GF(q) sage: P.T,z,X = F[] sage: pro = X - 1/z sage: def monics(n): :powers = [T^i for i in range(n)] :for v in F^n: :yield T^n + sum(c*Tk for c,Tk in zip(v, powers)) : sage: for p in monics(1): : time pro = pro*(X-p^q / (z+z^q)) : CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.04 s CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s sage: pro = X - 1/z sage: for p in monics(2): : time pro = pro*(X-p^q / (z+z^q)) : CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s [...] CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s Wall time: 0.01 s sage: time for p in monics(2): pro = pro*(X-p^q / (z+z^q)) CPU times: user 0.05 s, sys: 0.00 s, total: 0.05 s Wall time: 0.05 s - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Vertical and Horizontal join of matrices
On May 20, 2010, at 3:15 PM, VictorMiller wrote: Does the Matrix class have methods for vertical and horizontal joins of matrices (as in Magma)? That is if A is an m by n matrix and B is an r by n matrix then VerticalJoin(A,B) would by the (m+r) by n matrix with A on top and B on the bottom. Similarly, if A is m by n and B is m by r then HorizontalJoin(A,B) would be an m by (n+r) matrix with A on the left and B on the right. I though that Numeric Python used to have something like this with a method called concatenate, but I can't find that in numpy. You're probably looking for stack and augment. sage: M = random_matrix(ZZ, 3, 3) sage: M.stack(M) [ -1 1 -5] [ 72 -2 1] [ -2 2 -20] [ -1 1 -5] [ 72 -2 1] [ -2 2 -20] sage: M.augment(M) [ -1 1 -5 -1 1 -5] [ 72 -2 1 72 -2 1] [ -2 2 -20 -2 2 -20] - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: parametric_plot with Piecewise doesn't work ?
On May 15, 2010, at 5:31 PM, kcrisman wrote:
Thanks for your email. Unfortunately, Piecewise functions were
implemented very early in the history of Sage, and so do not support
tons of newer Sage functionality. Although there are a number of us
interested in improving this situation, thus far time and expertise
has not been there. Unless a Sage Days devoted to this magically
happens :) I don't see that changing in the near future, as ideally
such Piecewise functions would come from Pynac/Ginac, but I don't
think they support this (and see http://wiki.sagemath.org/symbolics/pynac_todo
for a long-term wishlist, much of which will definitely eventually be
implemented).
I'm sorry that this is the current situation. To do this particular
examples, you could probably do four separate parametric plots, I
think? Please let us know if that doesn't work!
Another option is to wrap these in Python functions:
sage: parametric_plot([lambda a: f(a), lambda a: g(a)], (0, 2))
...
On May 14, 5:51 am, bourbabis bourba...@gmail.com wrote:
Hello folks !
Look at this :
var('a')
f = Piecewise([[(0, 1), a], [(1, 2), 2*a]])
g = Piecewise([[(0, 1), 3*a], [(1, 2), 4*a]])
parametric_plot((f, g), (0, 2))
I get the following error message :
Traceback (click to the left of this block for traceback)
. ..
AttributeError: PiecewisePolynomial instance has no attribute
'__float__'
parametric_plot isn't implemented yet for sliced function ?
Thanks.
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Re: [sage-support] Can't use os.chdir with Sage in virtualbox
On May 14, 2010, at 9:32 AM, David Grudoski wrote:
Can anyone tell me how to use os.chdir to go to my C: drive when
running sage in virtual box? I can't get out of the '/home/'
directory.
executing the following in sage notebook
import os
os.chdir('C:')
gives an error No such file or Directory
I set C up a a permanent shared folder from the devices menu but
have no idea how to access it from within the virtual boxenvironment.
VirtualBox has its own filesystem completely separate from Windows.
Given you set up a permanent shared folder, there's probably a mount
point. Does
sage: os.system(ls /)
give anything that looks like it could be your C drive? Someone who
actually uses VirtualBox could probably answer better.
- Robert
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Re: [sage-support] Test if a variable is numerical
Try doing
x in RR
- Robert
On May 7, 2010, at 2:38 PM, Nathann Cohen wrote:
Hello everybody !!!
I am trying to find out how to check whether some Sage variable is
numerical (let's say real, as opposed to None, False, {}, Set([]),
etc..), but was not lucky on Google... ^^;
Do you know the function I am looking for ? :-)
Thank youu !!!
Nathann
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Re: [sage-support] RDF Sparse matrix.
On Apr 30, 2010, at 9:34 AM, Thierry Dumont wrote: I have questions about RDF (and CDF) sparse matrices. How are they implemented? -for dense matrices, sage uses Scipy matrices and this is transparent. -but, how are sparse matrices (RDF,CDF) implemented? 1) Are they Scipy matrices ? 2) if yes: there are different data structures for sparse matrices in scipy: a) an intermediate version which uses a list representation, not good for number crunching, b) csc and csr format, which are extremely common in numerical linear algebra (SuperLU uses them, and iterative methods too). How hare matrix(RDF,...sparse=True) stored? sage: m = matrix(RDF, 5, sparse=True) sage: type(m) type 'sage.matrix.matrix_generic_sparse.Matrix_generic_sparse' So it's our completely generic sparse implementation, stored as a dictionary of non-zero entries. http://hg.sagemath.org/sage-main/file/e2ccb846f296/sage/matrix/matrix_generic_sparse.pyx#l1 If it is possible for sage to build automatically csc or csr matrices, then using sparse solvers is trivial. Otherwise I think it is necessary to build Scipy matrices (lil matrices converted to csr or csc format). We don't have support for that, but it would probably be a nice thing to have. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] power function with runtime error
On Apr 23, 2010, at 1:37 AM, bb wrote:
Mike Hansen schrieb:
On Mon, Apr 19, 2010 at 11:52 AM, bb bblo...@arcor.de wrote:
I get a runtime error, but just would expect infinity! Is there
something
wrong or any explanation?
This is because when you do 2^3^4^5 you are computing that number
exactly as an integer, and that number is definitely not infinity.
If
you wanted to use floating point arithmetic, then you should start
with something like 2.0:
sage: 2.0^3^4^5
+infinity
Doing something like float(2^3^4^5) computes 2^3^4^5 as an integer
and
then tries to convert that to a float.
Also, note that when you type in such an expression, the operations
are done in the following manner:
var(sage: var('x, y, z')
(x, y, z)
sage: x^y^z
x^(y^z)
which is different than
sage: (x^y)^z
(x^y)^z
Since exponentiation is non-associative, you need to be careful with
such differences.
--Mike
Thank you for your answer! I think there is a fundamental question
left apart from the question of assoziativity/non-assoziativity.
There Sage (I think coming from python) does not follow the common
rule to evaluate an expression with operators of the same precedence
from left tor right.
The exponentiation operator is a common exception to the left-to-right
rule. This is probably because a^(b^c) is more useful than (a^b)^c =
a^(b*c). Magma, Mathematica, and even bc follow the right-to-left rule
for exponentiation. (Maple actually raises an error if you don't have
the parenthesis.)
Since Georg Cantor there is a difference between countable infinity
(in the actual example) and noncountable infinity ( in the example
calculated with a float). I would not say, that infinity is wrong in
this case, only just because there is existing an infinite set of
integers so that infinity never might be reached.
The infinity given here has nothing to do with set cardinalities, it
is better understood as the compactification of the real line.
(I think that is the line of argument of your explanation?) The
essential point is, one has to map the unlimited ideas of math to
the restricted possibilities of a computer.
From a mathamatical point of view one can call the result of the
calculation
sage: 2^(3^(4^5))
---
RuntimeError Traceback (most recent
call last)
/home/bb/sage-4.3.5/ipython console in module()
/home/bb/sage-4.3.5/local/lib/python2.6/site-packages/sage/rings/
integer.so in sage.rings.integer.Integer.__pow__ (sage/rings/
integer.c:12114)()
RuntimeError: exponent must be at most 9223372036854775807
sage:
just a bug! Infinity is infinity, if countable or not countable. The
correct math-answer only could be countable infinity! But I think
infinity would in any case be better than RuntimeError as an answer!
I strongly disagree--infinity is an approximation to very large
numbers, not an exact answer. This is fine for floating point numbers
where one is only working with approximations to real numbers anyways,
but integer arithmetic is supposed to be exact. The error above is
desirable, as it tells you it can't to the computation because it
can't represent the result in memory (in particular, no one I know has
a place to store all 9223372036854775807 x 8 bytes of the answer).
- Robert
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Re: [sage-support] Load data from from other worksheet
On Apr 21, 2010, at 4:52 PM, Michael Rybalkin wrote: I have installed local Sage server. I need some kind of workspace with multiple worksheets and common data storage while working via web interface. What can you recommend in this case? There aren't currently any good solutions to this unless you have access to the filesystem the computer is running on (e.g. you're running your own server) in which case you could use absolute paths. There was a lot of talk about improving this at the Sage Education Day last December, but I don't think anyone's actually had the time to implement it (or even work it out fully). I want to have a bunch of common files for different worksheets. But I don't want to link them explicity to other worksheets (by creating a linked copy via web interface), because this data files are generated dynamically. For example in one worksheet I wants to generate 1000 files with data and in another worksheet I want to load some of them. I have found 2 solutions: 1. Little hack. Create some common directory in user's home directory with worksheets and load data as load(DATA + ../../common_dir/some_file) But in this case I cannot use web interface to work with files in such common directory. 2. Other hack. I can load data (or script) from another worksheet by doing another hack: load(DATA + ../../number/data/some_file) In this case I can work with data via web interface via worksheet with number number. But how can I get worksheet number (or path to it) but its name? I need to call sagenb.notebook.worksheet.directory() for some worksheet. Is it possible to get current notebook object or something like this. No, you can't get at that, because (for security reasons) the notebook server itself is running in a completely different process (and often as a different user) than the sage session you're working in. If no good solution will be found then I will use 1st variant with common directory in sage user's home directory. That would probably be the best approach for now, though it may be a bit brittle as there are no guarantees about the future layout above DATA. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: loading a PARI script into SAGE
On Apr 24, 2010, at 11:32 PM, Alex P wrote:
Actually it does not seem to work, I get
--
| Sage Version 4.3.4, Release Date: 2010-03-19 |
| Type notebook() for the GUI, and license() for information.|
--
sage: gp(\\r cryptpr.gp)
---
TypeError Traceback (most recent call
last)
/Users/aleksandarpetrov/Desktop/Macaulay2/sage/ipython console in
module()
/Users/aleksandarpetrov/Desktop/Macaulay2/sage/local/lib/python2.6/
site-packages/sage/interfaces/expect.pyc in __call__(self, x, name)
1030
1031 if isinstance(x, basestring):
- 1032 return cls(self, x, name=name)
1033 try:
1034 return self._coerce_from_special_method(x)
/Users/aleksandarpetrov/Desktop/Macaulay2/sage/local/lib/python2.6/
site-packages/sage/interfaces/expect.pyc in __init__(self, parent,
value, is_name, name)
1449 except (TypeError, KeyboardInterrupt,
RuntimeError, ValueError), x:
1450 self._session_number = -1
- 1451 raise TypeError, x
1452 self._session_number = parent._session_number
1453
TypeError: Error executing code in GP/PARI:
CODE:
sage[1]=\r cryptpr.gp;
GP/PARI ERROR:
*** unexpected character: sage[1]=\rcryptpr.gp;
^-
sage:
Same thing if I try the other command that William Stein suggested.
You have to do
sage: gp.eval(r\r cryptpr.gp;)
As gp(foo) only works if foo is an expression.
- Robert
On Apr 24, 4:21 pm, Alex P alexvpetr...@gmail.com wrote:
To William Stein: Great thanks.
To John Cremona: Sorry about that, won't happen again.
On Apr 24, 3:10 pm, William Stein wst...@gmail.com wrote:
On Fri, Apr 23, 2010 at 5:23 PM, Alex P alexvpetr...@gmail.com
wrote:
Hi all,
I was trying to use a PARI/GP script in SAGE. I tried gp('\r
name_of_file.gp'), but SAGE said could not get the file.
So is there any way to do this.
You need
sage: gp(\\r name.gp)
or
sage: gp(r\r name.gp)
William
10x in advance.
Alex
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William Stein
Professor of Mathematics
University of Washingtonhttp://wstein.org
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Re: [sage-support] Large monomial exponents
On Apr 24, 2010, at 5:36 PM, Michael Rybalkin wrote: How to get monomial with large exponent in the polynomial rings? For example I hsave polynomial ring over large finite field: p = next_prime(10^20) R.x = PolynomialRing(GF(p), sparse=True) Monomial x^(10^7) construction takes 2 seconds: time tmp = x^(10^7) Monomial x^(10^8) construction uses all 6 Gb server memory and cannot finish. And without 'sparse=True' option I cannot even get x^(10^6). What is the limitations for monomial exponents in polynomial rings? What can be done in my case? For example GAP handles this case without any problem. Seems like the sparse=True flag is horribly broken for GF(p)[x]: sage: p = next_prime(10^20) sage: R.x = PolynomialRing(GF(p), sparse=True) sage: type(x) type 'sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX' sage: R.x = PolynomialRing(QQ, sparse=True) sage: x^(10^8) x^1 - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: list vs. integer instances
On Apr 19, 2010, at 4:05 PM, wb wrote: On Apr 20, 12:25 am, Robert Bradshaw rober...@math.washington.edu wrote: On Apr 19, 2010, at 2:50 PM, wb wrote: coming from C I'm confused about this behavior in assignment: Since you know C, it may make sense to think of lists as being similar to pointers. that makes sense - I guess I was expecting lists to behave like list *classes* which have an overloaded assignment operator. Turning this around: is there a 'list-like' data type in sage which has 'true' assignment, i.e. copying all its content ? Python inherits a lot from C. It is practically nothing like C++ (despite both being object oriented). There's no such thing as assignment overloading--everything is heap allocated and you're just passing around references under the hood. Try doing sage: import copy sage: copy.tab to if some of the functions there work for you. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] list vs. integer instances
On Apr 19, 2010, at 2:50 PM, wb wrote: coming from C I'm confused about this behavior in assignment: Since you know C, it may make sense to think of lists as being similar to pointers. 1) using only integers -- sage: a=2 sage: b=2 sage: b=b+a sage: b 4 sage: a 2 so (at least), after b=b+a, 'b' seems to have gotten its own instance, however 2) using lists sage: a=[1,2] sage: b=a sage: b[0]=b[0]+a[0] sage: b [2, 2] sage: a [2, 2] --- ?!? (which results also if done directly in python). So, after b[0]=b[0]+a[0], 'b' does not seem to get its own instance and 'a' therefore also gets modified ..!? ... which somehow seems inconsistent with 1) and very strange anyway ... Finally 3) - sage: a=[1,2] sage: b=a+[] ! Trying to force (maybe?) an own instance for 'b' sage: b[0]=b[0]+a[0] sage: b [2, 2] sage: a [1, 2] ok in exmpl. 3) the list behaves similar to the integers in exmpl. 1). Question: is the assignment b=a+[] the only way to achieve this ? Thanks, wb -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Invoking Lisp from within Sage
On Apr 13, 2010, at 11:20 PM, Adam Getchell wrote: Hi all, I realize this maybe a bit of an insane question, but I'm looking for a way to use ecl within sage besides: ./sage -ecl I have googled for relevant results, but documentation on sage.interfaces.lisp seems broken right now: http://sage.math.washington.edu/home/mhansen/sage-epydoc/sage.interfaces.lisp-module.html That just happened to be a file sitting in someone's directory. It doesn't look like its in the user manual, http://hg.sagemath.org/sage-main/file/ea02bc44fa94/sage/interfaces/lisp.py can serve as a reference though. Basically, you can do sage: lisp((+ 1 2)) '3' and whatever else you want, including reading in files, etc. You can also do sage: a = lisp(1) sage: b = lisp(2) sage: a + b 3 sage: type(a+b) class 'sage.interfaces.lisp.LispElement' If it helps, here's the background: We've got some rather neat causal dynamical triangulation (2d quantum gravity) code running in Lisp. The lisp environment lacking certain facilities, I thought it would be neat to find a way to run it within Sage and take advantage of all the nice facilities provided. I'm looking to avoid rewriting it in python for now, though I would certainly do it if advised that was the only way. One of the primary goals of all the interfaces is so you can use your existing code right from Sage. Give the above a try. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Inverses of Large Sparse Matrices
On Apr 9, 2010, at 10:53 AM, Leo Maloney wrote: I'm trying to compute the inverse of a 5000 x 5000 sparse matrix. What is the basering? I'm getting an EOF error after it runs for about 5 hours, and then it states that sage is trying to access unallocated memory. Is there a way I can increase the memory for this computation? Every time I Google it, all I can find is the benefits sage(plant) has on memory. What operating system are you on. Are you using Sage in a VM (on Windows)? If so, you can increase the amount of memory allocated to the virtual machine. Otherwise, have you checked to see if you even have any memory left on your computer when doing the computation? (Perhaps the only way to increase the memory is to buy more RAM or run it on a different computer.) - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org To unsubscribe, reply using remove me as the subject.
Re: [sage-support] Some experiences
On Apr 6, 2010, at 11:22 PM, Rolandb wrote: Hi, some experiences. I moved from Vista 32 to Windows 7 64 during Easter. I have a Q6700 PC. Three issues are maybe of general interest. 1) Virtualbox 4.3.4: A clumsy environment so I switched back to (the new) VMware player 3.01 and (the old) Sage 4.1. Now I was positively surprised how cool Sage works, and also the fact that I could run multiple Sage sessions all calculating ... But maybe my Virtualbox isn't properly installed? Probably, though Virtualbox is rough around the edges (as are all options of running Sage on Windows). 2) I hoped for a considerable increase in speed, because 64bit optimized c code or assembly instructions are superior to 32bit. So I tested a few simple operations, and I noticed hardly any improvement! Did I installed the wrong version of Sage 4.1? I used sage- vmware-4.1.7z. Without recompiling for your machine, you won't be able to fully take advantage of all it has to offer. In any case, you're running it inside a VM which is probably fixed to be either 32 or 64 bit. 3) Whilst looking for need for speed, I found that many relatively simple standard sage functions aren't optimized. For instance CRT_list(v,moduli)?? states: if len(v) == 0: return 0 x = v[0] m = moduli[0] for i in range(1,len(v)): x = CRT(x,v[i],m,moduli[i]) m *= moduli[i] return x%m And CRT(a,b,m,n)??: if isinstance(a,list): return CRT_list(a,b) g, alpha, beta = XGCD(m,n) if g != 1: raise ValueError, arguments a and b must be coprime return a+(b-a)*alpha*m Just combining both gives: def crt_faster(v,moduli): x = v[0] m = moduli[0] for i in range(1,len(v)): x +=(v[i]-x)*xgcd(m,moduli[i])[1]*m m *= moduli[i] return x%m This improves speed by a factor of 1.5 to 2. I'm assuming you're timing very small examples? - Is there in the near future an effort to optimize those relatively simple, but probably often used, routines? Yes, you just did it :) We'd love for you to submit a patch. There's tons of stuff in Sage that could use optimization and cleanup (and sage/rings/arith.py is high on the list). Often what happens is someone needs some functionality, so they implement it, and then later someone else needs it to be fast, so they optimize it. Some areas for future improvement may be using CRT_basis, and it's asymptotically faster (for a single call at least) to to CRT in a binary tree rather than linearly. - What is the best way to check the most efficient routine? Installing packages like FLINT? FLINT is installed by default already. If your list consists of elements of Z[x], it will be used already under the hood. - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org To unsubscribe, reply using remove me as the subject.
Re: [sage-support] problems with sage and brian simulator
On Apr 7, 2010, at 2:10 AM, Uri wrote: I'm having some problems trying to use a program called Brian Simulator (www.briansimulator.org) through Sage. This program is written in Python an can be used as a python package (I've tried it and I had no problem). However, when I try to use it in Sage I get some problems involving units, which are defined inside Brian. For example, if I write: sage: from brian import * sage: 1*mV I get the following error: AttributeErrorTraceback (most recent call last) /home/uri/ipython console in module() /home/uri/sage-4.3.1/local/lib/python2.6/site-packages/sage/structure/ element.so in sage.structure.element.RingElement.__mul__ (sage/ structure/element.c:10382)() /home/uri/sage-4.3.1/local/lib/python2.6/site-packages/sage/structure/ coerce.so in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:6145)() /home/uri/sage-4.3.1/local/lib/python2.6/site-packages/brian/units.pyc in __mul__(self, other) 1063 if isinstance(other,Unit): 1064 u = Unit(float(self)*float(other)) - 1065 u.name = self.name + other.name 1066 u.dispname = self.dispname + ' ' + other.dispname 1067 u.dim = self.dim * other.dim AttributeError: name Does somebody know why it happens and how to avoid this error? What I don't understand is that if I just write: sage: mV there's no problem at all. Thank you in advance!! It appears that brian.units doesn't behave well with Sage integers (perhaps assuming anything that's not a float or int is a briansimulator unit). Try sage: from brian import * sage: int(1)*mV or sage: 1r*mV - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org To unsubscribe, reply using remove me as the subject.
Re: [sage-support] standard deviations in sage
On Apr 7, 2010, at 9:29 AM, Kenneth A. Ribet wrote: Hello All, I asked myself how I could use sage to compute the standard deviation of a grade distribution for one of my courses. Rooting around, I found that I can compute for example sage: vector(RDF,[1,2,2,1]).standard_deviation() and get the answer 0.57735026919. However, if I try the same command with RDF replaced by RR, I get anAttributeError. My first question is: What's going on here; how come RDF and RR are so different in this context? Their respective descriptions look very similar -- Because no one's yet taken the time to unify the interfaces yet (the two different rings use different implementations under the hood-- the one for RDF is optimized as a double* whereas the one for RR is just the generic one). It would probably make sense to put a standard_deviation method higher up the inheritance tree. To be clear, I consider this a bug (fortunately easy to fix) and a ticket should be filed. An approximation to the field of real numbers using double precision floating point numbers. Answers derived from calculations in this approximation may differ from what they would be if those calculations were performed in the true field of real numbers. This is due to the rounding errors inherent to finite precision calculations. An approximation to the field of real numbers using floating point numbers with any specified precision. Answers derived from calculations in this approximation may differ from what they would be if those calculations were performed in the true field of real numbers. This is due to the rounding errors inherent to finite precision calculations. If I had found some documentation about the standard deviation command, I would probably have have found the answer to my first question. This leads to my second question: Why I don't I see information about standard_deviation when I type standard_deviation? at the command line? Sage has an object-oriented design, which is to say that functions are attached to objects rather than all dumped into the global session. This allows stuff like sage: v = vector(RDF, [1,2,2,1]) sage: v.norm() 3.16227766017 sage: I = NumberField(x^3-x+1, 'a').ideal(2) sage: I.norm() 8 where doing v.norm? and I.norm? can give good contextual information given the wide variety of objects and paradigms that Sage supports (and it makes tab completion work much smoother too). I could see a case for standard_deviation being a top-level function though, like we do for many other basic operations. (Typically f(X) calls X.f()). - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org To unsubscribe, reply using remove me as the subject.
Re: [sage-support] Difference between sage and pyhton calculations
On Apr 5, 2010, at 9:44 PM, William Stein wrote: On Mon, Apr 5, 2010 at 9:12 PM, Michael Welsh yom...@yomcat.geek.nz wrote: On 6/04/2010, at 3:56 PM, Eugene Goldberg wrote: Hello! Here is my pyhtons results: python Python 2.6.5 (r265:79063, Mar 23 2010, 04:49:54) [GCC 4.4.3] on linux2 Type help, copyright, credits or license for more information. 1+1 2 6e-6 % 10e-6 6.0002e-06 and here is sage: ./ sage Sage Version 4.3.5, Release Date: 2010-03-28 sage: 1+1 2 sage: 6e-6 % 10e-6 -4.00e-6 I'm sure sage is wrong.. :( Well, at least the two answers are equivalent mod 10e-6. They're both the same... No they aren't. If you type sage: s = 6e-6 sage: s.__mod__?? then you can read the documentation for Sage's % on real numbers. Definitely the result sage: 6e-6 - 10e-6 -4.00e-6 matches what is claimed in the docstring. The actual function calls the MPFR function mpfr_remainder, which is documented here: http://www.mpfr.org/algorithms.pdf See Section 3.8. This web page: http://pyref.infogami.com/operator-mod describes the Python semantics for Python's __mod__ on float's. They are different than MPFR's. I would be in favor of following Python's conventions here--they at least seem more natural to me (after all, % is related to floor division not round division. :) - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org To unsubscribe, reply using remove me as the subject.
Re: [sage-support] Difference between sage and pyhton calculations
On Apr 6, 2010, at 12:17 AM, Paul Zimmermann wrote: If one wants to have the same answer as Python does (always nonnegative), then function math.fmod can be used. For example, sage: from math import fmod sage: fmod(6e-6,10e-6) 6.0002e-06 first Python does not always give a nonnegative result: (6e-6) % (-10e-6) -4.0007e-06 secondly this does not match the math.fmod function either: sage: from math import fmod sage: fmod(6e-6,-10e-6) 6.0002e-06 I would recommend that Sage % follows one of the C99 standard functions, fmod or remainder. Maybe fmod would be better, and remainder could be provided as a different method. I would rather agree with integers here sage: -1 % 10 9 (Personally, I think C got % wrong, or at least the easy to implement choice won over the more useful, as x%n gives different results for various x in the same residue class mod n.) - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org To unsubscribe, reply using remove me as the subject.
Re: [sage-support] Re: adding noise
On Apr 2, 2010, at 9:41 PM, G B wrote:
Thanks for the detailed response, Simon. Please understand that I'm
not being critical of Sage-- quite the contrary, I'm excited about
what it might offer me once I master it.
I think you touch on one key to the problem-- I'm not a
mathematician, I'm an engineer. While most of the world would
certainly accuse us of being sloppy dressers, mathematicians are one
of the few groups that can legitimately accuse us of being sloppy
thinkers. I think that brand of sloppy thinking is what is at issue
here, and when I say work around I mean become tolerant of.
Sage has already encouraged me to learn more about ring theory than
I ever would have needed otherwise, but getting completely different
results when executing plot(f(x),(x,0,2*pi)) vs. executing plot(f,
(0,2*pi)) started playing on my patience a bit and has me wondering
if I'm simply using an irreconcilably wrong tool for the job. I
think the intention of both of those statements is the same, and
thus should yield the same result, and my suspicion is that the
reason they don't is an artifact of the plumbing, but I may be
missing something.
A good way to think about it is this: Python expressions are evaluated
greedily, from the inside out. Thus
sage: plot(f(x),(x,0,2*pi))
is the same as
sage: A = f(x)# A is now sin(x) + 0.619...
sage: B = (x,0,2*pi)
sage: plot(A, B)
When you write something like sin(x), sin is actually getting called
with the argument x, and the result is sin evaluated at the
indeterminate x (in other words, it's not just returning the old thing
back again). As a more concrete example.
sage: g(x) = sin(x) + sqrt(x)
sage: g(x)
sqrt(x) + sin(x) # g was called with x and plugged in x for x
sage: g(5)
sqrt(5) + sin(5)
sage: var('y')
y
sage: g(y)
sqrt(y) + sin(y)
sage: g(x+y)
sqrt(x + y) + sin(x + y)
It's not the f(x)=sin(x)+T.get_random_element() form that troubles
me though, for the record, I did try 'f(x)=sin(x)
+T.get_random_element(x)'. Expectedly, it doesn't like having an
unwanted argument shoved down its throat.
What still feels awkward to me is how constructs like this behave:
var('x')
T=RealDistribution('gaussian',1)
f=lambda x: T.get_random_element()
g(x)=sin(x)+f(x)
To my mind, the way that is handled is particularly confusing.
[f(1),f(2),f(3)] -- [-0.568652852118, 0.912307924442, 1.35997405644]
but,
[g(1),g(2),g(3)] -- [sin(1) - 0.176035204293, sin(2) -
0.176035204293, sin(3) - 0.176035204293]
In other words, calling f repeatedly gives different results each
time, but calling g repeatedly does not.
That may be a case where the parenthetical syntax conspires with the
overloaded meanings of function to expose my sloppy thinking, but
it also kind of looks like a trap waiting to be triggered.
If sin(x) and f(x) are fundamentally different entities, and my
engineering mind isn't completely convinced that they should be,
Yes, they are very different. The first are expression-like
functions, where it makes sense to differentiate, integrate, typeset,
and otherwise manipulate them as mathematical objects. Sin falls
into this category. The other type are procedures which are are
really arbitrary chunks of code which are the ones native to Python
(and essentially every other procedural programming language). These
are the ones that generate random numbers, test for primality, fetch
webpages, save files, etc. Plot itself is such a function. It
doesn't makes much sense to differentiate or typeset such functions,
but they can be called.
Both types of functions are clearly essential, the confusion arises in
the fact that it's possible to evaluate (and, sometimes, plot) both
kinds. That being said, I think it should easier (and more natural) to
try to do what you're trying to do here.
then the syntax should prevent the construction of g in such a
manner. Either execution of f should be deferred until g is called
with a parameter, as I would expect, or an error should be thrown
for providing illegal arguments to operator '+'.
The problem is that the two terms are evaluated before the + operator
is hit, i.e.
sage: g(x) = sin(x) + f(x)
is the same as
sage: A = sin(x) # actually calls sin (resulting in sin(x))
sage: B = f(x) # actually calls f (resulting in 0.619)
sage: g(x) = A + B # tries to add (which is just fine)
If I want g(x) defined as sin(x) plus the result of f(x) as x is
defined at the definition of g, then the syntax should highlight
that by forcing something like g(x)=sin(x) + `f(x)`
To get something deferred, which sounds like what you want, you could
abandon the g(x) = ... syntax completely and always use lambda (or def)
sage: g = lambda x: sin(x) + f(x)
or
sage: def g(x):
...return sin(x) + f(x)
It may take some getting used to, but functions can even return other
functions. For example, you
Re: [sage-support] Potential Security Hole -- sh (shell) in Notebook
On Apr 1, 2010, at 6:04 PM, TianWei wrote: The sh option in the sage notebook allows anyone to access the command-line shell on the sage server. This grants users access to any directory on the server, including configuration settings, etc. Even on the Try Sage Online link on the main page (www.sagenb.org) lets users do this. This is a potential security hole for all sage servers. (The sh option I'm talking about is in the drop-down menu that selects the backend to process user commands, such as sage, maxima, r, gap, gp, python, and so on) Letting users run arbitrary Python commands (the default) is just as dangerous, e.g. anything one can do from the shell one can do with os.system(). This is a well-known potential vulnerability and should always be mitigated via other means (e.g. only letting trusted users use the server, granting the worksheet processes limited privileges, and/or running the whole thing inside a jail/zone/virtual machine). - Robert -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org To unsubscribe, reply using remove me as the subject.
Re: [sage-support] Re: Print only outputs?
On Apr 1, 2010, at 9:11 PM, TianWei wrote: I for one would find hiding input cells useful because when I use sage for my math homework, I like the pretty printing feature of the text cells (using $...$), and often times I will use the output of the calculation cells (e.g. graphs) to accompany the text, but the actual sage commands themselves are sometimes irrelevant. Probably not irrelevant to whoever is grading it :). In any case, there is the %hide mode for hiding input cells, but it doesn't seem to affect the printed view. This is just my view. On Apr 1, 7:39 pm, William Stein wst...@gmail.com wrote: On Thu, Apr 1, 2010 at 10:27 AM, Eugene Goldberg omegat...@gmail.com wrote: Hi! Is it possible to print only output content of worksheet? No, this isn't currently supported. It would likely be easy to implement. Nobody has ever requested this feature before, as far as I can remember. Can you explain more about why you want it. William -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group athttp://groups.google.com/group/sage-support URL:http://www.sagemath.org To unsubscribe, reply using remove me as the subject. -- William Stein Associate Professor of Mathematics University of Washingtonhttp://wstein.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Is there an efficient method of producing indexed variables?
On Apr 1, 2010, at 9:21 PM, scott.h wrote: That did exactly what I wanted to do! Thank you very much for taking the time to reply. The command C = [var(C_%s % i) for i in range(n)] in particular is what I was looking for. I think I can glean how %s works from how you've used it and will experiment a little. However if you, or anyone else, could point me in the direction of some documentation for it that would be much appreciated. It's sort of hard to google/search. How about http://diveintopython.org/native_data_types/formatting_strings.html On Apr 1, 7:50 pm, Minh Nguyen nguyenmi...@gmail.com wrote: Hi, On Fri, Apr 2, 2010 at 12:36 PM, scott.h scott.he...@gmail.com wrote: SNIP It seems like this should be simple but for the life of me I can't figure out how to do it. Here I'm taking a guess at what you really want to do. See the following Sage session: [mv...@sage ~]$ sage -- | Sage Version 4.3.5, Release Date: 2010-03-28 | | Type notebook() for the GUI, and license() for information.| -- sage: n = 3 sage: M = random_matrix(ZZ, nrows=n); M [ 2 2 -2] [ 4 2 -7] [ 2 -1 1] sage: # create a list of unknown constants; these are actually symbolic variables sage: C = [var(C_%s % i) for i in range(n)]; C [C_0, C_1, C_2] sage: X = [randint(1, 10) for i in range(n)]; X [2, 3, 2] sage: F = [C[i] * exp(M[i,i] * x) for i in range(n)]; F [C_0*e^(2*x), C_1*e^(2*x), C_2*e^x] sage: [F[i].substitute(x=X[i]) for i in range(n)] [C_0*e^4, C_1*e^6, C_2*e^2] -- Regards Minh Van Nguyen -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org To unsubscribe, reply using remove me as the subject. -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
