[sage-support] enumerating vectors in Z^d
Problem background: I want to find the smallest (in l_2 norm) vectors that satisfy a certain condition - creating a minimal set of coset representatives for Z^d/A(Z^d) for a dilation matrix A. My idea is to start with 0 and enumerate vectors in Z^d one at a time. For each new vector that I consider, I can test whether it is in a new coset, or in a coset that I already have a representative for. I know the number of cosets in advance, so can stop when I reach the right number of coset representatives. My question: what is the best way to enumerate vectors in Z^d (for an arbitrary d that my function will be passed as a parameter, so I don't know its value in advance) starting with 0, then going through all vectors with just a single 1 and all other entries 0, then going through all vectors with a single -1 and all other entries 0, then going through all vectors with two 1's or -1's and all other entries 0, etc.? Ideally I could find the next vector in my sequence of vectors to consider one-at-a-time, so that I don't generate more vectors than I need to, but I suspect it will be easier to generate vectors in the sequence in batches, such as all vectors with a single 1 entry, then all vectors with a single -1 entry, and so on. -- 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] enumerating vectors in Z^d
On Wed, 05 May 2010 at 05:38PM -0700, Eva wrote: My question: what is the best way to enumerate vectors in Z^d (for an arbitrary d that my function will be passed as a parameter, so I don't know its value in advance) starting with 0, then going through all vectors with just a single 1 and all other entries 0, then going through all vectors with a single -1 and all other entries 0, then going through all vectors with two 1's or -1's and all other entries 0, etc.? Ideally I could find the next vector in my sequence of vectors to consider one-at-a-time, so that I don't generate more vectors than I need to, but I suspect it will be easier to generate vectors in the sequence in batches, such as all vectors with a single 1 entry, then all vectors with a single -1 entry, and so on. One starting point is IntegerVectors -- try IntegerVectors? in a Sage session. You can do IntegerVectors(5,3) to get an iterator for all vectors of nonnegative integers of length 3 that sum to 5. Others may have better ideas, but my first guess is that you'll work with IntegerVectors(n,d) (for n = 1, 2, 3...) and for each vector, look at all the nonzero entries and flip the signs in all possible ways. For a integer vector v, you can find the nonzero entries with something like [i for i, val in enumerate(v) if val != 0] and then call Subsets on that list and flip signs: for indices in Subsets([i for i, val in enumerate(v) if val != 0]): w = v[:] for index in indices: w[index] *= -1 # now do your coset test stuff There are probably much better ways to do this, but the above will work, I think. You can also ask your question in the sage-combinat-devel group. Dan -- --- Dan Drake - http://mathsci.kaist.ac.kr/~drake --- signature.asc Description: Digital signature
[sage-support] Re: enumerating vectors in Z^d
On May 6, 5:21 am, Dan Drake dr...@kaist.edu wrote: One starting point is IntegerVectors -- try IntegerVectors? in a Sage session. You can do IntegerVectors(5,3) to get an iterator for all vectors of nonnegative integers of length 3 that sum to 5. Others may have better ideas, but my first guess is that you'll work with IntegerVectors(n,d) (for n = 1, 2, 3...) and for each vector, look at all the nonzero entries and flip the signs in all possible ways. For a integer vector v, you can find the nonzero entries with something like [i for i, val in enumerate(v) if val != 0] and then call Subsets on that list and flip signs: for indices in Subsets([i for i, val in enumerate(v) if val != 0]): w = v[:] for index in indices: w[index] *= -1 # now do your coset test stuff There are probably much better ways to do this, but the above will work, I think. You can also ask your question in the sage-combinat-devel group. Dan -- --- Dan Drake - http://mathsci.kaist.ac.kr/~drake --- signature.asc 1KViewDownload Hmmm, that will give me vectors ordered by l_1 norm, which would get me off to a good start! Is there anything to test/find the l_2 norm of a vector? Thanks, Eva -- 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: rational function arithmetic
On May 5, 10:09 am, Mike Hansen mhan...@gmail.com wrote: Hello, On Wed, May 5, 2010 at 5:03 AM, Matt Bainbridge bainbridge.m...@gmail.com wrote: I wrote a sage program which does a lot of arithmetic in the field of rational functions Frac(Q[x,y,z]). The problem is that sage doesn't check for common divisors of the numerator and denominator, so after doing a lot of arithmetic operations, I end up with rational functions whose numerator and denominator are divisible by huge integers (on the order of 2^3000). Is there a reasonable way to get sage to eliminate common factors after each arithmetic operation? Currently, the easiest way to do this is just to work over Frac(ZZ[x,y,z]) which is equivalent. Yes indeed. The basic problem is that QQ is, morally Frac(ZZ), so you are nesting Frac constructors. This is, generally speaking, a bad idea, as we found in Axiom, but hard to prevent. -- 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
[sage-support] Making a movie or animation with 3d plotting of sage: animate() fails with 3D
Hello there, First of all, a very big thank you for this piece of gold: sagemath. Im loving it! I could get it to do all i wanted so far without much less fuss! I have now tried to make an animation or movie with it of some 3d plot i have. I want to capture the changes occur in the plot with one variable. I used animate() but it failed. I'd really appreciate if anyone can shine some light regarding how this is possible in Sagemath? Thank you, Isuru -- 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] Making a movie or animation with 3d plotting of sage: animate() fails with 3D
use : @interact On Thu, May 6, 2010 at 4:04 PM, isurug isurugod...@gmail.com wrote: Hello there, First of all, a very big thank you for this piece of gold: sagemath. Im loving it! I could get it to do all i wanted so far without much less fuss! I have now tried to make an animation or movie with it of some 3d plot i have. I want to capture the changes occur in the plot with one variable. I used animate() but it failed. I'd really appreciate if anyone can shine some light regarding how this is possible in Sagemath? Thank you, Isuru -- 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 -- Ajay Rawat Kalpakkam, IGCAR - Save Himalayas - -- 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: Making a movie or animation with 3d plotting of sage: animate() fails with 3D
If you search this group for animate or animation you can see a lot of other responses. One approach is to using ffmpeg to make a movie out of a sequence of frames you save somewhere (e.g. the DATA directory). Another is to use Jmol, but that requires learning a bit more about Jmol since the functionality isn't wrapped in Sage well yet. There has also been some recent progress in including the Theora codec in Sage, which can be used with html5 (see http://trac.sagemath.org/sage_trac/ticket/7298). Eventually the animate command should be able to use that last option for 3d objects but I'm not sure how long that's going to take. -M. Hampton On May 6, 5:34 am, isurug isurugod...@gmail.com wrote: Hello there, First of all, a very big thank you for this piece of gold: sagemath. Im loving it! I could get it to do all i wanted so far without much less fuss! I have now tried to make an animation or movie with it of some 3d plot i have. I want to capture the changes occur in the plot with one variable. I used animate() but it failed. I'd really appreciate if anyone can shine some light regarding how this is possible in Sagemath? Thank you, Isuru -- 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 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: Making a movie or animation with 3d plotting of sage: animate() fails with 3D
I just noticed that saving 3d objects to a file has finally been fixed: http://trac.sagemath.org/sage_trac/ticket/2872 That means we are one step closer to handling 3d animations. I can't find a trac ticket that explicitly targets that but maybe I'm just missing it. -M. Hampton On May 6, 7:10 am, Marshall Hampton hampto...@gmail.com wrote: If you search this group for animate or animation you can see a lot of other responses. One approach is to using ffmpeg to make a movie out of a sequence of frames you save somewhere (e.g. the DATA directory). Another is to use Jmol, but that requires learning a bit more about Jmol since the functionality isn't wrapped in Sage well yet. There has also been some recent progress in including the Theora codec in Sage, which can be used with html5 (seehttp://trac.sagemath.org/sage_trac/ticket/7298). Eventually the animate command should be able to use that last option for 3d objects but I'm not sure how long that's going to take. -M. Hampton On May 6, 5:34 am, isurug isurugod...@gmail.com wrote: Hello there, First of all, a very big thank you for this piece of gold: sagemath. Im loving it! I could get it to do all i wanted so far without much less fuss! I have now tried to make an animation or movie with it of some 3d plot i have. I want to capture the changes occur in the plot with one variable. I used animate() but it failed. I'd really appreciate if anyone can shine some light regarding how this is possible in Sagemath? Thank you, Isuru -- 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 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 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] enumerating vectors in Z^d
On Wed, May 5, 2010 at 8:38 PM, Eva eva.cu...@acadiau.ca wrote: Problem background: I want to find the smallest (in l_2 norm) vectors that satisfy a certain condition - creating a minimal set of coset representatives for Z^d/A(Z^d) for a dilation matrix A. My idea is to start with 0 and enumerate vectors in Z^d one at a time. For each new vector that I consider, I can test whether it is in a new coset, or in a coset that I already have a representative for. I know the number of cosets in advance, so can stop when I reach the right number of coset representatives. Do you require that the L2 norm is weakly increasing for the order in which they're produced? There are a number of ways to get the norm: sage: v = vector([1,2,3]) sage: v.norm() sqrt(14) sage: def l2norm(v): : return sqrt(sum([i^2 for i in v])) : sage: l2norm([0,1,2]) sqrt(5) --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
Re: [sage-support] Re: converting strings to latex
Hi Alex,
If I understand correctly your question, you would like to
convert arithmetical expressions directly into Latex.
I would like to convert a string into a sage-Latex-expression (in
sagetex).
I don't know if it is possible to do it in Sage, but you could
always write your own function. I've written a small one that
should do the trick.
[...]
sage: sarrus(matrix)
'[1 \\cdot 0 \\cdot 1 + 1 \\cdot (-1) \\cdot (-1) + 1 \\cdot 1
\\cdot 0] - [1 \\cdot 0 \\cdot (-1) + 1 \\cdot 1 \\cdot 1 + 1
\\cdot (-1) \ \cdot 0]'
sage: print sarrus(matrix)
[1 \cdot 0 \cdot 1 + 1 \cdot (-1) \cdot (-1) + 1 \cdot 1 \cdot 0]
- [1 \cdot 0 \cdot (-1) + 1 \cdot 1 \cdot 1 + 1 \cdot (-1) \cdot
0]
Does that answer your problem ?
Thank you for the code (it's more elegant than my first try :) ). It
doesn't work too, because the problem is that sagetex is putting the
string in some kind of (typewriter-)enviroment. After some
experimentation i found a possible solution is to replace \cdot
with $\cdot$. It doesn't look nice, but better than before.
Georg
On 5 mai, 11:28, Dr. Georg Damm georg.d...@web.de wrote:
Hi all,
i've written a function to explain the rule of sarrus. Is there
a possibility to return latex code insted of a text? I'd like
to use something like $\sage{sarrus(A)}$ in sagetex.
Thanks a lot,
Georg
P.S.: I expirimented with JSMathExpr from sage.misc.latex, but
i couldn't improve the output.
def sarrus(A):
res=
for i in range(3):
if (A[0,i]=0):
res+=++latex(A[0,i])
else:
res+=+(+latex(A[0,i])+)
if (A[1,(i+1)%3]=0):
res+=*+latex(A[1,(i+1)%3])
else:
res+=*(+latex(A[1,(i+1)%3])+)
if (A[2,(i+2)%3]=0):
res+=*+latex(A[2,(i+2)%3])
else:
res+=*(+latex(A[2,(i+2)%3])+)
for i in range(2,5):
if (A[0,i%3]=0):
res+=-+latex(A[0,i%3])
else:
res+=-(+latex(A[0,i%3])+)
if (A[1,(i-1)%3] = 0):
res+=*+latex(A[1,(i-1)%3])
else:
res+=*(+latex(A[1,(i-1)%3])+)
if (A[2,(i-2)%3]=0):
res+=*+latex(A[2,(i-2)%3])
else:
res+=*(+latex(A[2,(i-2)%3])+)
return res
--
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[sage-support] Re: Sagetex wont plot
I tried export PATH=/Applications/sage/:$PATH in Terminal and got this: export: Command not found. I'm running Mac OS 10.5.8. Oscar Chavez On May 5, 7:54 pm, Dan Drake dr...@kaist.edu wrote: On Wed, 05 May 2010 at 07:38AM -0600, jrodri1...@gmail.com wrote: Thanks!!! I got that working. But, I stumbled onto something else... I tried copying my file into the same directory as the sage file and running it from there. The interesting thing is that I can only run sage if I type sage\sage (when in the Applications folder) or /Applications/sage/sage. I can't actually cd into the sage folder itself and simply type in sage. Is that normal? It's normal if you haven't added the right directory to your $PATH. While in a terminal, you can do export PATH=/Applications/sage/:$PATH and after that, you should be able to just type sage and get Sage to run. If you run Sage from inside TeXShop, you don't need to do anything because (IIRC) it automatically looks for Sage in /Applications/sage. Dan -- --- Dan Drake - http://mathsci.kaist.ac.kr/~drake --- signature.asc 1KViewDownload -- 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] How to add grid lines to plot?
Hello! There is plot: p=plot(sin,0,2*pi) How to add grid lines to this plot? -- 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 add grid lines to plot?
Hello, On Thu, May 6, 2010 at 2:14 PM, Eugene Goldberg omegat...@gmail.com wrote: There is plot: p=plot(sin,0,2*pi) How to add grid lines to this plot? plot(sin,0,2*pi,gridlines=True) You can look at the documentation of plot for more examples. --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
[sage-support] Re: converting strings to latex
Ok, I think I understand your problem. I had something similar before.
The problem is that the object returned by the function sarrus is a
'str',
which sagetex format so that it replaces every underscore, etc. with
\_ to make it work in Latex. If you don't want the output to be
modified,
you have to use LatexExpr object
def sarrus(A):
bracket_neg = lambda i:str(i) if i = 0 else '(' + str(i) + ')'
res = '['
for i in range(3):
for j in range(3):
a_ij = A[j, (i+j)%3]
if j 0: res += ' \\cdot '
res += bracket_neg(a_ij)
if i 2: res += ' + '
res += '] - ['
for i in range(3):
for j in range(3):
a_ij = A[j, (2-i-j)%3]
if j 0: res += ' \\cdot '
res += bracket_neg(a_ij)
if i 2: res += ' + '
res += ']'
from sage.misc.latex import LatexExpr
return LatexExpr(res)
and when you call \sage{sarrus(A)}, you must put in between dollar
signs. Feel free to ask further if it doesn't solve your problem !
Alex
On 6 mai, 10:29, Georg Damm georg.d...@web.de wrote:
Hi Alex,
If I understand correctly your question, you would like to
convert arithmetical expressions directly into Latex.
I would like to convert a string into a sage-Latex-expression (in
sagetex).
I don't know if it is possible to do it in Sage, but you could
always write your own function. I've written a small one that
should do the trick.
[...]
sage: sarrus(matrix)
'[1 \\cdot 0 \\cdot 1 + 1 \\cdot (-1) \\cdot (-1) + 1 \\cdot 1
\\cdot 0] - [1 \\cdot 0 \\cdot (-1) + 1 \\cdot 1 \\cdot 1 + 1
\\cdot (-1) \ \cdot 0]'
sage: print sarrus(matrix)
[1 \cdot 0 \cdot 1 + 1 \cdot (-1) \cdot (-1) + 1 \cdot 1 \cdot 0]
- [1 \cdot 0 \cdot (-1) + 1 \cdot 1 \cdot 1 + 1 \cdot (-1) \cdot
0]
Does that answer your problem ?
Thank you for the code (it's more elegant than my first try :) ). It
doesn't work too, because the problem is that sagetex is putting the
string in some kind of (typewriter-)enviroment. After some
experimentation i found a possible solution is to replace \cdot
with $\cdot$. It doesn't look nice, but better than before.
Georg
On 5 mai, 11:28, Dr. Georg Damm georg.d...@web.de wrote:
Hi all,
i've written a function to explain the rule of sarrus. Is there
a possibility to return latex code insted of a text? I'd like
to use something like $\sage{sarrus(A)}$ in sagetex.
Thanks a lot,
Georg
P.S.: I expirimented with JSMathExpr from sage.misc.latex, but
i couldn't improve the output.
def sarrus(A):
res=
for i in range(3):
if (A[0,i]=0):
res+=++latex(A[0,i])
else:
res+=+(+latex(A[0,i])+)
if (A[1,(i+1)%3]=0):
res+=*+latex(A[1,(i+1)%3])
else:
res+=*(+latex(A[1,(i+1)%3])+)
if (A[2,(i+2)%3]=0):
res+=*+latex(A[2,(i+2)%3])
else:
res+=*(+latex(A[2,(i+2)%3])+)
for i in range(2,5):
if (A[0,i%3]=0):
res+=-+latex(A[0,i%3])
else:
res+=-(+latex(A[0,i%3])+)
if (A[1,(i-1)%3] = 0):
res+=*+latex(A[1,(i-1)%3])
else:
res+=*(+latex(A[1,(i-1)%3])+)
if (A[2,(i-2)%3]=0):
res+=*+latex(A[2,(i-2)%3])
else:
res+=*(+latex(A[2,(i-2)%3])+)
return res
--
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URL:http://www.sagemath.org
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