[sage-support] Re: loading maxima

2010-04-11 Thread Mathieu Roux
and so?
What to do so that it works?
Mathieu

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Re: [sage-support] strange n()

2010-04-11 Thread bb

Mike Hansen schrieb:

On Sat, Apr 10, 2010 at 3:37 AM, bb bblo...@arcor.de wrote:
  

sage: n(sqrt(2.), digits=40)
1.414213562373095145474621858738828450441
sage: n(sqrt(2), digits=40)
1.414213562373095048801688724209698078570
sage:



If you wanted this to be more like Maxima, the appropriate thing to do
would some something like:

sage: RealNumber = RealField(137)
sage: sqrt(2.0)
1.414213562373095048801688724209698078570
sage: sqrt(2).n(digits=40)
1.414213562373095048801688724209698078570

  

Sage is missing the errror forwarding of Mathematica.



Yes, Sage does not have a numerical type that does Mathematica's
significance arithmetic.  An interesting thread about the merits and
demerits of significance arithmetic is
http://sci.tech-archive.net/Archive/sci.math.symbolic/2008-03/msg00014.html
.

One could do a little work to get Sage's interval arithmetic to do
something similar.

--Mike

  
Tnx for helping. I did some more experimentation. I dont want to bother 
you, but if you have some time and some pation I would be thankfull for 
one more explanation. Your tip works as expected, but if I use the 
method n() I still get 53 bit of significant bits??? (see last 
expression of the snippet.)


I argue, that the parameter of n() is set elsewhere in another Variable 
than RealNumber?


sage: RealNumber = RealField(137)
sage: sqrt(2.)
1.414213562373095048801688724209698078570
sage: _.prec()
137
sage: 
sqrt(2.000)

1.414213562373095048801688724209698078570
sage: _.prec()
137
sage: 
n(sqrt(2.000), 
digits=60)

1.41421356237309504880168872420969807856967336610324780267484
sage: _.prec()
203
sage: 
n(sqrt(2.000))

1.41421356237310
sage: _.prec()
53
sage:

Regards BB

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[sage-support] Question about numerical linear algebra.

2010-04-11 Thread Thierry Dumont

I want to use RDF linear algebra.

As far as i understand, operations are implemented using numpy/scipy.
But many things differ from a direct call to scipy modules; for example:

(computing the Singular Value Decomposition of a matrix):

sage: A=matrix(RDF,[[1,3,2],[1,2,3],[0,5,2],[1, 1, 1]])
sage: U,Sig,V=A.SVD()

but, a direct call to scipy (even in sage) is:

from scipy import *
from scipy.linalg import *
A=mat('[1 3 2; 1 2 3; 0 5 2; 1, 1, 1]')
M,N=A.shape
U,s,Vh=svd(A)

 -Qusetion: is there some dictionary, some documentation about how 
the scipy functions are mapped to sage? and what can be directly used?
One can use A.LU(), A.QR()... witeh A a matrix(RDF,...), all this 
without importing explicitly anything.


-Remark:
 In the preceding examples, if you compare as given by U,Sig,V=A.SVD()
and U given by U,s,Vh=svd(A) they are transposed :-(

Yours, sincerely

t.




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attachment: tdumont.vcf

[sage-support] Re: points on elliptic curves mod N

2010-04-11 Thread John Cremona
Here's the problem.  For an elliptic curve defined over a ring, not a
field, the _point_class (which is the class used to hold its points)
is the class EllipticCurvePoint, but that class has almost no methods
at all defined for it, not even an __init__ method.  By contrast,  for
elliptic curves defined over fields the point class is
EllipticCurvePoint_field (or EllipticCurvePoint_finite_field, etc),
which all have a huge amount of functionality.

One could defined a new class called something like
EllipticCurvePoint_commutative_ring, and move most of the
functionality from the field class to the ring class, but that would
be a lot of work, and there would be a danger that the operations over
fields would be slowed down.  And one would have to decide how to deal
with the group law now only being partial (which I know can be done,
but I forget the details).

It would be a good student project to at least handle the case where
the base ring was of the form Integers(n), where the error message
produced by trying to invert a non-invertible constant would helpfully
tell you the factorization of the modulus.

John

On Apr 11, 5:17 am, Alec Mihailovs alec.mihail...@gmail.com wrote:
 On Apr 10, 8:27 pm, Robert Bradshaw rober...@math.washington.edu
 wrote:

  This particular point however seems to have order 3 on both E(GF(67))  
  and E(GF(89)).

 E=EllipticCurve([1,R(1)])

 seems to be working,

 7*E([0,1])

 Traceback (click to the left of this block for traceback)
 ...
 ZeroDivisionError: Inverse of 5092 does not exist

 Alec

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Re: [sage-support] strange n()

2010-04-11 Thread Mike Hansen
On Sun, Apr 11, 2010 at 10:01 AM, bb bblo...@arcor.de wrote:
 Tnx for helping. I did some more experimentation. I dont want to bother you,
 but if you have some time and some pation I would be thankfull for one more
 explanation. Your tip works as expected, but if I use the method n() I still
 get 53 bit of significant bits??? (see last expression of the snippet.)

 I argue, that the parameter of n() is set elsewhere in another Variable than
 RealNumber?

Yes, in the code for n, we have the following:

if prec is None:
if digits is None:
prec = 53
else:
prec = int((digits+1) * 3.32192) + 1

so it just defaults to 53 if nothing is passed in.  The RealNumber =
RealField(137) just changes the precision for floating point literals
entered on the command line.

--Mike

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Re: [sage-support] Re: loading maxima

2010-04-11 Thread Mike Hansen
On Sun, Apr 11, 2010 at 8:18 AM, Mathieu Roux mthr...@gmail.com wrote:
 and so?
 What to do so that it works?

Did Maxima get installed?  Does the following file exist:
/Applications/sage-4.3.5/local/bin/maxima ? If not, then it doesn't
seem like Maxima installed correctly.  You could try running sage -f
/Applications/sage-4.3.5/spkg/standard/maxima* and report back what
happens.

--Mike

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Re: [sage-support] strange n()

2010-04-11 Thread bb

Mike Hansen schrieb:

On Sun, Apr 11, 2010 at 10:01 AM, bb bblo...@arcor.de wrote:
  

Tnx for helping. I did some more experimentation. I dont want to bother you,
but if you have some time and some pation I would be thankfull for one more
explanation. Your tip works as expected, but if I use the method n() I still
get 53 bit of significant bits??? (see last expression of the snippet.)

I argue, that the parameter of n() is set elsewhere in another Variable than
RealNumber?



Yes, in the code for n, we have the following:

if prec is None:
if digits is None:
prec = 53
else:
prec = int((digits+1) * 3.32192) + 1

so it just defaults to 53 if nothing is passed in.  The RealNumber =
RealField(137) just changes the precision for floating point literals
entered on the command line.

--Mike

  

Tnx for clearing that n()-question!

In an earlier posting (I am always thankful for any help!) you wrote:
One could do a little work to get Sage's interval arithmetic to do
something similar. Would be an interesting experiment.

I found an internet page about that topic concerning MPFR from 2/5/2006:
http://www.ma.utexas.edu/users/kschalm/mpfr-in-sage.html
(MPFR seems to be very broadly used by different Progs under GNU Lesser 
GPL. Added is a list of related software.)


There are used some Sage-examples with a strange line-numbering with 
underscores? May be that is an outdated Sage-Version? Actual versions do 
not do any line numbering.


I did not find any evidence that MPFR or MAPM is included in Sage? I do 
not understand if MPFR is compiled with Sage in this examples on that 
page? I cannot find any evidence that MPFR is loaded?


In an extension of the floating point issue I am actually interested in: 
I found a list of libs to support floating point arithmetics that are 
not in the list of included libs to Sage. I found some examples to 
include tools with a CLI via http in the documentatin. I did not find 
hints how to include C/C++ or other language libs to Sage? (To clear 
that statement: The fact I could not find it does not mean it is not 
documented in some place!)


Again - please ignore my boring question if you feel bothered - I can 
understand that! With yor response you opened a door for floting point 
questions.


Tnx anyway - regards BB




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Re: [sage-support] strange n()

2010-04-11 Thread Mike Hansen
On Sun, Apr 11, 2010 at 12:47 PM, bb bblo...@arcor.de wrote:
 In an earlier posting (I am always thankful for any help!) you wrote:
 One could do a little work to get Sage's interval arithmetic to do
 something similar. Would be an interesting experiment.

Here's a brief example

sage: RIF
Real Interval Field with 53 bits of precision
sage: R = RealIntervalField(200); R
Real Interval Field with 200 bits of precision
sage: f = RIF(pi) + 0.5; f
3.641592653589794?
sage: g = R(f); g
3.641592653589794?
sage: g.parent()
Real Interval Field with 200 bits of precision

Even when you increase the precision, it doesn't print out more digits
since it knows the upper and lower bounds.  However, this does not
currently play nice with the .n() stuff.


 I found an internet page about that topic concerning MPFR from 2/5/2006:
 http://www.ma.utexas.edu/users/kschalm/mpfr-in-sage.html
 (MPFR seems to be very broadly used by different Progs under GNU Lesser GPL.
 Added is a list of related software.)

 There are used some Sage-examples with a strange line-numbering with
 underscores? May be that is an outdated Sage-Version? Actual versions do not
 do any line numbering.

This page is indeed quite outdated.


 I did not find any evidence that MPFR or MAPM is included in Sage? I do not
 understand if MPFR is compiled with Sage in this examples on that page? I
 cannot find any evidence that MPFR is loaded?

MPFR is included in Sage by default.  Sage's RealNumber class is a
wrapper around an MPFR object.  Any high-precision floating point
arithmetic in Sage uses MPFR.

 In an extension of the floating point issue I am actually interested in: I
 found a list of libs to support floating point arithmetics that are not in
 the list of included libs to Sage. I found some examples to include tools
 with a CLI via http in the documentatin. I did not find hints how to include
 C/C++ or other language libs to Sage? (To clear that statement: The fact I
 could not find it does not mean it is not documented in some place!)

If you want to interface with other C/C++ libraries, the easiest way
to do so is using Cython [1].  There are also lots of examples in the
Sage library; for example,
$SAGE_ROOT/devel/sage/sage/rings/real_mpfr.pyx

--Mike

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[sage-support] Re: Inverses of Large Sparse Matrices

2010-04-11 Thread Leo Maloney
When I try to make a dense matrix, I get a MemoryError: out of memory
allocating a matrix.  I was able to output my matrix into a .txt file
and tweak it to be read into Matlab.  Matlab was able to compute it
pretty quickly, so I feel like it is doable in Sage as well.  Maybe I
have a problem with my code?  I'm unsure how to fix this problem.

On Apr 9, 12:00 pm, William Stein wst...@gmail.com wrote:
 On Friday, April 9, 2010, Leo Maloney leo.b.malo...@gmail.com wrote:
  My Matrix consists of zeros ones, and -1/9s, so I was intially
  computing it over Q.  I'm trying to re-run the program over R in hopes
  that it will use approximations rather than try to explicitly state
  the fractions.  I am using a Macintosh OSX with 4 gigs of ram, it
  seems that this should be sufficient.

 Definitely try doing it with a dense matrix over QQ too; it might be
 possible, though the answer will be big.   If you provide me the
 matrix I could try on my 128gb computer...  I also know the matrix
 inversion code over QQ well, since I wrote some of it.





  On Apr 9, 11:03 am, Robert Bradshaw rober...@math.washington.edu
  wrote:
  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

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 University of Washingtonhttp://wstein.org

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[sage-support] Inverses of Large Sparse Matrices

2010-04-11 Thread William Stein
On Sunday, April 11, 2010, Leo Maloney leo.b.malo...@gmail.com wrote:
 When I try to make a dense matrix, I get a MemoryError: out of memory
 allocating a matrix.  I was able to output my matrix into a .txt file
 and tweak it to be read into Matlab.  Matlab was able to compute it
 pretty quickly, so I feel like it is doable in Sage as well.  Maybe I
 have a problem with my code?  I'm unsure how to fix this problem.

Do you want a floating point answer or an exact rational answer?
Matlab will not give you a correct exact rational answer (it will
appeat to in a certain mode but will in fact return nonsense).


 On Apr 9, 12:00 pm, William Stein wst...@gmail.com wrote:
 On Friday, April 9, 2010, Leo Maloney leo.b.malo...@gmail.com wrote:
  My Matrix consists of zeros ones, and -1/9s, so I was intially
  computing it over Q.  I'm trying to re-run the program over R in hopes
  that it will use approximations rather than try to explicitly state
  the fractions.  I am using a Macintosh OSX with 4 gigs of ram, it
  seems that this should be sufficient.

 Definitely try doing it with a dense matrix over QQ too; it might be
 possible, though the answer will be big.   If you provide me the
 matrix I could try on my 128gb computer...  I also know the matrix
 inversion code over QQ well, since I wrote some of it.





  On Apr 9, 11:03 am, Robert Bradshaw rober...@math.washington.edu
  wrote:
  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

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 --
 William Stein
 Associate Professor of Mathematics
 University of Washingtonhttp://wstein.org

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Associate Professor of Mathematics
University of Washington
http://wstein.org

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[sage-support] Re: Question about numerical linear algebra.

2010-04-11 Thread Alec Mihailovs
On Apr 11, 1:22 pm, Thierry Dumont tdum...@math.univ-lyon1.fr wrote:
   In the preceding examples, if you compare as given by U,Sig,V=A.SVD()
 and U given by U,s,Vh=svd(A) they are transposed :-(

U is the same, Sig is a diagonal matrix with diagonal entries being
elements of vector s, and V is Hermitian transposed to Vh, as it
supposed to be according to the help pages - it should be
U*Sig*V.conjugate().transpose() == A

Alec

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[sage-support] (1 - i) == -(i + 1) ??

2010-04-11 Thread Mike Witt

[m...@vector ~]$ sage
--
| Sage Version 4.3.1, Release Date: 2010-01-20   |
| Type notebook() for the GUI, and license() for information.|
--
sage: (1-I)/(sqrt(2)-1)
-(I + 1)/(sqrt(2) - 1)
sage:

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[sage-support] Re: (1 - i) == -(i + 1) ??

2010-04-11 Thread Alec Mihailovs
On Apr 11, 4:51 pm, Mike Witt msg...@gmail.com wrote:
 [m...@vector ~]$ sage
 --
 | Sage Version 4.3.1, Release Date: 2010-01-20                       |
 | Type notebook() for the GUI, and license() for information.        |
 --
 sage: (1-I)/(sqrt(2)-1)
 -(I + 1)/(sqrt(2) - 1)

In Sage 4.3.4 (in Windows) that I am using,

(1-I)/(sqrt(2)-1)
(-I + 1)/(sqrt(2) - 1)

Alec

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Re: [sage-support] (1 - i) == -(i + 1) ??

2010-04-11 Thread Mike Witt

On 04/11/2010 01:56:45 PM, Minh Nguyen wrote:

Hi Mike,

On Mon, Apr 12, 2010 at 6:51 AM, Mike Witt msg...@gmail.com wrote:
 [m...@vector ~]$ sage
  
--
 | Sage Version 4.3.1, Release Date: 2010-01-20                      
  |
 | Type notebook() for the GUI, and license() for information.        
 |
  
--

 sage: (1-I)/(sqrt(2)-1)
 -(I + 1)/(sqrt(2) - 1)

This has been fixed in Sage 4.3.5:


Ahh, thanks! Do you happen to know if 4.3.5 builds on Fedora 12?
(I remember seeing that one of the recent ones had problems)

-Mike

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Re: [sage-support] (1 - i) == -(i + 1) ??

2010-04-11 Thread Jaap Spies

Mike Witt wrote:

On 04/11/2010 01:56:45 PM, Minh Nguyen wrote:

Hi Mike,

On Mon, Apr 12, 2010 at 6:51 AM, Mike Witt msg...@gmail.com wrote:
 [m...@vector ~]$ sage
 --
 | Sage Version 4.3.1, Release Date: 2010-01-20   |
 | Type notebook() for the GUI, and license() for information.|
 --
 sage: (1-I)/(sqrt(2)-1)
 -(I + 1)/(sqrt(2) - 1)

This has been fixed in Sage 4.3.5:


Ahh, thanks! Do you happen to know if 4.3.5 builds on Fedora 12?
(I remember seeing that one of the recent ones had problems)



It builds ok, but there are a few issues with some tests.

Jaap



-Mike



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Re: [sage-support] (1 - i) == -(i + 1) ??

2010-04-11 Thread Mike Witt

On 04/11/2010 02:39:58 PM, Jaap Spies wrote:

Mike Witt wrote:

On 04/11/2010 01:56:45 PM, Minh Nguyen wrote:

Hi Mike,

On Mon, Apr 12, 2010 at 6:51 AM, Mike Witt msg...@gmail.com wrote:
 [m...@vector ~]$ sage
  
--
 | Sage Version 4.3.1, Release Date:  
2010-01-20   |
 | Type notebook() for the GUI, and license() for  
information.|
  
--

 sage: (1-I)/(sqrt(2)-1)
 -(I + 1)/(sqrt(2) - 1)

This has been fixed in Sage 4.3.5:


Ahh, thanks! Do you happen to know if 4.3.5 builds on Fedora 12?
(I remember seeing that one of the recent ones had problems)



It builds ok, but there are a few issues with some tests.

Jaap


I notice it says this on the download page:

 Mirror network is currently synchronizing. Please try again later.
 A new release is upcoming. Maybe come back later for the next version  
of Sage?


I don't remember ever seeing either of those messages before.
I guess I should wait?

-Mike

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[sage-support] Re: loading maxima

2010-04-11 Thread Mathieu Roux
Hello,

in fact, the file  /Applications/sage-4.3.5/local/bin/maxima does not
exist!
it is very surprising because it is said that sage would install all
that it needs...

when i run:
sage -f /Applications/sage-4.3.5/spkg/standard/maxima*
there is a long answer which finishes with
***
Failed to make Maxima.
***

real0m7.326s
user0m1.202s
sys 0m2.460s
sage: An error occurred while installing maxima-5.20.1
Please email sage-devel http://groups.google.com/group/sage-devel
explaining the problem and send the relevant part of
of /Applications/sage-4.3.5/install.log.  Describe your computer,
operating system, etc.
If you want to try to fix the problem yourself, *don't* just cd to
/Applications/sage-4.3.5/spkg/build/maxima-5.20.1 and type 'make
check' or whatever is appropriate.
Instead, the following commands setup all environment variables
correctly and load a subshell for you to debug the error:
(cd '/Applications/sage-4.3.5/spkg/build/maxima-5.20.1'  '/
Applications/sage-4.3.5/sage' -sh)
When you are done debugging, you can type exit to leave the
subshell.


Any idea?

Mathieu

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Re: [sage-support] (1 - i) == -(i + 1) ??

2010-04-11 Thread Jaap Spies

Mike Witt wrote:

On 04/11/2010 02:39:58 PM, Jaap Spies wrote:

Mike Witt wrote:

On 04/11/2010 01:56:45 PM, Minh Nguyen wrote:

Hi Mike,

On Mon, Apr 12, 2010 at 6:51 AM, Mike Witt msg...@gmail.com wrote:
 [m...@vector ~]$ sage

--
 | Sage Version 4.3.1, Release Date: 2010-01-20 |
 | Type notebook() for the GUI, and license() for information. |

--
 sage: (1-I)/(sqrt(2)-1)
 -(I + 1)/(sqrt(2) - 1)

This has been fixed in Sage 4.3.5:


Ahh, thanks! Do you happen to know if 4.3.5 builds on Fedora 12?
(I remember seeing that one of the recent ones had problems)



It builds ok, but there are a few issues with some tests.

Jaap


I notice it says this on the download page:

Mirror network is currently synchronizing. Please try again later.
A new release is upcoming. Maybe come back later for the next version of
Sage?

I don't remember ever seeing either of those messages before.
I guess I should wait?



I see no problems downloading from North America:
http://www.sagemath.org/download-source.html

The European mirrors seem to be in trouble?

Jaap





-Mike



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Re: [sage-support] Re: loading maxima

2010-04-11 Thread Mike Hansen
On Sun, Apr 11, 2010 at 2:55 PM, Mathieu Roux mthr...@gmail.com wrote:
 Any idea?

I need to know what error(s) came before Failed to make Maxima in
order to figure out what's going on.

--Mike

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Re: [sage-support] (1 - i) == -(i + 1) ??

2010-04-11 Thread Jaap Spies

Mike Witt wrote:



I notice it says this on the download page:

Mirror network is currently synchronizing. Please try again later.
A new release is upcoming. Maybe come back later for the next version of
Sage?

I don't remember ever seeing either of those messages before.
I guess I should wait?



Look here for a mirror in your neighbourhood:
http://www.sagemath.org/mirrors.html

Jaap




-Mike



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Re: [sage-support] (1 - i) == -(i + 1) ??

2010-04-11 Thread Mike Witt

On 04/11/2010 03:05:02 PM, Jaap Spies wrote:

Mike Witt wrote:



I notice it says this on the download page:

Mirror network is currently synchronizing. Please try again later.
A new release is upcoming. Maybe come back later for the next  
version of

Sage?

I don't remember ever seeing either of those messages before.
I guess I should wait?



Look here for a mirror in your neighbourhood:
http://www.sagemath.org/mirrors.html


Ok, downloading now. Thanks again.

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[sage-support] Re: Gap packages

2010-04-11 Thread Dima Pasechnik


On Apr 10, 9:43 pm, Simon King simon.k...@nuigalway.ie wrote:
 Hi!

 On 10 Apr., 15:06, Stochastix laurent.decreusef...@gmail.com wrote:

  It doesn't seem to be in the optional GAP packages available for SAGE.
  Can I install it directly in SAGE or should I have a stand-alone
  installation of GAP ?

 Sage *has* a stand-alone installation of GAP. If you run sage -gap
 then this installation will be used.

 I would try to start a sage shell (i.e., do sage -sh on the command
 line).

 Inside this shell, gap is the same as sage -gap. So, it should be
 possible to install any gap package in exactly the same way as in a
 Sage-independent installation of GAP. The packages are in SAGE_ROOT/
 local/lib/gap-4.4.12/pkg.

this certainly does not quite address the question how to compile the
executables
for this package. Do you have GNU Pascal installed in some way (e.g.
via fink?) on your machine?
If yes, you might need to modify PATH in the sage shell before doing
configure and make...

Best,
Dmitrii


 Note that it might then be necessary to update GAP's workspace, in
 order to make the new package effective: Start Sage, and then do
   sage: gap_reset_workspace()

 Best regards,
 Simon

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[sage-support] Re: Question about numerical linear algebra.

2010-04-11 Thread Alec Mihailovs
On Apr 11, 1:22 pm, Thierry Dumont tdum...@math.univ-lyon1.fr wrote:

   -Qusetion: is there some dictionary, some documentation about how
 the scipy functions are mapped to sage? and what can be directly used?

What can be used can be seen by typing A. and hitting Tab key. The
documentation for every method is available by entering A.(name of the
method)? , for example, A.SVD? and Tab, and the source is available as
A.SVD?? and then Tab.

Alec

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