[sage-support] Optional GAP packages in Sage 6.2

2014-05-09 Thread Michael Hind
Hi,
I just built Sage 6.2 from source (ex .git) and it brings in GAP 4.7.4.

Now the sage --optional lists
... 
database_gap-4.6.4 .. not installed
...
gap_packages-4.6.4.p1 ... not installed
...

I am not too happy about installing these

I already have GAP 4.7.4 installed on my system.  Is there a way to link to 
this, or conversely get the later versions?

I get this at the moment.

from Sage:

mhh@mhh-Desktop:~$ sage --gap
 ┌───┐   GAP, Version 4.7.4 of 20-Feb-2014 (free software, GPL)
 │  GAP   │   http://www.gap-system.org
 └───┘   Architecture: x86_64-unknown-linux-gnu-gcc-default64
 Libs used:  gmp, readline
 Loading the library and packages ...
 Packages:   GAPDoc 1.5.1
 Try '?help' for help. See also  '?copyright' and  '?authors'
gap quit;

and from GAP

mhh@mhh-Desktop:~/src/gap$ 
./gap   



 ┌───┐   GAP, Version 4.7.4 of 20-Feb-2014 (free software, 
GPL)


 │  GAP   │   
http://www.gap-system.org   

  

 └───┘   Architecture: 
x86_64-unknown-linux-gnu-gcc-default64  



 Libs used:  gmp, 
readline

 

 Loading the library and packages 
... 

 

 Components: trans 1.0, prim 2.1, small* 1.0, id* 
1.0 
 

 Packages:   AClib 1.2, Alnuth 3.0.0, AtlasRep 1.5.0, AutPGrp 1.6, Browse 
1.8.3, Carat 2.1.4, CRISP 1.3.8, Cryst 4.1.12, CrystCat 1.1.6, CTblLib 
1.2.2, FactInt 1.5.3, FGA 1.2.0, GAPDoc 1.5.1, 
 IO 4.2, IRREDSOL 1.2.4, LAGUNA 3.6.4, Polenta 1.3.1, 
Polycyclic 2.11, RadiRoot 2.6, ResClasses 3.3.2, Sophus 1.23, SpinSym 1.5, 
TomLib 1.2.4
 Try '?help' for help. See also  '?copyright' and  '?authors'
gap quit;

I am running Kubuntu 14.04 64bit

BTW how do I avoid: Architecture: x86_64-unknown-linux-gnu-gcc-default64, 
when I build?

Cheers,
Michael

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[sage-support] Re: Optional GAP packages in Sage 6.2

2014-05-09 Thread leif

Michael Hind wrote:

Hi,
I just built Sage 6.2 from source (ex .git) and it brings in GAP 4.7.4.

Now the sage --optional lists
...
database_gap-4.6.4 .. not installed
...
gap_packages-4.6.4.p1 ... not installed
...

I am not too happy about installing these

I already have GAP 4.7.4 installed on my system.  Is there a way to link
to this, or conversely get the later versions?


Sorry, the output of 'sage --optional' is currently still a bit 
misleading, as it doesn't show *available* new style spkgs.


Just do

sage -f gap_packages
sage -f database_gap

and you'll get the new style 4.7.4 versions.

(After that, 'sage --optional' will correctly report that they're 
installed.)



-leif

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[sage-support] Jacobian in characteristic 3

2014-05-09 Thread Gabriel Furstenheim Milerud
I'd like to create an elliptic curve from a degree 3 polynomial without a 
base point, but when I use the Jacobian method I get a division by zero 
error. 

This is my data:
A=GF(3^2,'c')
S.a,b,c=A[]
gS=a^3 - a^2*b + b^3 - a^2*c - a*b*c + b^2*c + a*c^2 + b*c^2 + c^3
Jacobian(gS)

My intuition is that Jacobian tries to compute a short Weierstrass 
polynomial and this is not necessarily possible in characteristic 3 (I 
didn't have any problem in characteristic 5). I also checked that the curve 
was smooth, so it is indeed genus 1

Is there any way to make it work?


This is the error I get:
 
Traceback (most recent call last):
  File sag.py, line 16, in module
Jacobian(gS)
  File 
/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/schemes/elliptic_curves/jacobian.py,
 
line 116, in Jacobian
return Jacobian_of_equation(X, **kwds)
  File 
/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/schemes/elliptic_curves/jacobian.py,
 
line 225, in Jacobian_of_equation
f, g = WeierstrassForm(polynomial, variables=variables)
  File 
/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/schemes/toric/weierstrass.py,
 
line 506, in WeierstrassForm
return WeierstrassForm_P2(polynomial, variables)
  File 
/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/schemes/toric/weierstrass.py,
 
line 771, in WeierstrassForm_P2
S = cubic.S_invariant()
  File 
/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/rings/invariant_theory.py,
 
line 1769, in S_invariant
a,b,c,a2,a3,b1,b3,c1,c2,m = self.scaled_coeffs()
  File 
/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/rings/invariant_theory.py,
 
line 1753, in scaled_coeffs
1/F(3)*a[3], 1/F(3)*a[4], 1/F(3)*a[5],
  File element.pyx, line 1813, in 
sage.structure.element.RingElement.__div__ (sage/structure/element.c:15219)
  File coerce.pyx, line 783, in 
sage.structure.coerce.CoercionModel_cache_maps.bin_op 
(sage/structure/coerce.c:7325)
  File element.pyx, line 1811, in 
sage.structure.element.RingElement.__div__ (sage/structure/element.c:15198)
  File element_givaro.pyx, line 1201, in 
sage.rings.finite_rings.element_givaro.FiniteField_givaroElement._div_ 
(sage/rings/finite_rings/element_givaro.cpp:10695)

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Re: [sage-support] Re: Complex embedding with quotient()

2014-05-09 Thread François Colas
That's exactly what I wanted to do

f = F([omega],check=False)

Thank you :)

Le jeudi 8 mai 2014 08:16:41 UTC+2, Martin Albrecht a écrit :

 Hi Nils, 

 On Wednesday 07 May 2014 16:43:03 Nils Bruin wrote: 
  On Wednesday, May 7, 2014 9:58:48 AM UTC-7, François Colas wrote: 
   What I want to do is a way to evaluate polynomials of K in a power of 
 a 
   primitive square root of unity: 
   
   omega = CC(e^(2*I*pi/m)) 
   F = Hom(K, CC) 
   f = F([omega]) 
   TypeError: images do not define a valid homomorphism 
   
   Does anyone see another way to do this? 
  
  Have you tried using CyclotomicField(m) ? I think that uses specialized 
  code, which should handle high degrees much better than generic number 
  field code: 

 unfortunately that's not the case for the OP, see: 

 https://groups.google.com/forum/#!searchin/sage-devel/QuotientRing| 
 sort:date/sage-devel/qxGMiYDF4eQ/zDcTmXWJH9UJhttps://groups.google.com/forum/#!searchin/sage-devel/QuotientRing%7Csort:date/sage-devel/qxGMiYDF4eQ/zDcTmXWJH9UJ
  
   
  sage: K=CyclotomicField(3*5*7*11) 
  sage: K.coerce_embedding() 
  Generic morphism: 
From: Cyclotomic Field of order 1155 and degree 480 
To:   Complex Lazy Field 
Defn: zeta1155 - 0.852033056930? + 0.00543996044764063?*I 
  
  Alternatively, if you really want to use an explicit quotient ring 
  construction: 
  
  f = F([omega],check=False) 
  
  The error you run into otherwise is: 
  
  sage: sage.rings.morphism.RingHomomorphism_im_gens(H,[omega]) 
  ValueError: relations do not all (canonically) map to 0 under map 
  determined by images of generators. 
  
  i.e., the cyclotomic polynomial evaluated at omega doesn't return an 
 exact 
  zero, because CC uses float arithmetic. 

 Cheers, 
 Martin

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[sage-support] Divisibility between Archimedean places

2014-05-09 Thread Yves Lignac
Hello all,

I am looking for a way to determine if an embedding $\sigma$ of a number 
field $L$ into the complex numbers restricts to a given embedding $\tau$ of 
a subfield $K$ (asking for equality between $\tau$ and $\sigma \circ i$ 
where $i$ is the embedding of $K$ into $L$ does not work). 
More specifically, I have a cubic field $K$ of signature (1,1) and a 
quadratic extension $L/K$ with $L$ of signature (0,3), and I want to be 
able to obtain one of the two complex places of $L$ that does not lie above 
the real place of $K$. I have tried to do this by taking a polynomial for 
$L$ over $K$, taking one of its (complex) roots at the complex place of $K$ 
and using create_embedding_from_approx, but this does not work (on my 
computer at least) because the latter seems to work only with real 
embeddings
(for completeness, here is the code I used (given the number fields K,L and 
the embedding i from K to L :

L_over_K.u,t = L.relativize(i)
g = L_over_K.relative_polynomial()
coef = g.coefficients()
expo = g.exponents()
Q = K.places() ; q = Q[1]
coef2 = []
for c in coef :
coef2.append(q(c))
h = 0
y = polygen(CC)
for i in range(0,len(coef)) :
h = h + coef2[i] * y^(expo[i])
root = (complex_roots(h)[0][0]).center()
p = create_embedding_from_approx(L, root)

In any case, if there is a way to test divisibility between archimedean 
places of number fields without using the above uncomfortable way I would 
be very much happier to use it. 

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[sage-support] Re: reflexive @interact controls (control values update)

2014-05-09 Thread Jason Grout

On 5/8/14, 11:01, William Stein wrote:

@interact
def foo(functions=[sin(x)], f=sin(x)):
 show(plot(foo.functions))
 del foo.functions
 foo.functions = [f(x=x), f(x=x^2), f(x=x^3)]


Here's a corresponding one working in the cell server: 
http://sagecell.sagemath.org/?q=ribyjg


@interact
def foo(self, functions=[sin(x)], f=sin(x)):
show(plot(functions))
del self.functions
self.functions = [f(x=x), f(x=x^2), f(x=x^3)]

Here are a few differences I noticed:

1. Instead of making foo available in the namespace of the function 
(thereby possibly masking out a global variable foo), we follow the 
python object method convention of passing a self argument in as the 
first argument of the function.  If the first argument of an interact 
function does not have a default value, it is considered a 'self' 
argument and is assigned a object that represents the interact itself. 
This has its own problems, and I'd be interested in people weighing in 
on each approach.


2. William has show(plot(foo.functions)).  For the cell server, 
self.functions is the *index* into the list of functions, rather than 
the actual function.  Of course, the actual function is available via 
the normal interact way of just using the parameter name, functions. 
This makes it less ambiguous to set the value of the selector---you just 
set an index, rather than setting a value and then having sage try to 
guess from the value what the index is.


3. This doesn't affect the above example, but it seems that when you 
have functions=[single value], the cell server interacts creates a 
single button, rather than a selector.  This has implications for what 
self.functions returns.  I'm not sure if this is a backwards 
compatibility thing or a bug in our implementation.  It's in the code 
that automagically creates controls based on default values.


4. When you click on a selector button that is already selected, the 
cell server ignores the click (since it's already selected), while the 
cloud processes the click as a new selection.


Thanks,

Jason


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Re: [sage-support] Jacobian in characteristic 3

2014-05-09 Thread John Cremona
It is quite likely that the implementation of Jacobian for plane cubics
does not work in characteristic 3 (at least in general).  I had something
to do with early implementations but then it was all rewritten in terms of
Jacobians, so I cannot remember the details.  Perhaps Volker Braun can
comment.  You yourself can look at the code which is run to see what you
think -- and of course you are more than welcome to add code for char. 3.

John Cremona


On 9 May 2014 12:16, Gabriel Furstenheim Milerud furstenh...@gmail.comwrote:

 I'd like to create an elliptic curve from a degree 3 polynomial without a
 base point, but when I use the Jacobian method I get a division by zero
 error.

 This is my data:
 A=GF(3^2,'c')
 S.a,b,c=A[]
 gS=a^3 - a^2*b + b^3 - a^2*c - a*b*c + b^2*c + a*c^2 + b*c^2 + c^3
 Jacobian(gS)

 My intuition is that Jacobian tries to compute a short Weierstrass
 polynomial and this is not necessarily possible in characteristic 3 (I
 didn't have any problem in characteristic 5). I also checked that the curve
 was smooth, so it is indeed genus 1

 Is there any way to make it work?


 This is the error I get:

 Traceback (most recent call last):
   File sag.py, line 16, in module
 Jacobian(gS)
   File
 /usr/lib/sagemath/local/lib/python2.7/site-packages/sage/schemes/elliptic_curves/jacobian.py,
 line 116, in Jacobian
 return Jacobian_of_equation(X, **kwds)
   File
 /usr/lib/sagemath/local/lib/python2.7/site-packages/sage/schemes/elliptic_curves/jacobian.py,
 line 225, in Jacobian_of_equation
 f, g = WeierstrassForm(polynomial, variables=variables)
   File
 /usr/lib/sagemath/local/lib/python2.7/site-packages/sage/schemes/toric/weierstrass.py,
 line 506, in WeierstrassForm
 return WeierstrassForm_P2(polynomial, variables)
   File
 /usr/lib/sagemath/local/lib/python2.7/site-packages/sage/schemes/toric/weierstrass.py,
 line 771, in WeierstrassForm_P2
 S = cubic.S_invariant()
   File
 /usr/lib/sagemath/local/lib/python2.7/site-packages/sage/rings/invariant_theory.py,
 line 1769, in S_invariant
 a,b,c,a2,a3,b1,b3,c1,c2,m = self.scaled_coeffs()
   File
 /usr/lib/sagemath/local/lib/python2.7/site-packages/sage/rings/invariant_theory.py,
 line 1753, in scaled_coeffs
 1/F(3)*a[3], 1/F(3)*a[4], 1/F(3)*a[5],
   File element.pyx, line 1813, in
 sage.structure.element.RingElement.__div__ (sage/structure/element.c:15219)
   File coerce.pyx, line 783, in
 sage.structure.coerce.CoercionModel_cache_maps.bin_op
 (sage/structure/coerce.c:7325)
   File element.pyx, line 1811, in
 sage.structure.element.RingElement.__div__ (sage/structure/element.c:15198)
   File element_givaro.pyx, line 1201, in
 sage.rings.finite_rings.element_givaro.FiniteField_givaroElement._div_
 (sage/rings/finite_rings/element_givaro.cpp:10695)

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Re: [sage-support] Divisibility between Archimedean places

2014-05-09 Thread John Cremona
I have forwarded your posting to sage-nt which has readers who may help who
don't follow sage-support.  You are welcome to join sage-nt (for which I am
a moderator so if I see your name I'll let you in!)

Sorry not to have actually helped answer your question!

John Cremona


On 9 May 2014 13:30, Yves Lignac yhp...@gmail.com wrote:

 Hello all,

 I am looking for a way to determine if an embedding $\sigma$ of a number
 field $L$ into the complex numbers restricts to a given embedding $\tau$ of
 a subfield $K$ (asking for equality between $\tau$ and $\sigma \circ i$
 where $i$ is the embedding of $K$ into $L$ does not work).
 More specifically, I have a cubic field $K$ of signature (1,1) and a
 quadratic extension $L/K$ with $L$ of signature (0,3), and I want to be
 able to obtain one of the two complex places of $L$ that does not lie above
 the real place of $K$. I have tried to do this by taking a polynomial for
 $L$ over $K$, taking one of its (complex) roots at the complex place of $K$
 and using create_embedding_from_approx, but this does not work (on my
 computer at least) because the latter seems to work only with real
 embeddings
 (for completeness, here is the code I used (given the number fields K,L
 and the embedding i from K to L :

 L_over_K.u,t = L.relativize(i)
 g = L_over_K.relative_polynomial()
 coef = g.coefficients()
 expo = g.exponents()
 Q = K.places() ; q = Q[1]
 coef2 = []
 for c in coef :
 coef2.append(q(c))
 h = 0
 y = polygen(CC)
 for i in range(0,len(coef)) :
 h = h + coef2[i] * y^(expo[i])
 root = (complex_roots(h)[0][0]).center()
 p = create_embedding_from_approx(L, root)

 In any case, if there is a way to test divisibility between archimedean
 places of number fields without using the above uncomfortable way I would
 be very much happier to use it.

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[sage-support] Re: reflexive @interact controls (control values update)

2014-05-09 Thread Nils Bruin
Hi Jason,

Thank you very much for all the work on SageCell. It's an unbelievably 
useful tool to make little demonstrations.

On Friday, May 9, 2014 6:11:24 AM UTC-7, Jason Grout wrote:

 4. When you click on a selector button that is already selected, the 
 cell server ignores the click (since it's already selected), while the 
 cloud processes the click as a new selection. 

 
5. (i've tested this in Chrome and Firefox): If you select another button, 
you do get the plot you've asked for, but the interact is recreated with 
the first button highlighted. Due to 4., that means you can't get the plot 
for the first button any more.

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Re: [sage-support] possible bug in DiscreteHiddenMarkovModel - NaN produced in output matrices

2014-05-09 Thread Jesse Hersch
On Thursday, May 8, 2014 5:59:10 PM UTC-7, William wrote:

  Do you recall if you handled the underflow problem in your 
 implementation? 

 I believe it does not. 

  I haven't studied the code yet, but it seems like this could be the 
 culprit. 

 I think you're right.  You should implement it! 


I had a look at the code an it appears that it *is* already handling the 
underflow problem.  

The scaling factors are computed in _forward_scale_all() and used in both 
_forward_scale_all() and _backward_scale_all().  Also _viterbi_scale() is 
using log probabilities to avoid underflow in products of small 
probabilities.

So I need to dig deeper.  btw I am new to both sage and cython.  I am eager 
to find the cause and fix this though.  So here's my question:

If I make a change to hmm.pyx, how do I get sage to pick up that change 
without having to rebuild all of sage from source? (that took a few hours). 

I read here that I can attach a .pyx file which should force a cython 
recompilation of hte file whenever the .pyx file is changed.  Is that 
right? 
http://www.sagemath.org/doc/developer/coding_in_cython.html#attaching-or-loading-spyx-files

I tried that and got a syntax error:

sage: attach /home/jhersch/bin/sage-6.2/src/sage/stats/hmm/hmm.pyx
  File ipython-input-4-162f4bbc7027, line 1
attach /home/jhersch/bin/sage-6.2/src/sage/stats/hmm/hmm.pyx
 ^
SyntaxError: invalid syntax


What is the usual way sage developers go about making changes in cython 
code without rebuilding everything?

Thanks!

Jesse

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[sage-support] Re: possible bug in DiscreteHiddenMarkovModel - NaN produced in output matrices

2014-05-09 Thread leif

Jesse Hersch wrote:

What is the usual way sage developers go about making changes in cython
code without rebuilding everything?


Edit the file(s), then run './sage -b' (which only rebuilds the 
necessary files of the Sage library).


'./sage -br' rebuilds the library and afterwards starts Sage, such that 
you can check the effects of your changes.


But before starting to modify the code, you should create a branch for 
your work such that you can always easily switch back to a clean 
version of Sage.  See [1].



-leif

P.S.:  Thanks for your very nice bug report!

[1] 
http://sagemath.org/doc/developer/walk_through.html#starting-without-a-ticket 
(as of now, still the documentation for Sage 6.1.1)


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[sage-support] Re: reflexive @interact controls (control values update)

2014-05-09 Thread Jason Grout

On 5/9/14, 11:14, Nils Bruin wrote:

Hi Jason,

Thank you very much for all the work on SageCell. It's an unbelievably
useful tool to make little demonstrations.

On Friday, May 9, 2014 6:11:24 AM UTC-7, Jason Grout wrote:

4. When you click on a selector button that is already selected, the
cell server ignores the click (since it's already selected), while the
cloud processes the click as a new selection.


5. (i've tested this in Chrome and Firefox): If you select another
button, you do get the plot you've asked for, but the interact is
recreated with the first button highlighted. Due to 4., that means you
can't get the plot for the first button any more.



Right---the interact always is recreating that control, which defaults 
to the first entry.  With a selector, our thinking was that if the item 
was already selected, then it didn't need to be selected again.  But I 
can see where it would be useful to 'select' an already-selected item. 
We can make that change, which would bring SMC and sage cell closer 
together.


Jason


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Re: [sage-support] possible bug in DiscreteHiddenMarkovModel - NaN produced in output matrices

2014-05-09 Thread William Stein
On Fri, May 9, 2014 at 12:12 PM, Jesse Hersch jesseher...@fastmail.fm wrote:
 On Thursday, May 8, 2014 5:59:10 PM UTC-7, William wrote:

  Do you recall if you handled the underflow problem in your
  implementation?

 I believe it does not.

  I haven't studied the code yet, but it seems like this could be the
  culprit.

 I think you're right.  You should implement it!


 I had a look at the code an it appears that it is already handling the
 underflow problem.

 The scaling factors are computed in _forward_scale_all() and used in both
 _forward_scale_all() and _backward_scale_all().  Also _viterbi_scale() is
 using log probabilities to avoid underflow in products of small
 probabilities.

 So I need to dig deeper.  btw I am new to both sage and cython.  I am eager
 to find the cause and fix this though.  So here's my question:

 If I make a change to hmm.pyx, how do I get sage to pick up that change
 without having to rebuild all of sage from source? (that took a few hours).

./sage -br, as Lief said.

By the way, 10 minutes ago I just gave a very, very basic lecture on
Cython, which will appear here shortly: http://youtu.be/YrO89QIizxI


 I read here that I can attach a .pyx file which should force a cython
 recompilation of hte file whenever the .pyx file is changed.  Is that right?
 http://www.sagemath.org/doc/developer/coding_in_cython.html#attaching-or-loading-spyx-files

 I tried that and got a syntax error:

 sage: attach /home/jhersch/bin/sage-6.2/src/sage/stats/hmm/hmm.pyx
   File ipython-input-4-162f4bbc7027, line 1
 attach /home/jhersch/bin/sage-6.2/src/sage/stats/hmm/hmm.pyx
  ^
 SyntaxError: invalid syntax


 What is the usual way sage developers go about making changes in cython code
 without rebuilding everything?

 Thanks!

 Jesse

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-- 
William Stein
Professor of Mathematics
University of Washington
http://wstein.org

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[sage-support] Re: reflexive @interact controls (control values update)

2014-05-09 Thread Nils Bruin
On Friday, May 9, 2014 1:05:23 PM UTC-7, Jason Grout wrote:

 Right---the interact always is recreating that control, which defaults 
 to the first entry.  With a selector, our thinking was that if the item 
 was already selected, then it didn't need to be selected again. 

But I can see where it would be useful to 'select' an already-selected 
 item. 


That would be a workaround, but ideally one would know which option got 
selected (if any) and then either not delete/recreate the control or 
recreate the control with the relevant button selected.
 

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