{5} Assigned, Active Tickets by Owner (Full Description) (9849 matches)

On Tue, Feb 9, 2010 at 1:22 PM, finotti <luis.finotti@gmail.com> wrote:
> Dear all,
>
> Cells starting with "%time" stopped working with 4.3.2.  (It works
> with 4.3.1.)  Is it no long supported or is it a bug? (time still
> works with the command line.)
>
> Running on Linux 32-bit, ubuntu binary.
>
> Thanks,

Wow, what a horrible, horrible regression! Indeed, I've confirmed that what happens is that doing %time causes the notebook to hang forever, and be pretty broken thereafter. Ouch. The issue was reported at these  sage-support and  sage-notebook threads.

So this is incredibly awful:

sage: gamma(RealField(100)(3/4))
1.2254167024651776451290983034
sage: gamma(3/4).n(100)
1.2254167024651776429777783051

(for the record, the first one is correct)

and this doesn't agree with that:

sage: log(2).n(100)
0.69314718055994530941723212146
sage: log(RealField(2))
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/Users/ncalexan/Devel/RiemannTheta/riemann_theta.py in <module>()

/Users/ncalexan/sage-3.4.rc0/local/lib/python2.5/site-packages/sage/calculus/calculus.pyc in log(x, base)
   9242             return x.log()
   9243         except AttributeError: 
-> 9244             return ln(x)
   9245     else:
   9246         try:

/Users/ncalexan/sage-3.4.rc0/local/lib/python2.5/site-packages/sage/calculus/calculus.pyc in ln(x)
   9189         0.693147180559945
   9190     """
-> 9191     return function_log(x)
   9192 
   9193 def log(x, base=None):

/Users/ncalexan/sage-3.4.rc0/local/lib/python2.5/site-packages/sage/calculus/calculus.pyc in __call__(self, x, *args)
   7542             return getattr(x, self._repr_())(*args)
   7543         except AttributeError:
-> 7544             return SymbolicComposition(self, SR(x))
   7545 
   7546     def _approx_(self, x):  # must *always* be called with a float x as input.

/Users/ncalexan/sage-3.4.rc0/local/lib/python2.5/site-packages/sage/calculus/calculus.pyc in __call__(self, x)
    504                 msg, s, pos = err.args
    505                 raise TypeError, "%s: %s !!! %s" % (msg, s[:pos], s[pos:])
--> 506         return self._coerce_impl(x)
    507 
    508     def _coerce_impl(self, x):

/Users/ncalexan/sage-3.4.rc0/local/lib/python2.5/site-packages/sage/calculus/calculus.pyc in _coerce_impl(self, x)
    566             return self(x._sage_())
    567         else:
--> 568             raise TypeError, "cannot coerce type '%s' into a SymbolicExpression."%type(x)
    569 
    570     def _repr_(self):

TypeError: cannot coerce type '<type 'sage.rings.real_mpfr.RealField'>' into a SymbolicExpression.
sage: log(RealField(2))

From suge-support

On Sep 1, 11:35 pm, Mani chandra <mchan...@…> wrote:

Mani chandra wrote:

sage: x = a + I*b
sage: real(x.conjugate().simplify())
real_part(a) + imag_part(b)
sage: real(x.conjugate())
real_part(a) - imag_part(b)

This seems to be happening because maxima(via simplify) treats variables as real whereas pynac treats as complex.

sage: x.conjugate()
conjugate(a) - I*conjugate(b)

sage: x.conjugate().simplify()
a - I*b

In 2.10.2 and 2.10.3.rc2:

sage: is_EuclideanDomain(ZZ)
False

I looked to whether any of Sage's rings would ever return True for this function, and came up with pAdicRingGeneric and no others:

sage: is_EuclideanDomain(pAdicRing(7))
True

So this idea (to have EuclideanDomains as a class) just has not been properly implemented. As a start we could make rings which are certainly Euclidean (e,g, ZZ and univariate polynomials over a field) be derived from EuclideanDomain instead of PrincipalIdealDomain as they are now.

That would not be a complete solution, since (for example) some rings of integers of number fields are Euclidean, though it is not easy to say which; and there is no functionality to answer the question "is R Euclidean" except to see if R's class is (derived from) EuclideanDomain, which for rings of integers it never will be!

One other puzzling -- and inconsistent -- thing is that EuclideanDomainElement has a broader scope than EuclideanDomain:

sage: is_EuclideanDomain(ZZ)
False
sage: is_EuclideanDomainElement(ZZ(1))
True

sage: is_EuclideanDomain(R)
False
sage: is_EuclideanDomainElement(x)
True

We have

sage: E = EllipticCurve('65a1')
sage: G = E.change_ring(QuadraticField(-56,'a'))
sage: G.simon_two_descent()
(3, 4, [(-9/4 : -3/8*a + 9/8 : 1), (-8/7 : -1/49*a + 4/7 : 1), (1 : 0 : 1), 
  (-6/25*a - 47/25 : 36/125*a - 368/125 : 1), (1/4 : 1/16*a - 1/8 : 1)])

The documentation for simon_two_descent says that the output of Simon 2-descent is

        OUTPUT:
            integer -- "probably" the rank of self
            integer -- the 2-rank of the Selmer group
            list    -- list of independent points on the curve.

Our curve does have rank 3, but the output list above contains *five* points, so they can't be independent!

Our curve has torsion of order 2, so E(K)/2 E(K) has rank four, so the 3 and four output by Simon descent are right. The only problem is the list, which has too many points in it.

Maybe this is simply a documentation issue, and the docs for simon_two_descent should be changed to say that list is a list of points that *generate* a subgroup of the MW group of rank r, where r is the first number output by simon_two_descent.

Reported by Alex Raichev on sage-support:

sage: var('n',ns=1)
n
sage: (QQbar(2)^3)^n
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

<...>
<...>/sage/rings/qqbar.pyc in __pow__(self, e)
   2808             1
   2809         """
-> 2810         e = QQ._coerce_(e)
   2811         n = e.numerator()
   2812         d = e.denominator()

<...>/sage/structure/parent_old.so in 
sage.structure.parent_old.Parent._coerce_ (sage/structure
/parent_old.c:4031)()

<...>/site-packages/sage/structure/parent.so in 
sage.structure.parent.Parent.coerce (sage/structure/parent.c:4185)()

TypeError: no canonical coercion from New Symbolic Ring to Rational
Field

Since pynac supports using arbitrary Sage objects as numeric objects in symbolic expressions, we should return a symbolic expression as a result of the above commands.

The attached patch adds conversion to polynomial rings. Two doctests fail at this time; they rely on being able to convert to CDF and ComplexField?(100). I didn't want them to get forgotten so I left them in.

John Cremona reports:

In 4.0.alpha0, this causes a segmentation fault:

----------------------------------------------------------------------
| Sage Version 4.0.alpha0, Release Date: 2009-05-15                  |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: K.<a>=NumberField(x^2-x+22)
sage: w=-13*a-14
sage: E=EllipticCurve([0,0,0,0,-1728*w])
sage: P1 = E.lift_x(-3*a-66)
sage: P2 = E.lift_x((-21*a-93)/4)
sage: P2.division_points(19)

It works fine to do

sage: g = P2.division_points(19, poly_only=True)

which defines a polynomial of degree 361 over Q(sqrt(-87)), but then g.roots() goes Boom.

ncalexan verified this on Mac OS X; it looks like the crash is in an NTL function:

(gdb) bt
#0  0x01293247 in modii ()
#1  0x014278bc in FpX_red ()

Converting symbolic expressions containing binomial coefficients to maxima elements does not work.

sage: maxima(binomial(2*x, x))
sage1

Also the conversions to mathematica and maple fail:

sage: mathematica(binomial(2*x, x))
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/home/huss/.sage/temp/bernoulli/6709/_home_huss__sage_init_sage_0.py in <module>()

/local/data/huss/software/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/interfaces/expect.pyc in __call__(self, x, name)                                                                                                    
   1024             return cls(self, x, name=name)                                                               
   1025         try:                                                                                             
-> 1026             return self._coerce_from_special_method(x)                                                   
   1027         except TypeError:                                                                                
   1028             raise                                                                                        

/local/data/huss/software/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/interfaces/expect.pyc in _coerce_from_special_method(self, x)                                                                                       
   1048             s = '_gp_'                                                                                   
   1049         try:                                                                                             
-> 1050             return (x.__getattribute__(s))(self)                                                         
   1051         except AttributeError:                                                                           
   1052             return self(x._interface_init_())                                                            

/local/data/huss/software/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/structure/sage_object.so in sage.structure.sage_object.SageObject._mathematica_ (sage/structure/sage_object.c:5033)()                               

/local/data/huss/software/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression._interface_ (sage/symbolic/expression.cpp:3293)()                                     

/local/data/huss/software/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/structure/sage_object.so in sage.structure.sage_object.SageObject._interface_ (sage/structure/sage_object.c:2828)()                                 

/local/data/huss/software/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/interfaces/expect.pyc in __call__(self, x, name)                                                                                                    
   1022                                                                                                          
   1023         if isinstance(x, basestring):                                                                    
-> 1024             return cls(self, x, name=name)                                                               
   1025         try:                                                                                             
   1026             return self._coerce_from_special_method(x)                                                   

/local/data/huss/software/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/interfaces/expect.pyc in __init__(self, parent, value, is_name, name)
   1426             except (TypeError, KeyboardInterrupt, RuntimeError, ValueError), x:
   1427                 self._session_number = -1
-> 1428                 raise TypeError, x
   1429         self._session_number = parent._session_number
   1430

TypeError: Error executing code in Mathematica
CODE:
        sage1=<function binomial at 0x917ddbc>[(x)*(2),x];
Mathematica ERROR:
        Syntax::sntxf: "sage1=" cannot be followed by
    "<function binomial at 0x917ddbc>[(x)*(2),x];".

sage: maple(binomial(2*x, x))                       
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/home/huss/.sage/temp/bernoulli/6709/_home_huss__sage_init_sage_0.py in <module>()

/local/data/huss/software/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/interfaces/expect.pyc in __call__(self, x, name)                                                                                                    
   1024             return cls(self, x, name=name)                                                               
   1025         try:                                                                                             
-> 1026             return self._coerce_from_special_method(x)                                                   
   1027         except TypeError:                                                                                
   1028             raise                                                                                        

/local/data/huss/software/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/interfaces/expect.pyc in _coerce_from_special_method(self, x)                                                                                       
   1048             s = '_gp_'                                                                                   
   1049         try:                                                                                             
-> 1050             return (x.__getattribute__(s))(self)                                                         
   1051         except AttributeError:                                                                           
   1052             return self(x._interface_init_())                                                            

/local/data/huss/software/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/structure/sage_object.so in sage.structure.sage_object.SageObject._maple_ (sage/structure/sage_object.c:4795)()                                     

/local/data/huss/software/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression._interface_ (sage/symbolic/expression.cpp:3293)()                                     

/local/data/huss/software/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/structure/sage_object.so in sage.structure.sage_object.SageObject._interface_ (sage/structure/sage_object.c:2828)()                                 

/local/data/huss/software/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/interfaces/expect.pyc in __call__(self, x, name)                                                                                                    
   1022                                                                                                          
   1023         if isinstance(x, basestring):                                                                    
-> 1024             return cls(self, x, name=name)                                                               
   1025         try:                                                                                             
   1026             return self._coerce_from_special_method(x)                                                   

/local/data/huss/software/sage-4.0.rc0/local/lib/python2.5/site-packages/sage/interfaces/expect.pyc in __init__(self, parent, value, is_name, name)                                                                               
   1426             except (TypeError, KeyboardInterrupt, RuntimeError, ValueError), x:                          
   1427                 self._session_number = -1
-> 1428                 raise TypeError, x
   1429         self._session_number = parent._session_number
   1430

TypeError: An error occured running a Maple command:
INPUT:
read "/home/huss/.sage//temp/bernoulli/6709//interface//tmp6709";
OUTPUT:
on line 1, syntax error, missing operator or `;`:
sage1:=<function binomial at 0x917ddbc>((x)*(2),x):;
                        ^
Error, while reading
`/home/huss/.sage//temp/bernoulli/6709//interface//tmp6709`

At  http://groups.google.com/group/sage-support/browse_thread/thread/d8e22deb18d97253 Michael Friedman asked how to get the multiplicities when solving a set of nonlinear equations.

It turns out that actually even the multiplicities for a single and rather simple equation are wrong:

----------------------------------------------------------------------
| Sage Version 4.0, Release Date: 2009-05-29                         |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: z = var('z')
sage: solve((z^3-1)^3,z,multiplicities=True)
([z == (sqrt(3)*I - 1)/2, z == (-sqrt(3)*I - 1)/2, z == 1], [1, 1, 3])

I am afraid that symbolics isn't my field of expertise. So, I don't know how to cure it.

In new symbolics, imaginary 'I' is typeset as 'I' which is not "textbook style". This is a regression compared to Sage 3.4

sage: latex( exp(i*x))
e^{I \, x}

Lower case letter 'i' should be used in the typeset version.

If a symbolic expression contains  symbolic derivative then checking whether it is zero, raises error:

sage: x.diff(x,2).is_zero()
True

sage: f(x) = function('f',x)
sage: f(x).diff(x).is_zero()
....
NotImplementedError: derivative

This fails because new symbolics tries to convert it to maxima expression for checking the relation.

Update:

* A patch to fix the issue is attached. The patch adds a new method ".has_fderivative()" for symbolic expressions and in __nonzero__ method adds a check whether it has fderivative.

Comments (for future works): A simple timing comparison that illustrates why we should avoid calling maxima to assert nonzero even for symbolic functions

sage: f(x) = function('f',x)
sage: timeit('sin(f(x)).is_zero()')
5 loops, best of 3: 85.8 ms per loop
sage: timeit('sin(f(x).diff(x)).is_zero()')
625 loops, best of 3: 132 µs per loop

It seems pynac is 400 times faster than maxima in this case.

From  sage-devel:

     sage: theta = var('theta')
     sage: solve(cos(theta)==sin(theta))

should produce

     [sin(theta) == cos(theta)]

but instead it produces

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/Users/palmieri/.sage/temp/Macintosh.local/69786/_Users_palmieri__sage_init_sage_0.py in <module>()

/Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/relation.pyc in solve(f, *args, **kwds)
    478     """
    479     try:
--> 480         return f.solve(*args,**kwds)
    481     except AttributeError:
    482         from sage.symbolic.ring import is_SymbolicVariable

/Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.solve (sage/symbolic/expression.cpp:21764)()

TypeError: solve() takes at least 1 positional argument (0 given)

Providing a second argument 'theta' gives another error:

    sage: solve(cos(theta)==sin(theta), theta)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/Users/palmieri/.sage/temp/Macintosh.local/69786/_Users_palmieri__sage_init_sage_0.py in <module>()

/Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/relation.pyc in solve(f, *args, **kwds)
    478     """
    479     try:
--> 480         return f.solve(*args,**kwds)
    481     except AttributeError:
    482         from sage.symbolic.ring import is_SymbolicVariable

/Applications/sage/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.solve (sage/symbolic/expression.cpp:22291)()

/Applications/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.pyc in __call__(self, *args, **kwds)
   1380 
   1381     def __call__(self, *args, **kwds):
-> 1382         return self._obj.parent().function_call(self._name, [self._obj] + list(args), kwds)
   1383 
   1384     def help(self):

/Applications/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.pyc in function_call(self, function, args, kwds)
   1288                                        [s.name() for s in args],
   1289                                        ['%s=%s'%(key,value.name()) for key, value in kwds.items()])
-> 1290         return self.new(s)
   1291 
   1292     def _function_call_string(self, function, args, kwds):

/Applications/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.pyc in new(self, code)
   1084 
   1085     def new(self, code):
-> 1086         return self(code)
   1087 
   1088     ###################################################################


/Applications/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.pyc in __call__(self, x, name)
   1019 
   1020         if isinstance(x, basestring):
-> 1021             return cls(self, x, name=name)
   1022         try:
   1023             return self._coerce_from_special_method(x)

/Applications/sage/local/lib/python2.6/site-packages/sage/interfaces/expect.pyc in __init__(self, parent, value, is_name, name)
   1423             except (TypeError, KeyboardInterrupt, RuntimeError, ValueError), x:
   1424                 self._session_number = -1
-> 1425                 raise TypeError, x
   1426         self._session_number = parent._session_number
   1427 

TypeError: Error executing code in Maxima
CODE:
	sage4 : to_poly_solve(sage0,sage3)$
Maxima ERROR:
	
Nonalgebraic argument given to 'topoly'
#0: to_poly_solve(e=cos(theta) = sin(theta),vars=theta)(topoly_solver.mac line 10)

The first version of this -- solve(cos(theta)==sin(theta)) -- is in the tutorial, and so presumably used to work.

See #6572 for a related ticket which, among other things, tells doctesting to skip this test in the tutorial. If the underlying problem is solved, the test in the tutorial should be restored, and of course a test should be put into the main Sage code illustrating that it now works.

I found out that sage comes with old versions of the files ell.gp, ellQ.gp, qfsolve.gp. This should be updated. The newest version can be found at  http://www.math.unicaen.fr/~simon/ .

On Sep 30, 11:07 am, lutusp <lut...@…> wrote:

I find I cannot make more than one of a certain kind of assume statement: sage: assume(a,'real') sage: assume(b,'real') If I do, I get an error message: AttributeError?: 'GenericDeclaration?' object has no attribute 'variables'

It's comparing your second assumption with the first one, presumably to make sure it doesn't conflict (?) ... but it is strange that it is talking about an attribute variables, since the attribute _var is being called, and b is real has that.

The problem is in symbolic/expression.pyx, where nonzero tries to find the variable of "a is real" - but it only has a _var, not variables like "t>0", which is a symbolic expression.

One such assumption is accepted, but not two. But more typical assumptions are accepted: sage: forget() sage: assume(a > 0) sage: assume(b > 0) sage: assume(c > 0) sage: assumptions() [a > 0, b > 0, c > 0] Am I using the wrong syntax or is this a bug?

I believe William is aware of this bug and said it can be fixed by installing OpenSSL or similar. But I am unable to find a trac ticket for it, so I thought I'd open one. It's interesting this issue does not arise on Solaris 10 (SPARC), despite OpenSSL libraries not being present there either. This bug seems to come up a lot on linux too, as a Google search shows.

On a Sun Ultra 27 (Intel Xeon processor), running Open Solaris 06/2009, I get the following problem when python is being built.

drkirkby@hawk:~/sage-4.3/spkg/installed$ ls
bzip2-1.0.5             libgcrypt-1.4.4.p1      python-2.6.2.p5
cliquer-1.2.p2          libgpg_error-1.6.p3     readline-6.0.p1
conway_polynomials-0.2  libpng-1.2.35.p0        sage_scripts-4.3
dir-0.1                 mercurial-1.3.1.p0      scons-1.2.0
eclib-20080310.p8       mpir-1.2.2              sqlite-3.6.19.p0
elliptic_curves-0.1     ntl-5.4.2.p9            termcap-1.3.1.p0
extcode-4.3             opencdk-0.6.6.p3        zlib-1.2.3.p5
gnutls-2.2.1.p5         pari-2.3.3.p5
graphs-20070722.p1      prereq-0.6

copying build/scripts-2.6/pydoc -> /export/home/drkirkby/sage-4.3.rc2/local/bin changing mode of /export/home/drkirkby/sage-4.3.rc2/local/bin/2to3 to 755 changing mode of /export/home/drkirkby/sage-4.3.rc2/local/bin/smtpd.py to 755 changing mode of /export/home/drkirkby/sage-4.3.rc2/local/bin/idle to 755 changing mode of /export/home/drkirkby/sage-4.3.rc2/local/bin/pydoc to 755 running install_egg_info Removing /export/home/drkirkby/sage-4.3.rc2/local/lib/python2.6/lib-dynload/Python-2.6.2-py2.6.egg-info Writing /export/home/drkirkby/sage-4.3.rc2/local/lib/python2.6/lib-dynload/Python-2.6.2-py2.6.egg-info if test -f /export/home/drkirkby/sage-4.3.rc2/local/bin/python -o -h /export/home/drkirkby/sage-4.3.rc2/local/bin/python; \

then rm -f /export/home/drkirkby/sage-4.3.rc2/local/bin/python; \ else true; \ fi

(cd /export/home/drkirkby/sage-4.3.rc2/local/bin; ln python2.6 python) rm -f /export/home/drkirkby/sage-4.3.rc2/local/bin/python-config (cd /export/home/drkirkby/sage-4.3.rc2/local/bin; ln -s python2.6-config python-config) /usr/bin/ginstall -c -m 644 ./Misc/python.man \

/export/home/drkirkby/sage-4.3.rc2/local/share/man/man1/python.1

make[2]: Leaving directory `/export/home/drkirkby/sage-4.3.rc2/spkg/build/python-2.6.2.p4/src' Sleeping for three seconds before testing python Traceback (most recent call last):

File "<string>", line 1, in <module> File "/export/home/drkirkby/sage-4.3.rc2/local/lib/python/hashlib.py", line 136, in <module>

md5 = get_builtin_constructor('md5')

File "/export/home/drkirkby/sage-4.3.rc2/local/lib/python/hashlib.py", line 63, in get_builtin_constructor

import _md5

ImportError?: No module named _md5

real 1m38.244s user 1m15.115s sys 0m13.132s sage: An error occurred while installing python-2.6.2.p4

}}}

I'm not sure if this should be reported upstream or not. Some feedback on that might be useful. If so, I will report it to a python bug tracker or similar. The issue seems to arrise often enough.

Dave

PS, to even get to this point, I had to delete the following list of files, to get around a gnutls issue in #7387.

    * SAGE_LOCAL/include/gcrypt-module.h
    * SAGE_LOCAL/include/gpg-error.h
    * SAGE_LOCAL/include/gcrypt.h
    * SAGE_LOCAL/lib/libgcrypt*
    * SAGE_LOCAL/lib/libgpg* 

The documentation of UniqueRepresentation says

    Similarly, the identity is used as hash function, which is also as
    fast as it can get. However this means that the hash function may
    change in between Sage sessions, or even within the same Sage
    session (see below). Subclasses should overload :meth:`__hash__`
    if this could be a problem.

But there is no implementation of __hash__.

I'm adding one.

Hi, I needed some calculation period benchmark for pairings. I could
not find anything build in, but the following implementation solved my
problem:

http://maths.straylight.co.uk/archives/104

They definitely very useful sometimes.  E.g., there is something
called the elliptic curve factorization method that is a brilliant trick
to factor integers.  You want to factor an integer N so you pretend
that it is prime, do a bunch of arithmetic with N, and if something goes
wrong, the error message gives just the information you need to factor N.
But it's important that the error message be an exception that you can
catch and that can contain some interesting Python data in it.  Custom
exceptions work very nicely for that. 

(This used to be trivial to implement in Sage, but for some reason
Sage changed and now it is isn't... :-(

sage: E = EllipticCurve(Integers(15),[1,-1])
sage: P = E.point([1,0,1], check=False)
goes boom but didn't used to...

William

The following is from code for evaluating Riemann theta functions on sage.math:

sage: %prun siegel_theta(tau3p, 1/10*vector([1/2 + I, 2/3*I, 1.222*I]))
         137700 function calls (136832 primitive calls) in 2.221 CPU seconds

   Ordered by: internal time

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
       23    1.668    0.073    1.674    0.073 {method 'gamma_inc' of 'sage.rings.complex_number.ComplexNumber' objects}
    791/1    0.153    0.000    0.380    0.380 riemann_theta.py:313(find_integer_points)
     1601    0.066    0.000    0.066    0.000 {method 'sin' of 'sage.rings.real_mpfr.RealNumber' objects}
     5706    0.056    0.000    0.077    0.000 free_module.py:742(__call__)
        1    0.029    0.029    0.137    0.137 riemann_theta.py:51(finite_sum_without_derivatives)
     1602    0.026    0.000    0.026    0.000 {method 'exp' of 'sage.rings.real_mpfr.RealNumber' objects}

The finite_sum_without_derivatives is the main loop, which calls sin, cos, and exp each iteration. But the dominant part is computing an initial error approximation, which computes gamma_inc to very high precision a bunch of times, optimizing a parameter. That takes longer than everything else! Could a party interested in special functions please speed this up?

In new symbolics, underlying "sage.symbolic.function.SFunction" class allows one to pass the keywords such as "latex_name=LaTeX". It would be really good if we expose this feature at the user interface level. This will directly allow LaTeX customization by users according to their need.

Currently, Sage (4.0.1) raises error if one tries to do so.

Couple of example usage:

(1) Define symbolic function with its latex representaion

riemann(x) = function('riemann', x, latex_name="\\mathcal{R}")
latex( riemann(x) )
\mathcal{R}\left(x\right)

(2) Printing arguments of a symbolic functions as its indices.

mu,nu = var('mu,nu')
def my_latex_print(*args): 
    return "\psi_{%s}"%(', '.join(map(latex, args)))

psi(mu,nu) = function('psi', mu,nu, print_latex_func=my_latex_print)

latex(psi(mu,nu))
\psi_{\mu, \nu}

Attached patch allows keyword arguments while defining symbolic functions.

One of the elementary tool that is often needed to compute equation of motion in Physics, is functional derivative. This along with the implementation of Euler-Lagrange equation will make Sage extremely useful for physicists.

Maple can simplify all but the first of the following examples:

%maple
print(simplify(binomial(n,2)+binomial(n+1,2)));
print(simplify(factorial(n)/factorial(n-2)/2 + factorial(n+1)/factorial(n-1)/2));
print(simplify(factorial(n+1)/factorial(n)));
print(simplify(binomial(n,k)*factorial(k)*factorial(n-k)));

returns

binomial(n,2)+binomial(n+1,2)
n^2
n+1
n!

Sage can simplify only the first:

var('n,k')
print (binomial(n,2) + binomial(n+1,2)).simplify_full()
print (factorial(n)/factorial(n-2)/2 + factorial(n+1)/factorial(n)/2).simplify_full()
print (factorial(n+1)/factorial(n)).simplify_full()
print (binomial(n,k)*factorial(k)*factorial(n-k)).simplify_full()

returns

n^2
1/2*(factorial(n - 2)*factorial(n + 1) + factorial(n)^2)/(factorial(n - 2)*factorial(n))
factorial(n + 1)/factorial(n)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/jason/.sage/sage_notebook/worksheets/admin/10/code/49.py", line 11, in <module>
    exec compile(ur'print (binomial(n,k)*factorial(k)*factorial(n-k)).simplify_full()' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "expression.pyx", line 4837, in sage.symbolic.expression.Expression.simplify_full (sage/symbolic/expression.cpp:19979)
  File "expression.pyx", line 4864, in sage.symbolic.expression.Expression.simplify_trig (sage/symbolic/expression.cpp:20076)
  File "expression.pyx", line 418, in sage.symbolic.expression.Expression._maxima_ (sage/symbolic/expression.cpp:3415)
  File "sage_object.pyx", line 364, in sage.structure.sage_object.SageObject._interface_ (sage/structure/sage_object.c:3384)
  File "sage_object.pyx", line 451, in sage.structure.sage_object.SageObject._maxima_init_ (sage/structure/sage_object.c:5065)
  File "expression.pyx", line 443, in sage.symbolic.expression.Expression._interface_init_ (sage/symbolic/expression.cpp:3544)
  File "/home/jason/sage-4.0/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/jason/sage-4.0/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 497, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/jason/sage-4.0/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 206, in __call__
    operator = ex.operator()
  File "expression.pyx", line 3088, in sage.symbolic.expression.Expression.operator (sage/symbolic/expression.cpp:15127)
RuntimeError: cannot find SFunction in table

It takes too long to check whether x is in a list in new symbolics

sage: var('x,x1,x2,x3,x4')
(x, x1, x2, x3, x4)
sage: f = function('f')
sage: mylist = [x1,x2,x3,x4,f(x1),f(x2),f(x3),f(x4)]

sage: timeit('x in mylist')
5 loops, best of 3: 461 ms per loop

If we need to check it couple of more times then it becomes worse

sage: timeit('x in mylist')
5 loops, best of 3: 1.26 s per loop
sage: timeit('x in mylist')
5 loops, best of 3: 3.4 s per loop

For a comparison

sage: timeit('x1 in mylist')
625 loops, best of 3: 473 ns per loop

Reason for this huge discrepancy stems from the fact that except for last example, in all previous cases maxima is called to check the equality.

See this thread for more:

 http://groups.google.com/group/sage-devel/browse_thread/thread/d2275cb5b3d63317

We should have a symbolic Kronecker delta in Sage.

Also, current implementation of signum (sgn) function returns wrong answer for symbolic input.

sage: sgn(x)
1
sage: sgn(-x)
1

So we should make sgn() symbolic aware. Given, implementation of these functions in new symbolics should be very similar to the existing generalized function Dirac delta and Heaviside, I am putting them together here.

Also, ticket #777 should be closed down as Sign is already in Sage and this ticket will further enhance it.

Patch:

Apart from implementing these two symbolic functions, attached patch slightly speeds up three other generalized functions by avoiding default __call__ method of PrimitiveFunction?. These functions take explicit value either 0,-1,1 so those checks are not needed.

Timing before the patches:

sage: timeit('dirac_delta(1.0)')
625 loops, best of 3: 179 µs per loop
sage: timeit('unit_step(1.0)')
625 loops, best of 3: 345 µs per loop
sage: timeit('heaviside(1.0)')
625 loops, best of 3: 344 µs per loop

Timing after the patches:

sage: timeit('dirac_delta(1.0)')
625 loops, best of 3: 159 µs per loop
sage: timeit('heaviside(1.0)')
625 loops, best of 3: 324 µs per loop
sage: timeit('unit_step(1.0)')
625 loops, best of 3: 323 µs per loop

Also, it does slight re-arrangements of references.

Comments welcome!

From a Maxima FAQ:

(%i1) load(fourier_elim)$

(%i2) fourier_elim([abs(x - abs(5-x)) < 1],[x]);
(%o2)                          [2<x,x<3]

(%i3) fourier_elim([x + y < 1, x - y > 9],[x,y]);
(%o3)                     [y+9<x,x<1-y,y<-4]

(%i4) fourier_elim([max(-x,x) < 7 * x + 1],[x]);
(%o4)                           [-1/8<x]

From pre-release codebase:

 (%i79) to_poly_solve((x-1)*(x-6) < 0,x);
 (%o79) %union([1 < x,x < 6])

 (%i80) to_poly_solve(min(x,1) < max(-5,x),x);
 (%o80) %union([1 < x],[x < -5])

 (%i81) to_poly_solve(min(x,1) # max(x,4),x);
 (%o81) %union([1 < x,x < 4],[4 < x],[x = 1],[x < 1],[x = 4])

 (%i82)  to_poly_solve((x+1)/(x-1) < 4,x);
 (%o82) %union([5/3 < x],[x < 1])

So it should not be too hard to wrap this, checking input/output for < or > or something. This is one of those basic things people want, but which we assume it's too hard to write from scratch (which it probably is!).

I have implemented the linear time preprocessing, constant-time queries algorithm for the lowest common ancestor (LCA) in the context of the suffix trees for words.

The only thing I'm not very sure about is where to place the bit manipulation functions.

While developing a command called transform_plot3d, that generalized ploting in diferent coordinate systems, Jason Grout suggested to me that such a command would be better implemented within plot3d.

I agreed to that, so I propose an adition to plot3d's syntax: "plot3d(function,var1range,var2range,transformation=None,**kwds)" where transformation is a 4-tuple containing 3 functions of arity 3, and a variable which is to be interpreted as the function to be ploted. Like this (r*cos(fi),r*sin(fi),z,r), so the function will be ploted as r.

Examples can be found in  http://www.sagenb.org/home/pub/1328/.

I've just added a patch.

Let e be a symbolic expression. It may happen that e.operator() has a certain callable attribute, say, foo, that is not a method of Function. In this situation, one would like to use e.foo(), which is supposed to return e.operator().foo(*e.operands()) - apparently this is useful for working with hypergeometric functions.

Example

sage: from sage.symbolic.function import BuiltinFunction
sage: class ExampleBuiltin(BuiltinFunction):
...     def __init__(self):
...         BuiltinFunction.__init__(self, 'ex_func', nargs=0) #arbitrary no of args
...     def some_function_name(self, *args):
...         return len(args)
...
sage: ex_func = ExampleBuiltin()
sage: ex_func
ex_func

We obtain a symbolic expression by calling ex_func:

sage: e = ex_func(x,x+1, x+2)
sage: type(e)
<type 'sage.symbolic.expression.Expression'>

We add a callable and a non-callable attribute to ex_func:

sage: def some_function(slf, *L): print slf,'called with',L
...
sage: ex_func.foo_bar = some_function
sage: ex_func.bar_foo = 4

Now, both the new method and the callable attribute foo_bar of ex_func are available from e, but not the non-callable:

sage: e.some_function_name()
3
sage: e.foo_bar()
ex_func called with (x, x + 1, x + 2)
sage: e.bar_foo
Traceback (most recent call last):
...
AttributeError: <type 'sage.symbolic.expression.Expression'> has no attribute 'bar_foo'

Tab completion and introspection work:

sage: 'foo_bar' in dir(e)     # indirect doctest
True
sage: 'some_function_name' in dir(e)
True
sage: 'bar_foo' in dir(e)
False
sage: import sagenb.misc.support as s
sage: s.completions('e.some', globals(), system='python')
['e.some_function_name']

Problems

When I ran sage -testall, several doctests segfaulted:

        sage -t  -verbose "devel/sage/sage/functions/hyperbolic.py"
        sage -t  -verbose "devel/sage/sage/games/hexad.py"
        sage -t  -verbose "devel/sage/sage/matrix/tests.py"
        sage -t  -verbose "devel/sage/sage/misc/sage_eval.py"
        sage -t  -verbose "devel/sage/sage/plot/animate.py"
        sage -t  -verbose "devel/sage/sage/quadratic_forms/quadratic_form__mass__Conway_Sloane_masses.py"
        sage -t  -verbose "devel/sage/sage/rings/polynomial/polynomial_element.pyx"

I tried (using sage -t -verbose) to find out what exactly fails. When I ran some of these failing examples in an interactive session, no segfault occured. So, is there a nasty side effect?

The torsion subgroup of an elliptic curve appears to be quite broken -- it barfs when trying to coerce in 0,

sage: E = EllipticCurve(1)
sage: T = E.torsion_subgroup()
sage: T(0)
...
...
TypeError: Argument x (= 0) is of wrong type.

further, it returns a mysterious 1 when coercing in a 1

sage: a = T(1); a
1
sage: b = T.gens()[0]-T.gens()[0]; b
(0 : 1 : 0)
sage: a+b
TypeError: unsupported operand parent(s) for '+': 'Abelian group of points on Elliptic Curve defined by y^2 + x*y + y = x^3 - 19*x + 26 over Rational Field' and 'Torsion Subgroup isomorphic to Multiplicative Abelian Group isomorphic to C6 x C2 associated to the Elliptic Curve defined by y^2 + x*y + y = x^3 - 19*x + 26 over Rational Field'

Yet, it's all cool with the original curve.

sage: E(0)
(0 : 1 : 0)
sage: E(1)
...
...
TypeError: v (=(1,)) must have 3 components
sage: 

In #6384, code was introduced to check whether the kernel polynomial provided by the user was valid, by checking that it divides the appropriate division polynomial.

This can be too expensive! I have been working with isogenies of degree 163 over QQ, for which computing the 163-division polynomial takes many hours. So I want to introduce a check parameter to the isogeny construction, default True, so that users (or other code) can switch off this check (when they "know" they are right!).

Kyle Schalm suggests:

 
 
here is a matrix constructor i would like to see:
 
Matrix(M, N, f):
   for i in range(1,M+1):
     for j in range(1,N+1):
       self[i][j] = f(i,j)   # or whatever the syntax is
 
 
i might use it like this:
 
A = Matrix(3, 3, lambda i,j: i+j)
 
i'd do it myself, but i don't have a development environment set up,
and don't wanna do that right now.
 
cheers,
kyle
 

We currently ship two copies of the jquery javascript library:

• jQuery 1.2.6 - New Wave Javascript - $Rev: 5685 $ in devel/sage-main/sage/dsage/web/static/jquery.js
• jQuery 1.2.3 - New Wave Javascript - $Rev: 4663 $ in data/extcode/notebook/javascript/jquery/jquery.js

But we should on ship one copy.

Cheers,

Michael

The gfan SPKG.txt says:

License

• GPL

it does not say which version of the GPL it is.

try it at home:

$ echo 'print "ok"' > 'test file.sage'
$ sage "test file.sage"

It would be great to have a plot_region function which would plot a region where a system of equations/inequalities were true.

Here is an initial version:

def plot_region(funcs, var1_range, var2_range, plot_points=400, **kwds):
    if not isinstance(funcs, (list, tuple)):
        funcs = [funcs]
    hvar, hmin, hmax = var1_range
    vvar, vmin, vmax = var2_range
    funcs = prod([f._fast_float_("%r"%hvar, "%r"%vvar) for f in funcs])
    return contour_plot(funcs, var1_range, var2_range, plot_points=plot_points,**kwds)

This uses an idea from cwitty (to use contour_plot) and the patch from #2768. A screenshot is attached below.

This patch add the option of styling lines, either individually or all at once, and adding contour level labels.

Another one is coming to support this in combination with #2770.

Adds three functions to iterate over prefixes and palindrome prefixes of finite and infinite words.

When dealing with 2d word paths, it is very useful to know their height and their width.

In particular, one can compute a bounding box for a better displaying. The aim of this small ticket is to add those two functionalities.

By the way, while testing it, I noticed a strange behavior:

sage: Paths = WordPaths('abcABC')
sage: p = Paths('acABC')
sage: points = list(p.points())
sage: points
[(0, 0), (1, 0), (1/2, 1/2*sqrt3), (-1/2, 1/2*sqrt3), (-1, 0), (-1/2, -1/2*sqrt3)]
sage: y_coords = map(lambda (_,y):y, points)
sage: y_coords
[0, 0, 1/2*sqrt3, 1/2*sqrt3, 0, -1/2*sqrt3]
sage: max(y_coords)
-1/2*sqrt3

Shouldn't 1/2*sqrt3 be the highest element ? This doesn't make sense.

Editing cells with a dark theme makes the text invisible (white text on a white background).

Instead of having /js, /css, etc, we should serve all static data files out of /data. For now this patch just adds /data using child_data = static.File(DATA), where static.File(path) is defined in twisted. It will serve files with the correct MIME type based on extension.

Eventually we should find all the /js and /css paths and change them to /data

At some point in the future we could even implement caching of all the static files easily by subclassing static.File(path), and making everything in /data cached.

If I add a bunch of graphics primitives to a Graphic object using the Graphic append() method, the __xmax, __xmin, __ymax, __ymin attributes are not updated. Therefore when I try to plot the graphic, nothing shows up. Code for the correct behaviour can be found in the Graphic.__add__() method.

Things are different in notebook and console:

• Because of underline trick, in notebook headings in docstring consists of only underline!

The patch provides automatic indentation for python after colons and same level identation. It works up to four levels of identation.

It was discovered in #8059 , that the parallel build of the Singular 3-1-1-4 packages still breaks in rare cases (many CPU cores, slow hard disk).

There are two patches which should fix this issue upstream:  http://www.singular.uni-kl.de:8002/trac/ticket/250, see

svn diff -r 13112:13110 http://www.singular.uni-kl.de/svn/

sage: eisenstein_series_qexp(10, 15, GF(17))
15 + q + 3*q^2 + 15*q^3 + 7*q^4 + 13*q^5 + 11*q^6 + 11*q^7 + 15*q^8 + 7*q^9 + 5*q^10 + 7*q^11 + 2*q^12 + 12*q^13 + 12*q^14 + O(q^15)

is wrong, whereas

sage: eisenstein_series_qexp(10, 15).change_ring(GF(17))
15 + q + 3*q^2 + 15*q^3 + 7*q^4 + 13*q^5 + 11*q^6 + 11*q^7 + 15*q^8 + 7*q^9 + 5*q^10 + 7*q^11 + 3*q^12 + 14*q^13 + 16*q^14 + O(q^15)

is right. We tracked this down to a change in the polynomials over finite fields constructor when check=False. We'll quickly fix this at the cost of making it slower; better fix will come soon.

David Loeffler ran into this bug:

sage: K.<zeta4> = CyclotomicField(4) 
sage: m = matrix(K, [186]) 
sage: n = matrix(K, [125]) 
sage: m * n 
[-23087] 

(See  http://groups.google.com/group/sage-devel/browse_thread/thread/4f8633d6acf1c4ef# for the full thread.)

The issue is that the bound for what modulus the entries can be computed modulo is off by a factor of 2, because it doesn't take the sign into consideration. (Amusingly, this was basically the same fix as in #4823.)

In matrix2.pyx, there is a doctest (line 6406):

            sage: all(imag(e) < 1.1e-15 for e in eigs)

We should replace "imag(e)" by "abs(imag(e))".

The attached patch depends on #9760.