On Feb 15, 9:50 am, Simon King <simon.k...@uni-jena.de> wrote:
> Hi!
>
> Working on #10771 (making gcd and lcm work nicer), I got trouble with
> the multiplication of symbolic expressions. The problem seems to boil
> down to examples of the following type:
>
> Without the patch
> sage: x = -sqrt(2)-1/5*I
> sage: x*x
> 1/25*(5*sqrt(2) + I)^2
>
> With the patch
> sage: x = -sqrt(2)-1/5*I
> sage: x*x
> 1/25*(-5*sqrt(2) - I)^2
>
> In another multiplication example, the patch even results in a
> segmentation fault:
> sage: F(x) = 1/sqrt(2*pi*1^2)*exp(-1/(2*1^2)*(x-0)^2)
> sage: G(x) = 1/sqrt(2*pi*n(1)^2)*exp(-1/(2*n(1)^2)*(x-n(0))^2)
> sage: (F-G)**2
> /mnt/local/king/SAGE/sage-4.6.2.alpha4/local/bin/sage-sage: Zeile 300:
> 19386 Speicherzugriffsfehler sage-ipython "$@" -i
>
> The first example seems to indicate that my gcd/lcm patch changes a
> sign when pulling a common factor out of a list of symbolic
> coefficients. The second example is totally obscure to me.
>
> I could trac down the code up to a call to new_Expression_from_GEx.
> But I have not been able to locate the definition of that function.
>
> To symbolists:
> Please tell me whether (and how) gcd or lcm occur in
> new_Expression_from_GEx, or at least show me the code!
This is just the standard thing that makes a Ginac/Pynac expression.
I can never remember where/if this is defined, either. At any rate,
that is not where the problem is - it must be in how it finds a
canonical form of the expression.
> What gcd/lcm would be computed in the two examples above, and what is
> the expected result?
The post-Pynac symbolics are a little weird. Burcin explained it to
me this way:
1) Sage creates a symbolic object.
2) Pynac/Ginac makes it.
3) But we don't have Ginac's underlying engine for numbers any more
(CLN), so it uses Sage itself for certain things.
Hence in symbolic/pynac.pyx we have the following:
#################################################################
# GCD
#################################################################
import sage.rings.arith
cdef public object py_gcd(object n, object k) except +:
if PY_TYPE_CHECK(n, Integer) and PY_TYPE_CHECK(k, Integer):
if mpz_cmp_si((<Integer>n).value,1) == 0:
return n
elif mpz_cmp_si((<Integer>k).value,1) == 0:
return k
return n.gcd(k)
if PY_TYPE_CHECK_EXACT(n, Rational) and PY_TYPE_CHECK_EXACT(k,
Rational):
return n.content(k)
try:
return sage.rings.arith.gcd(n,k)
except (TypeError, ValueError, AttributeError):
# some strange meaning in case of weird things with no usual
lcm.
return 1
So this is what Pynac actually does to get a gcd, I think. If not,
then the following remark on the Pynac to-do webpage is relevant
(originally from William):
Maybe change SAGE's Ginac to make a call to a cython gcd function,
then use
singular, since singular's gcd over QQ is much better than ginac's, I
think,
and ginac *only* does GCD over QQ. Actually, just make everything in
normal.cpp
be implemented via Singular, probably...
I hope this helps you track it down. I suspect you are right about
what is going on.
- kcrisman
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