#17703: use giac for symbolic multivar gcd
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Reporter: rws | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.3
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Changes (by rws):
* cc: burcin (added)
* milestone: sage-6.5 => sage-7.3
Comment:
A development version of Pynac using Giac is twice as fast as Singular
(used from ring polynomials for the example of #10284:
{{{
sage: u = var('u')
sage: v = var('v')
sage: w = var('w')
sage: x = var('x')
sage: y = var('y')
sage: z = var('z')
sage: e = 792*z^8*w^4*x^3*y^4*u^7 + 24*z^4*w^4*x^2*y^3*u^4 + \
264*z^8*w^3*x^2*y^7*u^5 + 198*z^4*w^5*x^5*y*u^6 + 110*z^2*w^3*x^5*y^4*u^6
\
- 120*z^8*w*x^4*u^6 - 480*z^5*w*x^4*y^6*u^8 - 720*z^7*x^3*y^3*u^7 + \
165*z^4*w^2*x^4*y*u^5 + 450*z^8*w^6*x^2*y*u^8 + 40*z^2*w^3*x^3*y^3*u^6 - \
288*z^7*w^2*x^3*y^6*u^6 + 250*z^6*w^4*x^2*y^4*u^8 + \
576*z^7*w^7*x^2*y^4*u^8 - 80*z^6*w^2*x^5*y^3*u^7 - 144*z^8*w^4*x^5*u^7 +
\
120*z^4*w*x^2*y^6*u^6 + 320*z^5*w^5*x^2*y^7*u^8 + 192*z^7*w^6*x*y^7*u^6 -
\
12*z^4*w^3*x^3*y^5*u^6 - 36*z^4*w^4*x^4*y^2*u^8 + 72*z^4*w^5*x^3*u^6 - \
20*z^2*w^2*x^4*y^5*u^8 + 660*z^8*w*x^2*y^4*u^6 + 66*z^4*w^4*x^4*y^4*u^4 +
\
440*z^6*w^2*x^3*y^7*u^7 - 30*z^4*w*x^3*y^2*u^7 - 48*z^8*w^3*x^4*y^3*u^5 +
\
72*z^6*w^2*x*y^6*u^4 - 864*z^7*w^3*x^4*y^3*u^8 + 480*z^7*w^4*x*y^4*u^7 + \
60*z^4*w^2*x^2*u^5 + 375*z^8*w^3*x*y*u^7 + 150*z^8*w^5*x*y^4*u^6 + \
180*z^6*x*y^3*u^5 + 216*z^6*w^3*x^2*y^3*u^6;
sage: d = e.diff(x)
sage: gcd(d,e)
u^4*z^2
sage: E = e.polynomial(QQ)
sage: D= e.diff(x)
sage: gcd(D,E)
u^4*z^2
sage: %timeit _=gcd(d,e)
100 loops, best of 3: 1.48 ms per loop
sage: %timeit _=gcd(d,e)
1000 loops, best of 3: 1.5 ms per loop
sage: %timeit _=gcd(D,E)
100 loops, best of 3: 3.06 ms per loop
sage: %timeit _=gcd(D,E)
100 loops, best of 3: 3.06 ms per loop
sage: %timeit _=gcd(D,E)
100 loops, best of 3: 3.05 ms per loop
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/17703#comment:2>
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