Hi,
at the scipy 09 conference I am going to compare Sage and sympy
approaches to factoring (and timings) and longer term approaches, so I
have a few questions about it, so that I understand things correctly.
If I do:
sage: var("x y z")
(x, y, z)
sage: a = (x+y+z)**20
sage: b = a.expand()
sage: %time c = factor(b)
CPU times: user 0.14 s, sys: 0.00 s, total: 0.15 s
Wall time: 0.15 s
1) it uses pari, right?
2) can it be made faster (=virtually instant) using singular? I don't
mean to call singular manually like this:
sage: R.<x,y,z> = QQ[]
sage: a = (x+y+z)**20
sage: time factor(a)
CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.01 s
(x + y + z)^20
it has to be done fully automatically below the hood.
3) if so, will it only work for polynomials, or for any symbolic expressions?
If I do:
sage: var("x y z")
(x, y, z)
sage: a = (x+y+sin(z))**20
sage: b = a.expand()
sage: %time c = factor(b)
CPU times: user 0.15 s, sys: 0.01 s, total: 0.16 s
Wall time: 0.59 s
4) it uses maxima, right? That's why it is slower, right?
5) can it be made faster using singular? I guess by substituting some
dummy symbol for sin(z) and substituting back.
E.g. in the long term, once everything is polished, all factoring will
be more or less as fast as singular? Or will there be some hidden cost
in converting the expressions back and forth between symbolics (pynac)
and singular.
Thanks,
Ondrej
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