No-expand() Poly construction per default (step 1)

[skirpichev]

• fix tests
• test coverage
• add docs
• mention closed/relevant issues
  • Cleanup polynomial initialization functions from polyutils, optimize like poly() #992
  • degree((x+1)**10000) takes too long sympy/sympy#6322
  • degree(f, var) is much slower than Poly(f).degree(var), (27x with this particular poly) sympy/sympy#12998
  • with gens, time taken for sqf increases orders of magnitude faster than factor as input size increases sympy/sympy#13029
  • cancel does not return expanded form sympy/sympy#12531
• remove poly() (use instead parrallel_poly_from_expr)
• is_polynomial right for wrong reasons (and sometimes wrong) sympy/sympy#22583

[skirpichev]

@user234683, I see no reproducible example in the sympy/sympy#12998. Could you provide one?

I suspect, that this SymPy's issue is fixed by the current PR in the Diofant, but want to be sure.

[user234683]

This appears to be the polynomial I was using at the time:
f = 6*(-2*e*(15*e - 13)*(c5**4 + 4*c5**3*c6 + 4*c5**3*c7 + 4*c5**3*c8 + 4*c5**3*c9 + 6*c5**2*c6**2 + 12*c5**2*c6*c7 + 12*c5**2*c6*c8 + 12*c5**2*c6*c9 + 6*c5**2*c7**2 + 12*c5**2*c7*c8 + 12*c5**2*c7*c9 + 6*c5**2*c8**2 + 12*c5**2*c8*c9 + 6*c5**2*c9**2 + 4*c5*c6**3 + 12*c5*c6**2*c7 + 12*c5*c6**2*c8 + 12*c5*c6**2*c9 + 12*c5*c6*c7**2 + 24*c5*c6*c7*c8 + 24*c5*c6*c7*c9 + 12*c5*c6*c8**2 + 24*c5*c6*c8*c9 + 12*c5*c6*c9**2 + 4*c5*c7**3 + 12*c5*c7**2*c8 + 12*c5*c7**2*c9 + 12*c5*c7*c8**2 + 24*c5*c7*c8*c9 + 12*c5*c7*c9**2 + 4*c5*c8**3 + 12*c5*c8**2*c9 + 12*c5*c8*c9**2 + 4*c5*c9**3 + c6**4 + 4*c6**3*c7 + 4*c6**3*c8 + 4*c6**3*c9 + 6*c6**2*c7**2 + 12*c6**2*c7*c8 + 12*c6**2*c7*c9 + 6*c6**2*c8**2 + 12*c6**2*c8*c9 + 6*c6**2*c9**2 + 4*c6*c7**3 + 12*c6*c7**2*c8 + 12*c6*c7**2*c9 + 12*c6*c7*c8**2 + 24*c6*c7*c8*c9 + 12*c6*c7*c9**2 + 4*c6*c8**3 + 12*c6*c8**2*c9 + 12*c6*c8*c9**2 + 4*c6*c9**3 + c7**4 + 4*c7**3*c8 + 4*c7**3*c9 + 6*c7**2*c8**2 + 12*c7**2*c8*c9 + 6*c7**2*c9**2 + 4*c7*c8**3 + 12*c7*c8**2*c9 + 12*c7*c8*c9**2 + 4*c7*c9**3 + c8**4 + 4*c8**3*c9 + 6*c8**2*c9**2 + 4*c8*c9**3 + c9**4) + (e + 1)**2*(-c0*c5**2*c8 - 4*c0*c5**2*c9 + 2*c0*c5*c6*c7 + 4*c0*c5*c6*c8 + 4*c0*c5*c6*c9 + 4*c0*c5*c7**2 + 16*c0*c5*c7*c8 + 24*c0*c5*c7*c9 + 16*c0*c5*c8**2 + 50*c0*c5*c8*c9 + 40*c0*c5*c9**2 - c0*c6**3 - 4*c0*c6**2*c7 - 4*c0*c6**2*c8 - 4*c0*c6**2*c9 - 6*c0*c6*c7**2 - 12*c0*c6*c7*c8 - 10*c0*c6*c7*c9 - 5*c0*c6*c8**2 - 4*c0*c6*c8*c9 + 4*c0*c6*c9**2 - 4*c0*c7**3 - 15*c0*c7**2*c8 - 16*c0*c7**2*c9 - 20*c0*c7*c8**2 - 44*c0*c7*c8*c9 - 24*c0*c7*c9**2 - 10*c0*c8**3 - 36*c0*c8**2*c9 - 45*c0*c8*c9**2 - 20*c0*c9**3 - c1*c5**2*c7 - 4*c1*c5**2*c8 - 10*c1*c5**2*c9 + c1*c5*c6**2 + 4*c1*c5*c6*c7 + 4*c1*c5*c6*c8 + 6*c1*c5*c7**2 + 20*c1*c5*c7*c8 + 26*c1*c5*c7*c9 + 19*c1*c5*c8**2 + 56*c1*c5*c8*c9 + 44*c1*c5*c9**2 - c1*c6**2*c9 + 2*c1*c6*c7*c8 + 4*c1*c6*c7*c9 + 4*c1*c6*c8**2 + 16*c1*c6*c8*c9 + 16*c1*c6*c9**2 - c1*c7**3 - 4*c1*c7**2*c8 - 4*c1*c7**2*c9 - 6*c1*c7*c8**2 - 12*c1*c7*c8*c9 - 5*c1*c7*c9**2 - 4*c1*c8**3 - 15*c1*c8**2*c9 - 20*c1*c8*c9**2 - 10*c1*c9**3 - c2*c5**2*c6 - 4*c2*c5**2*c7 - 10*c2*c5**2*c8 - 20*c2*c5**2*c9 - 4*c2*c5*c6*c8 - 14*c2*c5*c6*c9 + 4*c2*c5*c7**2 + 14*c2*c5*c7*c8 + 16*c2*c5*c7*c9 + 16*c2*c5*c8**2 + 48*c2*c5*c8*c9 + 40*c2*c5*c9**2 - c2*c6**2*c8 - 4*c2*c6**2*c9 + c2*c6*c7**2 + 4*c2*c6*c7*c8 + 4*c2*c6*c7*c9 + 6*c2*c6*c8**2 + 20*c2*c6*c8*c9 + 19*c2*c6*c9**2 + 2*c2*c7*c8*c9 + 4*c2*c7*c9**2 - c2*c8**3 - 4*c2*c8**2*c9 - 6*c2*c8*c9**2 - 4*c2*c9**3 + c3*c5**3 - 6*c3*c5**2*c7 - 16*c3*c5**2*c8 - 31*c3*c5**2*c9 - 4*c3*c5*c6*c7 - 14*c3*c5*c6*c8 - 32*c3*c5*c6*c9 + c3*c5*c7**2 + 4*c3*c5*c7*c8 + 10*c3*c5*c8**2 + 32*c3*c5*c8*c9 + 31*c3*c5*c9**2 - c3*c6**2*c7 - 4*c3*c6**2*c8 - 10*c3*c6**2*c9 - 4*c3*c6*c7*c9 + 4*c3*c6*c8**2 + 14*c3*c6*c8*c9 + 16*c3*c6*c9**2 - c3*c7**2*c9 + c3*c7*c8**2 + 4*c3*c7*c8*c9 + 6*c3*c7*c9**2 - c3*c9**3 + 4*c4*c5**3 + 6*c4*c5**2*c6 - 4*c4*c5**2*c7 - 19*c4*c5**2*c8 - 40*c4*c5**2*c9 + 4*c4*c5*c6**2 - 2*c4*c5*c6*c7 - 20*c4*c5*c6*c8 - 48*c4*c5*c6*c9 - 4*c4*c5*c7*c8 - 16*c4*c5*c7*c9 + 4*c4*c5*c8**2 + 14*c4*c5*c8*c9 + 20*c4*c5*c9**2 + c4*c6**3 - 6*c4*c6**2*c8 - 16*c4*c6**2*c9 - 4*c4*c6*c7*c8 - 14*c4*c6*c7*c9 + c4*c6*c8**2 + 4*c4*c6*c8*c9 + 10*c4*c6*c9**2 - c4*c7**2*c8 - 4*c4*c7**2*c9 + 4*c4*c7*c9**2 + c4*c8*c9**2))/(e + 1)**2

[skirpichev]

Thank you.

Well, I have these timings on this branch:

In [9]: %timeit degree(f, c5)
996 ms ± 2.91 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

In [10]: %timeit Poly(f).degree(c5)
178 ms ± 860 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

In [11]: %timeit Poly(f, c5).degree(c5)
998 ms ± 11.8 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

In [12]: %timeit degree(f, gen=c5)
179 ms ± 205 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

It seems apparent, that univariate polynomial construction (over variable c5) noticeably slower here (5x). You have reported 27x difference. For f_s = f.subs({e: 1}) is't about 2.2x:

In [18]: %timeit degree(f_s, c5)
105 ms ± 66.3 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

In [19]: %timeit Poly(f_s).degree(c5)
46.1 ms ± 95.4 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

In [20]: %timeit Poly(f_s, c5).degree(c5)
104 ms ± 115 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

In [21]: %timeit degree(f_s, gen=c5)
46.5 ms ± 75.6 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

[user234683]

Oh it appears I had fixed the issue already for degree but not degree_list: sympy/sympy#12999

[skirpichev]

Hmm, I'm not sure if that was a fix. You break function API a little, making it inconsistent with other polynomial functions, while don't fix the real issue: noticeable slowdown of Poly(f, c5) vs Poly(f). C.f. SymPy:

In [4]: %timeit Poly(f)
228 ms ± 2.98 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

In [5]: %timeit Poly(f, c5)
6.9 s ± 117 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

vs the current Diofant (on this branch):

In [3]: %timeit Poly(f)
176 ms ± 502 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)

In [4]: %timeit Poly(f, c5)
979 ms ± 2.17 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

[user234683]

It was a fix for the issue as it pertained to degree rather than Poly, so yes Poly will still have this issue. In fact, the fix was to switch degree from using e.g. Poly(f, c5) to Poly(f) due to the massive speed difference between them which your current pull is fixing.
EDIT: My bad; it seems I was confused and thought this was just a fix for the degree issue in Sympy. I hadn't realized this was a fork. Kudos on the fork, by the way; I looked over it. Hope it catches on.