Le mardi 21 décembre 2021 à 16:41:06 UTC+1, smi...@gmail.com a écrit :
> Are they using the same versions of SymPy?
Irrelevant : Sage's solution uses Sage's default (i. e. Maxima's) solver.
BTW, Sage 9.5.beta8 has sympy 1.9
>
> e1 is quadratic only if f and e2 is linear in g and quadratic in f...it is
> a pretty simple system but there are lots of extraneous symbols. Even
> paring down the symbols to the system `(F1*(F2 + F3*f + f**2), G3*(G4 +
> G6*f**2 + G7*g + f*(G1 + G5*g - g))` takes a long time to solve and
> simplify.
>
That’s my point… BTW : with check=False, solving with Sympy’s solver is
about as fast as with Maxima’s solver ; checking is slower, simplifying is
extremely slow :
>>> from sympy import symbols, solve
>>> from time import time as stime
>>> f, q, r, h, i, g = map(symbols, 'fqrhig')
>>> e1 = -4*f**2*q - 5*f**2*r - 5*f*r + 4*q**2 + 3*q*r
>>> e2 = -4*f**2*h*q - 4*f**2*i*q - 8*f*g*q - 10*f*g*r - 8*f*h*q - 20*f*h*r -
>>> 10*f*i*r + 8*f*q**2/5 - 5*g*r + 4*h*q**2 - 5*h*r + 4*i*q**2 + 4*q**2/5 +
>>> 10*q*r + 5*r**2
>>> t0 = stime() ; Sol = solve([e1, e2], [f, g], check=False, dict=True) ; t1 =
>>> stime() ; print(t1 - t0)
0.6349234580993652
>>> t0 = stime() ; Chk = [[e.subs(s).simplify() for e in (e1, e2)] for s in
>>> Sol] ; t1 = stime() ; print (t1 - t0)
64.00839900970459
>>> Chk
[[0, 0], [0, 0]]
>>> t0 = stime() ; SSol = [{u:s[u].simplify() for u in s.keys()} for s in Sol]
>>> ; t1 = stime() ; print(t1 - t0)
1.9784221649169922
>>> SSol
[{f: -(5*r + sqrt(64*q**3 + 128*q**2*r + 60*q*r**2 + 25*r**2))/(8*q + 10*r), g:
(-(4*q + 5*r)**2*sqrt(64*q**3 + 128*q**2*r + 60*q*r**2 + 25*r**2)*(160*h*q**3*r
+ 200*h*q**2*r**2 + 250*h*q*r**2 + 625*h*r**3 + 160*i*q**3*r + 200*i*q**2*r**2
+ 250*i*q*r**2 + 625*i*r**3 + 64*q**4 + 880*q**3*r + 2400*q**2*r**2 +
2250*q*r**3 + 625*r**4) + (-80*h*q**2 - 250*h*q*r - 250*h*r**2 - 50*i*q*r -
125*i*r**2 + 16*q**3 + 20*q**2*r)*(1024*q**5 + 4608*q**4*r + 7680*q**3*r**2 +
5600*q**2*r**3 + 400*q**2*r**2 + 1500*q*r**4 + 1000*q*r**3 + 625*r**4))/(5*(4*q
+ 5*r)**2*(1024*q**5 + 4608*q**4*r + 7680*q**3*r**2 + 5600*q**2*r**3 +
400*q**2*r**2 + 1500*q*r**4 + 1000*q*r**3 + 625*r**4))}, {f: (-5*r +
sqrt(64*q**3 + 128*q**2*r + 60*q*r**2 + 25*r**2))/(2*(4*q + 5*r)), g: ((4*q +
5*r)**2*sqrt(64*q**3 + 128*q**2*r + 60*q*r**2 + 25*r**2)*(160*h*q**3*r +
200*h*q**2*r**2 + 250*h*q*r**2 + 625*h*r**3 + 160*i*q**3*r + 200*i*q**2*r**2 +
250*i*q*r**2 + 625*i*r**3 + 64*q**4 + 880*q**3*r + 2400*q**2*r**2 + 2250*q*r**3
+ 625*r**4) + (-80*h*q**2 - 250*h*q*r - 250*h*r**2 - 50*i*q*r - 125*i*r**2 +
16*q**3 + 20*q**2*r)*(1024*q**5 + 4608*q**4*r + 7680*q**3*r**2 + 5600*q**2*r**3
+ 400*q**2*r**2 + 1500*q*r**4 + 1000*q*r**3 + 625*r**4))/(5*(4*q +
5*r)**2*(1024*q**5 + 4608*q**4*r + 7680*q**3*r**2 + 5600*q**2*r**3 +
400*q**2*r**2 + 1500*q*r**4 + 1000*q*r**3 + 625*r**4))}]
HTH,
/c
> On Tuesday, December 21, 2021 at 4:25:36 AM UTC-6 emanuel.c...@gmail.com
> wrote:
>
>> After :
>>
>> ```
>> from sympy import symbols, solve
>> f, q, r, h, i, g = map(symbols, 'fqrhig')
>> e1 = -4*f**2*q - 5*f**2*r - 5*f*r + 4*q**2 + 3*q*r
>> e2 = -4*f**2*h*q - 4*f**2*i*q - 8*f*g*q - 10*f*g*r - 8*f*h*q - 20*f*h*r -
>> 10*f*i*r + 8*f*q**2/5 - 5*g*r + 4*h*q**2 - 5*h*r + 4*i*q**2 + 4*q**2/5 +
>> 10*q*r + 5*r**2
>> ```
>> trying `solve([e1, e2], [f, g])` never returns.
>>
>> FWIW, in Sage, with equivalent definitions :
>>
>> ```
>> sage: %time solve([e1, e2], [f, g], solution_dict=True)
>> CPU times: user 935 ms, sys: 12.1 ms, total: 947 ms
>> Wall time: 671 ms
>> [{f: -1/2*(5*r + sqrt(64*q^3 + 128*q^2*r + 5*(12*q + 5)*r^2))/(4*q + 5*r),
>> g: -1/5*(5120*h*q^5 - 1024*q^6 + 625*(12*(2*h + i)*q + 10*h + 5*i)*r^4
>> + 50*(10*(94*h + 38*i - 1)*q^2 - 24*q^3 + 25*(5*h + i)*q)*r^3 +
>> 80*(5*(132*h + 36*i - 1)*q^3 - 44*q^4 + 25*h*q^2)*r^2 + 128*(5*(41*h +
>> 5*i)*q^4 - 26*q^5)*r + (80*(2*h + 2*i + 11)*q^3*r + 64*q^4 + 125*(5*h + 5*i
>> + 18*q)*r^3 + 625*r^4 + 50*(4*(h + i + 12)*q^2 + 5*(h +
>> i)*q)*r^2)*sqrt(64*q^3 + 128*q^2*r + 5*(12*q + 5)*r^2))/(1024*q^5 +
>> 4608*q^4*r + 125*(12*q + 5)*r^4 + 200*(28*q^2 + 5*q)*r^3 + 80*(96*q^3 +
>> 5*q^2)*r^2)},
>> {f: -1/2*(5*r - sqrt(64*q^3 + 128*q^2*r + 5*(12*q + 5)*r^2))/(4*q + 5*r),
>> g: -1/5*(5120*h*q^5 - 1024*q^6 + 625*(12*(2*h + i)*q + 10*h + 5*i)*r^4
>> + 50*(10*(94*h + 38*i - 1)*q^2 - 24*q^3 + 25*(5*h + i)*q)*r^3 +
>> 80*(5*(132*h + 36*i - 1)*q^3 - 44*q^4 + 25*h*q^2)*r^2 + 128*(5*(41*h +
>> 5*i)*q^4 - 26*q^5)*r - (80*(2*h + 2*i + 11)*q^3*r + 64*q^4 + 125*(5*h + 5*i
>> + 18*q)*r^3 + 625*r^4 + 50*(4*(h + i + 12)*q^2 + 5*(h +
>> i)*q)*r^2)*sqrt(64*q^3 + 128*q^2*r + 5*(12*q + 5)*r^2))/(1024*q^5 +
>> 4608*q^4*r + 125*(12*q + 5)*r^4 + 200*(28*q^2 + 5*q)*r^3 + 80*(96*q^3 +
>> 5*q^2)*r^2)}]
>> ```
>>
>> WTF ?
>>
>>
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