Comment #3 on issue 2033 by nicolas.pourcelot: solve should be able to
handle rational function systems
http://code.google.com/p/sympy/issues/detail?id=2033
That's already done in 1694 branch, since together() is used, and then
equation is solved for numerator.
However, in smichr/1694, both systems now fail:
In [2]: solve([r - x**2 - y**2, tan(t) - y/x], [x, y])
/home/nicolas/Programmation/sympy/sympy/solvers/solvers.py in solve(f,
*symbols, **flags)
421 else:
422
--> 423 syms, soln = solve_poly_system(polys, **{'simplfiied':
False})
424 assert list(syms) == symbols
425
/home/nicolas/Programmation/sympy/sympy/solvers/polysys.py in
solve_poly_system(system, *gens, **flags)
118 gave_gens = gens
119
--> 120 solutions = solve_reduced_system(system, gens, entry=True)
121
122 if solutions is None:
/home/nicolas/Programmation/sympy/sympy/solvers/polysys.py in
solve_reduced_system(system, gens, entry)
62 def solve_reduced_system(system, gens, entry=False):
63 """Recursively solves reduced polynomial systems. """
---> 64 basis = groebner(system, gens, polys=True)
65
66 if len(basis) == 1 and basis[0].is_ground:
/home/nicolas/Programmation/sympy/sympy/polys/polytools.pyc in groebner(F,
*gens, **args)
2373 F[i] = sdp_from_dict(f.rep.to_dict(), order)
2374
-> 2375 G = sdp_groebner(F, lev, order, dom)
2376
2377 G = [ Poly(DMP(dict(g), dom, lev), *gens) for g in G ]
/home/nicolas/Programmation/sympy/sympy/polys/groebnertools.pyc in
sdp_groebner(F, u, O, K)
620
621 p = sdp_mul_term(p, (monomial_div(M, p_LM), K.quo(K.one,
sdp_LC(p, K))), u, O, K)
--> 622 q = sdp_mul_term(q, (monomial_div(M, q_LM), K.quo(K.one,
sdp_LC(q, K))), u, O, K)
623
624 h = normal(sdp_sub(p, q, u, O, K), G)
/home/nicolas/Programmation/sympy/sympy/polys/algebratools.pyc in quo(self,
a, b)
462 """Quotient of `a` and `b`, implies `__floordiv__`. """
463 if a % b:
--> 464 raise ExactQuotientFailed('%s does not divide %s
in %s' % (b, a, self))
465 else:
466 return a // b
ExactQuotientFailed: DMP([[1, 0]], ZZ) does not divide DMP([[1]], ZZ) in
ZZ[_r,tan(_t)]
In [3]: solve([r - x**2 - y**2, tan(t) - y/x], [x, y])
...
ExactQuotientFailed: DMP([[1, 0]], ZZ) does not divide DMP([[1]], ZZ) in
ZZ[_r,tan(_t)]
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