Also, in order to prove a system of polynomials to be inconsistent, we can show that its reduced Gröbner basis is 1. [1]
In [13]: groebner(system, unknowns) Out[13]: GroebnerBasis([1], a_1, a_2, a_3, a_4, b_1, b_2, b_3, b_4, domain='ZZ', order='lex') In the problem at hand, we do get the desired result. Thus, we can say that the system is inconsistent. > I'm unsure if solve_poly_system returning None necessarily means that > there are no solutions, as Kshitij suggests. It may be the case, but > it isn't documented, so we would need to check the code to be sure. > The `solve_poly_sys` is limited by the ability of the root finding algorithms. And if no solutions are found, that doesn't necessarily mean that the system is inconsistent. I shouldn't have been so bold to assume this. Thanks for pointing this out. The algorithm we implement in `solve_generic` assumes the system to be zero-dimensional. However, I think we need to refactor the code to reflect that cases where the system is inconsistent or not using the reduced Groebner Basis of the system. Also, wouldn't it be a good idea to check whether the system is zero-dimensional or not before running the algorithm ? [1]: https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis#Solutions_of_a_system_of_algebraic_equations -------------------- Kshitij Saraogi -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/898b5ce2-edcc-44f5-b4a6-9ab1f27fc7fc%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
