decide if a given algebraic system is algebraically consistent
IsProper(J, X, characteristic=p)
a list or set of polynomials or a PolynomialIdeal
(optional) a list or set of variables, a ShortMonomialOrder, or a MonomialOrder
The IsProper command decides whether a set of polynomials J with respect to the indeterminates X is algebraically consistent (that is, whether J has at least one solution over the algebraic closure of the coefficient field). This is equivalent to testing whether 1 is a member of the ideal generated by J. The zero ideal is considered proper.
The variables of the system can be specified using an optional second argument X. If X is a ShortMonomialOrder then a Groebner basis of J with respect to X is computed. By default, X is the set of all indeterminates not appearing inside a RootOf command or radical when J is a list or set, or PolynomialIdeals[IdealInfo][Variables](J) if J is an ideal.
The optional argument characteristic=p specifies the ring characteristic when J is a list or set. This option has no effect when J is a PolynomialIdeal or when X is a MonomialOrder.
Note that the is_solvable command is deprecated. It may not be supported in a future Maple release.
F ≔ x2−2⁢x⁢z+5,x⁢y2+y⁢z3,3⁢y2−6⁢z3+1
J ≔ F,x
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