compute a univariate polynomial
UnivariatePolynomial(v, J, X, characteristic=p)
a list or set of polynomials or a PolynomialIdeal
(optional) list or set of variables of the system
The UnivariatePolynomial command returns a univariate polynomial in v of least degree in the ideal generated by J. If no such polynomial exists then zero is returned. A zero-dimensional ideal contains a univariate polynomial for every variable.
An optional third argument X specifies the variables of the system. By default every indeterminate not appearing in a RootOf or radical is considered a variable when J is a list or a set. If J is a PolynomialIdeal a default set of variables is stored as part of the data structure. See PolynomialIdeals[IdealInfo].
The optional argument characteristic=p specifies the ring characteristic when J is a list or a set. This option has no effect when J is a PolynomialIdeal, however you can specify J mod p as the first argument to obtain the desired result.
Note that the univpoly command is deprecated. It may not be supported in a future Maple release.
F ≔ x3−3⁢x⁢y,x2⁢y−2⁢y2+x
The ideal below has infinitely many solutions, yet a univariate polynomial in x exists.
J ≔ x4+z⁢y3,x⁢z⁢y3+1,z2⁢y6−x3
A univariate polynomial in y does not exist, however we can treat z as a parameter to obtain a univariate polynomial in y with coefficients in Q(z).
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