homogenize polynomials and ideals
Homogenize(f, h, vars)
polynomial or list or set of polynomials, or a PolynomialIdeal
(optional) list or set of variables
The Homogenize command homogenizes polynomials and polynomial ideals. If f is a polynomial, then a minimal power of h is added to each term so that all resulting terms have the same total degree. The variables of f can be specified explicitly by an optional third argument vars. Homogenize also maps onto lists and sets of polynomials automatically.
If the first argument f is a PolynomialIdeal, then Homogenize constructs the ideal generated by all homogenizations of polynomials in f. This is done by homogenizing a total degree Groebner basis for f.
f ≔ x5+x⁢y2+y4+1
It does not suffice to simply homogenize the generators of an ideal. In the example below x−y is in the ideal <F>, and since the polynomial is homogeneous it should be in the homogenization of <F> as well.
F ≔ x2−1,x⁢y−1
Fh ≔ Homogenize⁡F,h
Froberg, R. An Introduction to Grobner Bases. West Sussex: Wiley & Sons, 1997.
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