Homogenized(X:INDET,E:T):T
where T is of type IDEAL or POLY, or T is a LIST recursively
constructed of types IDEAL, POLY, and LIST.
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This function returns the homogenization of E with respect to the
indeterminate X, which must have weight 1. Note that in the case
where E is an ideal, 'Homogenized' returns the ideal generated by the
homogenizations of all the elements of E, not just the homogenization
of the generators of E (see the example, below). The coefficient ring
must be a field for this function to work reliably.
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Use R ::= Q[x,y,z,w];
Homogenized(w,x^3-y);
x^3 - yw^2
-------------------------------
Homogenized(w,[x^3-y,x^4-z]);
[x^3 - yw^2, x^4 - zw^3]
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I := Ideal(x^3-y,x^4-z);
Homogenized(w,I); -- don't just get the homogenizations of
-- the generators of I
Ideal(x^3 - yw^2, -xy + zw, x^2z - y^2w, y^3 - xz^2)
-------------------------------
Homogenized(w,[[I,y-z^2],z-y^4]);
[[Ideal(x^3 - yw^2, -xy + zw, x^2z - y^2w, y^3 - xz^2), -z^2 + yw], -y^4 + zw^3]
-------------------------------
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