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 Homogenized

homogenize with respect to an indeterminate
 Syntax
 ``` 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. ```

 Description
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.

 Example
 ``` Use R ::= QQ[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] ------------------------------- I := Ideal(x^3-y, x^4-z); -- same as Homogenized5(w, I); Homogenized([w], I); 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] ------------------------------- ```