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 Elim

eliminate variables
 Syntax
 ``` Elim(X:INDETS, M:IDEAL):IDEAL Elim(X:INDETS, M:MODULE):MODULE where X is an indeterminate or a list of indeterminates. ```

 Description
This function returns the ideal or module obtained by eliminating the indeterminates X from M. The coefficient ring needs to be a field.

As opposed to this function, there is also the modifier, Elim, used when constructing a ring (see Orderings and Predefined Term-Orderings).

 Example
 ``` Use R ::= QQ[t,x,y,z]; Set Indentation; Elim(t, Ideal(t^15+t^6+t-x,t^5-y,t^3-z)); Ideal( -z^5 + y^3, -y^4 - yz^2 + xy - z^2, -xy^3z - y^2z^3 - xz^3 + x^2z - y^2 - y, -y^2z^4 - x^2y^3 - xy^2z^2 - yz^4 - x^2z^2 + x^3 - y^2z - 2yz - z, -y^3z^3 + xz^3 - y^3 - y^2) ------------------------------- Use R ::= QQ[t,s,x,y,z,w]; t..x; [t, s, x] ------------------------------- Elim(t..x, Ideal(t-x^2zw,x^2-t,y^2t-w)); -- Note the use of t..x. Ideal(-zw^2 + w) ------------------------------- Use R ::= QQ[t[1..2],x[1..4]]; I := Ideal(x[1]-t[1]^4,x[2]-t[1]^2t[2],x[3]-t[1]t[2]^3,x[4]-t[2]^4); t; [t[1], t[2]] ------------------------------- Elim(t, I); -- Note the use t. Ideal(x[3]^4 - x[1]x[4]^3, x[2]^4 - x[1]^2x[4]) ------------------------------- ```