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 elim

eliminate variables

 Syntax
 ```elim(X: RINGELEM, M: IDEAL): IDEAL elim(L: LIST, M: IDEAL): IDEAL elim(X: RINGELEM, M: MODULE): MODULE elim(L: LIST, M: MODULE): MODULE```

 Description
This function returns the ideal or module obtained by eliminating the indeterminate X , or all indeterminates in L , 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).

 Example
 ```/**/ Use R ::= QQ[t,x,y,z]; /**/ E := elim(t, ideal(t^15+t^6+t-x, t^5-y, t^3-z)); /**/ indent(E); ideal( -z^5 +y^3, -y^4 -y*z^2 +x*y -z^2, -x*y^3*z -y^2*z^3 -x*z^3 +x^2*z -y^2 -y, -y^2*z^4 -x^2*y^3 -x*y^2*z^2 -y*z^4 -x^2*z^2 +x^3 -y^2*z -2*y*z -z, y^3*z^3 -x*z^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^2*z*w, x^2-t, y^2*t-w)); -- Note the use of t..x. ideal(-z*w^2 + w) /**/ Use R ::= QQ[t[1..2], x[1..4]]; /**/ I := ideal(x[1]-t[1]^4, x[2]-t[1]^2*t[2], x[3]-t[1]*t[2]^3, x[4]-t[2]^4); /**/ elim(indets(R,"t"), I); ideal(x[2]^4 -x[1]^2*x[4], -x[3]^4 +x[1]*x[4]^3) ```