up previous next
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 Term 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)

See Also