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4.8.8 Temporary Term-Orderings
For computations which temporarily require a different term-ordering (for example, to eliminate variables or to homogenize ideals), the system automatically changes the term-ordering to a more suitable one, performs the computation, and then restores the initial term-ordering and gives its output with respect to this one. In this way the user never has to deal with temporary changes.

  Use R ::= QQ[t,x,y,z];
  I := Ideal(t-x,y-z,t-z);
  Elim(y, I);
Ideal(t - z, -x + z)