I would like to convert a multi-variable polynomial with coefficients in a finite number field si with a primitive element into a polynomial whose variable is the primitive element. A simple example: say F=Q[sqrt(2)] is the number field and P(x,y,z)=sqrt(2)*x + 2*y +sqrt(2)*y +t is a polynomial of K[x,y,z,t]. I want to convert P(x,y,z,t) to P(sqrt(2))=(x+y)*sqrt(2) + 2*y +t. This surely standard stuff but I can't find a way to do this.
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