up previous next
PolyAlgebraHom

homomorphism of polynomial algebras

Syntax
PolyAlgebraHom(Domain: RING, Codomain: RING, images: LIST): RINGHOM

Description
This function creates the homomorphism of (polynomial) algebras from R to S with the same ring of coefficients. This is uniquely defined by the images of the indeterminates of R which are specified by the entries of images .

This is a cleaner mathematical implementation of the function image [OBSOLESCENT] in CoCoA-4.

Example
/**/  use R ::= QQ[x,y,z];
/**/  S ::= QQ[x[1..3]];
/**/  phi := PolyAlgebraHom(R, S, indets(S));
/**/  phi(x^2-y);
x[1]^2 -x[2]

/**/  S ::= QQ[a];
/**/  phi := PolyAlgebraHom(R, S, [RingElem(S,"a"),1,0]);
/**/  phi(x^2-y);
a^2 -1

/**/  phi := PolyAlgebraHom(R, QQ, [2,1,0]); --> evaluate at [2,1,0]
/**/  phi(x^2-y);
3

See Also