up previous next
Tutorial-11: homomorphisms

Tutorial-11: ring homomorphisms


Tutorial-11 for CoCoA-5

CoCoA-5 lets you create ring homomorphisms; these are useful for various purposes such as "moving" a value from one ring to another.

A homomorphism from a polynomial ring must state what the images of the indeterminates are; and, if the homomorphism is not an algebra homomorphism, how the coefficient ring is mapped.

/**/ P1 ::= QQ[x,y];   // polys in x,y with coefficients in QQ
/**/ P2 ::= QQ[a,b];   // polys in a,b with coefficients in ZZ/(2)
/**/ use P2; IndetImages := [a^2, b^3];
/**/ phi := PolyAlgebraHom(P1, P2, IndetImages);
/**/ use P1;
/**/ f := 2*x^2 + 3*y + 4;
/**/ phi(f);
2*a^4 + 3*b^3 + 4

See Also