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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. If the codomain is also a polynomial
ring with the same ring of coefficients then use
giving also the homomorphism saying
how the coefficient ring is mapped.
Some "special" homomorphisms can be created easily via dedicated functions.
If there is a canonical homomorphism between the rings then this
may be specified using
For the homomorphism which embed the coefficent ring into a polynomial
/**/ P1 ::= QQ[x,y]; // polys in x,y with coefficients in QQ
/**/ P2 ::= QQ[a,b]; // polys in a,b with coefficients in QQ
/**/ use P2; IndetImages := [a^2, b^3];
/**/ phi := PolyAlgebraHom(P1, P2, IndetImages);
/**/ use P1;
/**/ f := 2*x^2 + 3*y + 4;
2*a^4 + 3*b^3 + 4