up previous next
CanonicalHom

canonical homomorphism

Syntax
CanonicalHom(R: RING, S: RING): RINGHOM

Description
CanonicalHom(R, S) -- where R and S are rings, gives the canonical homomorphism from R to S. Currently it works only on the most natural constructions:
ZZ -> S    QQ -> S
R -> R/I   R -> FractionFiels(R)
R -> R[x[1..N]]


Example
/**/  use R ::= QQ[x,y];
/**/  RmodI := NewQuotientRing(R, ideal(x^2-1));

/**/  phi := CanonicalHom(R, RmodI);
/**/  phi(x^3*y);
(x*y)
/**/  RingOf(It) = RmodI;
true

/**/  RingElem(RmodI, x^3*y);  -- same as phi(x^3*y)
			      -- internally computes CanonicalHom

See Also