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ker

Kernel of a homomorphism

Syntax
ker(phi: RINGHOM): IDEAL

Description
This function returns the kernel of a homomorphism.

Example
/**/ R ::= QQ[x,y,z,w];
/**/ Use S ::= QQ[s,t];
/**/ phi := PolyAlgebraHom(R, S, [s^3, s^2*t, s*t^2, t^3]);
/**/ ker(phi);
ideal(z^2 -y*t, y*z -x*t, y^2 -x*z)

/**/ SmodJ := NewQuotientRing(S, ideal(RingElem(S,"t+s")));
/**/ Use SmodJ;
/**/ psi := PolyAlgebraHom(R, SmodJ, [s^3, s^2*t, s*t^2, t^3]);
/**/ ker(psi);
ideal(x +w, y -w, z +w)

/**/ RmodI := NewQuotientRing(R, ideal(RingElem(R,"x+y")));
/**/ ker(InducedHom(RmodI, psi));
ideal((-y +w), (y -w), (z +w))

See Also