IsInjective -- check if a RINGHOM is injective |
Syntax |
IsInjective(phi: RINGHOM): BOOL |
Description |
Example |
/**/ QQxyz ::= QQ[x,y,z]; /**/ QQab ::= QQ[a,b]; /**/ use QQab; /**/ phi := PolyAlgebraHom(QQxyz, QQab, [a+1, a*b+3, b^2]); /**/ IsInjective(phi); false /**/ ker(phi); ideal(-x^2*z +y^2 +2*x*z -6*y -z +9) /**/ IsSurjective(phi); false /**/ use QQab; /**/ preimage0(phi, b); 0 /**/ preimage0(phi, a^2); x^2 -2*x +1 /**/ phi(RingElem(QQxyz, "x^2 - 2*x + 1")); a^2 /**/ phi(RingElem(QQxyz, "x^2 - 2*x + 1 + (-x^2*z +y^2 +2*x*z -6*y -z +9)")); a^2 |
See Also |