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preimage0    --    preimage of a RINGELEM


Syntax 
preimage0(phi: RINGHOM, f: RINGELEM): RECORD

Description
This function returns a preimage of f via phi; if f is not in the image of phi, the function returns 0.

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(It);
a^2

See Also