up previous next
normal form
NF(F: RINGELEM, I: IDEAL): RINGELEM
NF(V: MODULEELEM, M: MODULE): MODULEELEM 
The first function returns the normal form of F with respect to I.
It also computes a Groebner basis of I if that basis has not been
computed previously.
The second function returns the normal form of V with respect to M. It
also computes a Groebner basis of M if that basis has not been
computed previously.
Currently (v 5.0.3) only full reduction is computed: each monomial in
the result cannot be reduced. CoCoA4 allowed setting the flag
FullRed (of the panel GROEBNER) to False so that only the leading term
is reduced.
Currently (v 5.0.3) polynomial ideals are implemented only with coeffs
in a field.
/**/ Use R ::= QQ[x,y,z];
/**/ I := ideal(z);
/**/ NF(x^2+x*y+x*z+y^2+y*z+z^2, I);
x^2 +x*y +y^2
/**/ I := ideal(z1);
/**/ NF(x^2+x*y+x*z+y^2+y*z+z^2, I);
x^2 +x*y +y^2 +x +y +1
