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NF

normal form

Syntax
NF(F: RINGELEM, I: IDEAL): RINGELEM
NF(V: MODULEELEM, M: MODULE): MODULEELEM

Description
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. CoCoA-4 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.

Example
/**/  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(z-1);
/**/  NF(x^2+x*y+x*z+y^2+y*z+z^2, I);
x^2 +x*y +y^2 +x +y +1

See Also