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NF

normal form

Syntax
NF(F:POLY, I:IDEAL):POLY
NF(V:VECTOR, M:MODULE):VECTOR

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.

The coefficient ring is assumed to be a field. Note that the definition of normal form depends on the current value of the option FullRed of the panel GROEBNER. If FullRed is False it means that a polynomial is in normal form when its leading term with respect to the the current term ordering cannot be reduced. If FullRed is True it means that a polynomial is in NF if and only if each monomial cannot be reduced.

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

See Also