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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]; Set FullRed; I := Ideal(z); NF(x^2+xy+xz+y^2+yz+z^2, I); x^2 + xy + y^2 ------------------------------- UnSet FullRed; NF(x^2+xy+xz+y^2+yz+z^2, I); x^2 + xy + y^2 + xz + yz + z^2 ------------------------------- ```

 See Also