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NF |
Syntax |
NF(F:POLY,I:IDEAL):POLY NF(V:VECTOR,M:MODULE):VECTOR |
Summary |
normal form |
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 ::= Q[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 ------------------------------- |
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