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normal form
NF(F:POLY, I:IDEAL):POLY
NF(V:VECTOR, M:MODULE):VECTOR
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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.
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
-------------------------------
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