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NF(F: RINGELEM, I: IDEAL): RINGELEM
NF(V: MODULEELEM, M: MODULE): MODULEELEM |
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 only full reduction is computed: each monomial in
the result cannot be reduced.
(CoCoA-4 allowed setting the flag FullRed, of the panel GROEBNER,
so that only the leading term is reduced)
Currently polynomial ideals are implemented only with coeffs
in a field.
/**/ 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
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