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QuotientBasisSorted    --    vector space basis for zero-dimensional quotient rings

QuotientBasisSorted(I: IDEAL): LIST

This function determines a vector space basis (of power products) for the quotient space associated to a zero-dimensional ideal. It is the same as QuotientBasis , but sorted in increasing order according to the term-ordering of the ring.

/**/  use P ::= QQ[x,y,z];
/**/  I := intersection(ideal(x,y,z)^2, ideal(x-1, y+1, z)^2);
/**/  QBS := QuotientBasisSorted(I);   QBS;
[1, z, y, x, y*z, y^2, x*y, y^3]

/**/  QB := QuotientBasis(I);   QB;
[1, z, y, y*z, y^2, y^3, x, x*y]

See Also