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localAlgebraBasis -- produces a basis for a local finitely generated algebra over a field k



Given an endomorphism of affine space, $f=(f_1,\dots ,f_n)$, given as a list of polynomials called L and the prime ideal of an isolated zero, this command returns a list of basis elements of the local k-algebra $Q_p(f)$ by computing a normal basis for $(I:(I:p^{\infty}))$ (vis. [S02, Proposition 2.5]).

i1 : QQ[x,y];
i2 : f = {x^2+1-y,y};
i3 : p = ideal(x^2+1,y);

o3 : Ideal of QQ[x..y]
i4 : localAlgebraBasis(f,p) 

o4 = {1, x}

o4 : List


See also

Ways to use localAlgebraBasis :

For the programmer

The object localAlgebraBasis is a method function.