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gbs -- get the list of Groebner bases corresponding to the height-one primes in the support of a divisor



This function returns the list of Groebner bases associated to the height-one prime ideals corresponding to the components of a BasicDivisor (or a WeilDivisor, QWeilDivisor or RWeilDivisor). Note that this list of Groebner bases is made when the divisor is constructed.

i1 : R = ZZ/7[x,y,u,v]/ideal(x*y-u*v);
i2 : D = divisor(x)

o2 = Div(v, x) + Div(u, x)

o2 : WeilDivisor on R
i3 : gbs(D)

o3 = {{v, x}, {u, x}}

o3 : List

Note, the Grobner basis can be different from a minimal set of generators the user provides.

i4 : R = ZZ/2[x,y,z]/ideal(z^2+x*y*z+x^2*y+x*y^2);
i5 : J = ideal(x+y, x^2+z);

o5 : Ideal of R
i6 : D = divisor({2}, {J})

o6 = 2*Div(x+y, x^2+z)

o6 : WeilDivisor on R
i7 : gbs(D)

o7 = {{x + y, y  + z}}

o7 : List
i8 : primes(D)

o8 = {ideal (x + y, x  + z)}

o8 : List

See also

Ways to use gbs :

For the programmer

The object gbs is a method function.