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

• Usage:
gbs( D1 )
• Inputs:
• Outputs:

## Description

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) 2 o7 = {{x + y, y + z}} o7 : List i8 : primes(D) 2 o8 = {ideal (x + y, x + z)} o8 : List