coefficients(BasicDivisor) -- get the list of coefficients of a divisor

Synopsis

• Function: coefficients

• Usage:

  coefficients( D1 )

• Inputs:
  • D1, an instance of the type BasicDivisor,
• Optional inputs:
  • Monomials => ..., default value null,
  • Variables => ..., default value null,
• Outputs:
  • a list,

Description

i1 : R = QQ[x,y,u,v]/ideal(x*y-u*v);

i2 : D = divisor(x);

o2 : WeilDivisor on R

i3 : coefficients(D)

o3 = {1, 1}

o3 : List

i4 : E = divisor(x*u);

o4 : WeilDivisor on R

i5 : coefficients(E)

o5 = {1, 1, 2}

o5 : List

i6 : F = divisor({0, 1/2, -2/3}, {ideal(y, u), ideal(x,u), ideal(x,v)}, CoefficientType => QQ)

o6 = 0*Div(y, u) + 1/2*Div(x, u) + -2/3*Div(x, v)

o6 : QWeilDivisor on R

i7 : coefficients(F)

         1    2
o7 = {0, -, - -}
         2    3

o7 : List

i8 : G = divisor({0.5, -0.667}, {ideal(x,u), ideal(x,v)}, CoefficientType => RR)

o8 = .5*Div(x, u) + -.667*Div(x, v)

o8 : RWeilDivisor on R

i9 : coefficients(G)

o9 = {.5, -.667}

o9 : List

See also

• coefficient(Ideal,BasicDivisor) -- get the coefficient of an ideal for a fixed divisor
• primes -- get the list of height-one primes in the support of a divisor
• gbs -- get the list of Groebner bases corresponding to the height-one primes in the support of a divisor