polynomials -- convert support set of exponents to polynomial

• Usage:

  f = polynomial(coef, vars, supp)

• Inputs:
  • coefs, a ring element, coefficients of the polynomial
  • vars, a ring element, variables of output polynomial
  • supp, a list, family of support sets determining a system of polynomials
• Outputs:
  • f, a list, of polynomial with fixed or indeterminate coefficients

i1 : supp = { {{1,1,3},{0,2,1},{2,0,4}}, {{0,1,3},{2,5,0}} };

i2 : A = QQ[c_1..c_(#flatten supp)];

i3 : R = A[t_1..t_(#(supp#0#0))];

i4 : f = polynomials(gens A, gens R, supp)

         2 4          3      2       2 5        3
o4 = {c t t  + c t t t  + c t t , c t t  + c t t }
       3 1 3    1 1 2 3    2 2 3   5 1 2    4 2 3

o4 : List