templateSolve -- polynomial system solver using elimination templates

• Usage:

  sols = templateSolve(et)

  sols = templateSolve(J)

  sols = templateSolve(a, J)

• Inputs:
  • a, a ring element, the action polynomial defining a multiplication matrix
  • J, an ideal, a zero-dimensional ideal
  • et, an instance of the type EliminationTemplate, the elimination template for this problem
• Optional inputs:
  • MonomialOrder (missing documentation) => a thing, default value null, the monomial order used on the ambient ring
  • Strategy (missing documentation) => a thing, default value null, null (default), "Larsson", or "Greedy"
  • AdjustParams (missing documentation) => a Boolean value, default value true, true (default) runs the full Greedy commit; false stops at the particular solution α := 0 ("MatrixHi mode")
• Outputs:
  • sols, a list, a list of solutions; each solution is itself a list of complex numbers, one per ring variable of the ambient ring, in declaration order

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : J = ideal(x^2+y^2-1,x^2+x*y+y^2-1)

             2    2       2          2
o2 = ideal (x  + y  - 1, x  + x*y + y  - 1)

o2 : Ideal of R

i3 : actVar = x + 2*y

o3 = x + 2y

o3 : R

i4 : templateSolve(actVar, J)

o4 = {{1, 0}, {-1, 0}, {7.85046e-17, 1}, {-4.71028e-16, -1}}

o4 : List