getTemplate -- construct the shifts and monomial partition for an elimination template

• Usage:

  (sh, mp) = getTemplate E

• Inputs:
  • E, an instance of the type EliminationTemplate,
• Optional inputs:
  • Strategy => a string, default value null, the algorithm used to compute the template: "Greedy" (default), "Larsson", or null (standard GB)
  • AdjustParams => a Boolean value, default value true, whether to run the greedy parameter-commit step (α-commit) for Martyushev's strategy
  • MonomialOrder => a symbol, default value null, override the default monomial order of the ring
• Outputs:
  • sh, an instance of the type ShiftSet (missing documentation) , a list of shift monomials applied to the generators of the ideal
  • mp, an instance of the type MonomialPartition (missing documentation) , a list of three sets of monomials: {excess, residual, basis}

i1 : R = QQ[x,y];

i2 : I = ideal(x^2-y, y^2-x);

o2 : Ideal of R

i3 : E = eliminationTemplate(x, I);

i4 : (sh, mp) = getTemplate(E, Strategy => "Greedy");

i5 : mp

        2     2    2
o5 = {{y }, {x y, x }, {x*y, x, y, 1}}

o5 : MonomialPartition