getTemplateMatrix -- computes template matrix

• Usage:

  M = (a, B, J)

  M = getTemplateMatrix(sh, mp, J)

  getTemplateMatrix(E)

• Inputs:
  • a, a ring element, the action polynomial defining a multiplication matrix
  • B, a matrix,
  • E, an instance of the type EliminationTemplate, the elimination template for this problem
  • J, an ideal,
  • mp, an instance of the type MonomialPartition (missing documentation) ,
  • sh, an instance of the type ShiftSet (missing documentation) ,
• 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, the strategy used to compute H0
  • AdjustParams (missing documentation) => ..., default value true,
• Outputs:
  • M, a matrix,

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(x^4+x*y+y^2-3, x^2*y+y^3-2)

             4          2       2     3
o2 = ideal (x  + x*y + y  - 3, x y + y  - 2)

o2 : Ideal of R

i3 : E = eliminationTemplate(x,I)

o3 =  action variable: x

o3 : EliminationTemplate

i4 : getTemplateMatrix(E)

o4 = | 1 0 0 0 0 0 0  0 1 1 0 0 0 0  0 -3 0 0  0  |
     | 0 1 0 0 0 0 0  0 0 0 0 1 1 0  0 0  0 -3 0  |
     | 0 0 0 0 1 0 0  0 0 0 0 0 0 0  1 1  0 0  -3 |
     | 1 0 1 0 0 0 -2 0 0 0 0 0 0 0  0 0  0 0  0  |
     | 0 1 0 1 0 0 0  0 0 0 0 0 0 -2 0 0  0 0  0  |
     | 0 0 0 0 0 1 0  0 0 1 0 0 0 0  0 0  0 -2 0  |
     | 0 0 0 0 0 0 1  0 0 0 0 0 1 0  0 0  0 0  -2 |

              7       19
o4 : Matrix QQ  <-- QQ