copyTemplate -- copies EliminationTemplate object

Usage:

F = copyTemplate(E, J)
Inputs:
- E, an instance of the type EliminationTemplate, the elimination template to copy
- J, an ideal, a zero-dimensional ideal
Outputs:
- F, an instance of the type EliminationTemplate, an EliminationTemplate object

Description

This method copies an elimination template object, using the same action variable and basis, but a different defining ideal. The new ideal is expected to share the Groebner-basis structure of the original (same leading monomials, same |B|) — this is the specialization regime of copyTemplate. Note (possible typo in an earlier draft of this docstring): the example below originally paired I = ideal(x^4+x*y+y^2-3, x^2*y+y^3-2) with J = ideal(x^3+y^2-1, x^2+y^3-1), which violates this requirement — deg(R/I) = 12 but deg(R/J) = 9, so no single template can serve both. The example below uses a structurally-compatible replacement J.

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 : J = ideal(x^4+2*x*y+y^2-1, 3*x^2*y+y^3-5)

             4           2        2     3
o3 = ideal (x  + 2x*y + y  - 1, 3x y + y  - 5)

o3 : Ideal of R

i4 : E = eliminationTemplate(x,I)

o4 =  action variable: x

o4 : EliminationTemplate

i5 : F = copyTemplate(E, J)

o5 =  action variable: x

o5 : EliminationTemplate

Ways to use copyTemplate:

copyTemplate(EliminationTemplate,Ideal)

For the programmer

The object copyTemplate is a method function with options.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/EliminationTemplates.m2:987:0.

copyTemplate -- copies EliminationTemplate object

Description

See also

Ways to use copyTemplate:

For the programmer