EliminationTemplate -- type for elimination template objects

Description

The type `EliminationTemplate` represents objects that store the data required for elimination template computations. An `EliminationTemplate` object encodes the action variable, the ideal, and a cache for storing computed template data such as shifts, monomial partitions, and template matrices. These objects are constructed using the function `eliminationTemplate` and are used as input to other functions in this package, such as `getTemplateMatrix`, `getActionMatrix`, and `templateSolve`.

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 : E = eliminationTemplate(x, J)

o3 =  action variable: x

o3 : EliminationTemplate

i4 : E

o4 =  action variable: x

o4 : EliminationTemplate

Methods that use an object of class EliminationTemplate:

actionVariable(EliminationTemplate) -- see actionVariable -- returns the action variable associated to the elimination template
basis(EliminationTemplate) -- access the quotient basis of an EliminationTemplate
copyTemplate(EliminationTemplate,Ideal) -- see copyTemplate -- copies EliminationTemplate object
getActionMatrix(EliminationTemplate) -- see getActionMatrix -- computes or retrieves a template's action matrix
getTemplate(EliminationTemplate) -- see getTemplate -- construct the shifts and monomial partition for an elimination template
getTemplateMatrix(EliminationTemplate) -- see getTemplateMatrix -- computes template matrix
ideal(EliminationTemplate) -- access the ideal of an EliminationTemplate
net(EliminationTemplate) -- display an EliminationTemplate
templateSolve(EliminationTemplate) -- see templateSolve -- polynomial system solver using elimination templates

For the programmer

The object EliminationTemplate is a type, with ancestor classes HashTable < Thing.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/EliminationTemplates.m2:822:0.