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isPommaretBasis -- check whether or not a given Janet basis is also a Pommaret basis

Synopsis

Usage:
P = isPommaretBasis J
Inputs:
- J, an object of class InvolutiveBasis, a Janet basis as returned by janetBasis
Outputs:
- P, a Boolean value, the result equals true if and only if J is a Pommaret basis

Description

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(x^3,y^2)

             3   2
o2 = ideal (x , y )

o2 : Ideal of R

i3 : J = janetBasis I

o3 = InvolutiveBasis{0 => | y2 xy2 x3 x2y2 |                                                          }
                     1 => {HashTable{x => 0}, HashTable{x => 0}, HashTable{x => 1}, HashTable{x => 0}}
                                     y => 1             y => 1             y => 1             y => 1

o3 : InvolutiveBasis

i4 : isPommaretBasis J

o4 = true

i5 : R = QQ[x,y]

o5 = R

o5 : PolynomialRing

i6 : I = ideal(x*y,y^2)

                  2
o6 = ideal (x*y, y )

o6 : Ideal of R

i7 : J = janetBasis I

o7 = InvolutiveBasis{0 => | y2 xy |                             }
                     1 => {HashTable{x => 0}, HashTable{x => 1}}
                                     y => 1             y => 1

o7 : InvolutiveBasis

i8 : isPommaretBasis J

o8 = false

See also

janetBasis -- compute Janet basis for an ideal or a submodule of a free module
basisElements -- extract the matrix of generators from an involutive basis
multVar -- extract the sets of multiplicative variables for each generator from an involutive basis
janetMultVar -- return table of multiplicative variables for given module elements as determined by Janet division
pommaretMultVar -- return table of multiplicative variables for given module elements as determined by Pommaret division

Ways to use `isPommaretBasis` :

isPommaretBasis(InvolutiveBasis)