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

## Synopsis

• Usage:
P = isPommaretBasis J
• Inputs:
• Outputs:
• P, , the result equals true if and only if J is a Pommaret basis

## Description

 i1 : R = QQ[x,y]; i2 : I = ideal(x^3,y^2); o2 : Ideal of R i3 : J = janetBasis I +----+------+ | 2 | | o3 = |y |{y} | +----+------+ | 2| | |x*y |{y} | +----+------+ | 3 | | |x |{y, x}| +----+------+ | 2 2| | |x y |{y} | +----+------+ o3 : InvolutiveBasis i4 : isPommaretBasis J o4 = true
 i5 : R = QQ[x,y]; i6 : I = ideal(x*y,y^2); o6 : Ideal of R i7 : J = janetBasis I +---+------+ | 2 | | o7 = |y |{y} | +---+------+ |x*y|{y, x}| +---+------+ o7 : InvolutiveBasis i8 : isPommaretBasis J o8 = false

• janetBasis -- compute Janet basis for an ideal or a submodule of a free module
• basisElements -- extract the matrix of generators from an involutive basis or factor module basis
• multVar -- extract the sets of multiplicative variables for each generator (in several contexts)
• 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)

## For the programmer

The object isPommaretBasis is .