pommaretMultVar -- return table of multiplicative variables for given module elements as determined by Pommaret division

Synopsis

• Usage:

  pommaretMultVar M

• Inputs:

  • M, a matrix or a list
• Outputs:

  • a list, list of sets of variables of the polynomial ring; the i-th set consists of the multiplicative variables for the i-th generator in J

Description

i1 : R = QQ[x1,x2,x3]

o1 = R

o1 : PolynomialRing

i2 : M = matrix {{ x1*x2*x3, x2^2*x3, x1*x2*x3^2 }}

o2 = | x1x2x3 x2^2x3 x1x2x3^2 |

             1       3
o2 : Matrix R  <--- R

i3 : pommaretMultVar M

o3 = {set {x3}, set {x3}, set {x3}}

o3 : List

See also

• janetMultVar -- return table of multiplicative variables for given module elements as determined by Janet division
• janetBasis -- compute Janet basis for an ideal or a submodule of a free module
• multVar -- extract the sets of multiplicative variables for each generator from an involutive basis
• isPommaretBasis -- check whether or not a given Janet basis is also a Pommaret basis