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

Synopsis

• Usage:

  P = isPommaretBasis J

• Inputs:
  • J, an instance of the type 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];

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

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 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