multVar -- extract the sets of multiplicative variables for each generator from an involutive basis

Synopsis

• Usage:

  m = multVar(J) or m = multVar(C,n)

• Inputs:

  • J, an object of class InvolutiveBasis
  • C, a chain complex
  • n, an integer
• Outputs:

  • m, a list, list of sets of variables of the polynomial ring

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;

i4 : multVar J

o4 = {set {y}, set {y}, set {y, x}, set {y}}

o4 : List

i5 : R = QQ[x,y,z]

o5 = R

o5 : PolynomialRing

i6 : I = ideal(x,y,z)

o6 = ideal (x, y, z)

o6 : Ideal of R

i7 : C = res(I, Strategy => Involutive)

      1      3      3      1
o7 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o7 : ChainComplex

i8 : multVar(C, 2)

o8 = {set {z, y, x}, set {z, y, x}, set {z, y}}

o8 : List

See also

• janetBasis -- compute Janet basis for an ideal or a submodule of a free module
• 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
• basisElements -- extract the matrix of generators from an involutive basis
• janetResolution -- construct a free resolution for a given ideal or module using Janet bases
• Involutive -- name for an optional argument