invSyzygies -- compute involutive basis of syzygies

Synopsis

• Usage:

  invSyzygies J

• Inputs:
  • J, an instance of the type InvolutiveBasis
• Outputs:
  • an instance of the type InvolutiveBasis, an involutive basis for the syzygies of J

Description

i1 : R = QQ[x,y,z];

i2 : I = ideal(x,y,z);

o2 : Ideal of R

i3 : J = janetBasis I

     +-+---------+
o3 = |z|{z}      |
     +-+---------+
     |y|{z, y}   |
     +-+---------+
     |x|{z, y, x}|
     +-+---------+

o3 : InvolutiveBasis

i4 : invSyzygies J

     +------+---------+
o4 = ||  x ||{z, y, x}|
     ||  0 ||         |
     || -z ||         |
     +------+---------+
     ||  y ||{z, y}   |
     || -z ||         |
     ||  0 ||         |
     +------+---------+
     ||  0 ||{z, y, x}|
     ||  x ||         |
     || -y ||         |
     +------+---------+

o4 : InvolutiveBasis

Caveat

See also

• janetBasis -- compute Janet basis for an ideal or a submodule of a free module
• janetResolution -- construct a free resolution for a given ideal or module using Janet bases