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invSyzygies -- compute involutive basis of syzygies

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

cannot be iterated because schreyerOrder is not used; call janetResolution instead

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

Ways to use invSyzygies:

invSyzygies(InvolutiveBasis)

For the programmer

The object invSyzygies is a method function.

The source of this document is in InvolutiveBases.m2:1149:0.