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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 /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/InvolutiveBases.m2:1149:0.