syz Matrix -- compute the syzygy matrix

syz Matrix -- compute the syzygy matrix

Synopsis:

Usage: f = syz h

Function: syz -- the syzygy matrix

Input:

h, an instance of class Matrix: a matrix

Output:

f, an instance of class Matrix: the matrix of minimal generators for the syzygies among the columns of h

Optional arguments :

syz(..., BasisElementLimit) -- stop when this number of basis elements is obtained

syz(..., ChangeMatrix => ...) -- whether to produce the change of basis matrix

syz(..., CodimensionLimit => ...) -- stop when this codimension is reached

syz(..., DegreeLimit) -- compute up to a certain degree

syz(..., PairLimit) -- stop when this number of pairs is handled

syz(..., StopBeforeComputation => ...) -- whether to stop the computation immediately

syz(..., StopWithMinimalGenerators => ...) -- stop when minimal generators have been determined

syz(..., Strategy => ...) -- specify the strategy used to compute the Groebner basis

syz(..., SubringLimit) -- stop after finding enough elements of a subring

syz(..., Syzygies) -- whether to collect syzygies

syz(..., SyzygyLimit) -- stop when this number of syzygies is obtained

syz(..., SyzygyRows) -- the number rows of the syzygy matrix to collect

Code:

     -- ../../../Macaulay2/m2/matrix2.m2:44-50
     syz Matrix := Matrix => options -> (f) -> (
          if not isFreeModule target f or not isFreeModule source f
          then error "expected map between free modules";
          if ring f === ZZ or not isHomogeneous f
          then syz gb (f, options, Syzygies=>true)
          else mingens image syz gb (f, options, Syzygies=>true)
          )