calling mingens after syz gb

[mahrud]

Here's the main hook for syz(Matrix):

M2/M2/Macaulay2/m2/matrix2.m2

Lines 315 to 320 in 562aea5

	addHook((syz, Matrix), Strategy => Default, (opts, 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, opts, Syzygies=>true)
	else mingens image syz gb (f, opts, Syzygies=>true)

Notice that if the ring isn't the integers and the matrix is homogeneous, it calls mingens image syz gb ...

Question 1: what's the point of mingens image here?

I think there are many cases when this takes a long time and is probably not necessary at all. Consider this truncation of a free module:

i1 : R = ZZ/101[x_0..x_5];

i2 : elapsedTime M = truncate(12, R^1);
 -- 12.5273s elapsed

i3 : elapsedTime syz gb(M.generators, Syzygies => true);
 -- 11.7873s elapsed

             6188      28560
o3 : Matrix R     <-- R

i4 : elapsedTime mingens image oo;
 -- 9.87205s elapsed

             6188      28560
o4 : Matrix R     <-- R

This is a problem because almost everything calls this, for instance presentation:

i6 : elapsedTime presentation truncate(12, R^1);
 -- 43.4177s elapsed

             6188      28560
o6 : Matrix R     <-- R

Notice that the matrices are the same size, but probably have a different order.

Question 2: does the order matter? for instance does freeResolution assume anything about the order of columns in the presentation?

cc: @mikestillman

[mahrud]

@Devlin-Mallory you might also be interested in this.