freeResolution after canonicalTruncation

[mahrud]

I ran into something that surprised me, but I'm not sure if it's a bug or what I expected was unreasonable or I'm misusing something.

Say I start with a free resolution, canonically truncate the end, then take the free resolution of that complex. I would expect the result to be identical, but it doesn't seem to be:

R = ZZ/101[a,b,c,d,e]
J = intersect(ideal(a,b,c^2), ideal(b^2,c,d,e))

C = freeResolution J
E = canonicalTruncation(C, (0, 3))
D = freeResolution E

C == D                   -- false
C.module === D.module    -- true
dd^C_4 == (dd^D_4)_{1,0} -- true, permuted columns

I don't necessarily expect two resolutions to be identical, but can canonicalTruncation produce a syzygy module whose free resolution is identical to the original?

cc: @mikestillman @ggsmith