This algorithm is based upon the methods described in the book of Evans and Griffith (Syzygies. London Mathematical Society Lecture Note Series, 106. Cambridge University Press, Cambridge, 1985.)
i1 : kk=ZZ/32003
o1 = kk
o1 : QuotientRing
|
i2 : S=kk[a..d]
o2 = S
o2 : PolynomialRing
|
i3 : F=res (ideal vars S)^2
1 10 20 15 4
o3 = S <-- S <-- S <-- S <-- S <-- 0
0 1 2 3 4 5
o3 : ChainComplex
|
NOTE: We are viewing a syzygy module as a cokernel of an appropriate map.
i4 : isSyzygy(coker F.dd_3,3) -- the cokernel defined by the 3rd map is not a 3rd syzygy
o4 = false
|
i5 : isSyzygy(coker F.dd_4,3) -- the cokernel defined by the 4th map is a 3rd syzygy
o5 = true
|
This function is called within evansGriffith.