The routine reduces the target of M by elementary moves (see elementary) involving just d+1 variables. The outcome is probabalistic, but if the routine fails, it gives an error message.
i1 : kk=ZZ/32003 o1 = kk o1 : QuotientRing |
i2 : S=kk[a..e] o2 = S o2 : PolynomialRing |
i3 : i=ideal(a^2,b^3,c^4, d^5)
2 3 4 5
o3 = ideal (a , b , c , d )
o3 : Ideal of S
|
i4 : F=res i
1 4 6 4 1
o4 = S <-- S <-- S <-- S <-- S <-- 0
0 1 2 3 4 5
o4 : ChainComplex
|
i5 : f=F.dd_3
o5 = {5} | c4 d5 0 0 |
{6} | -b3 0 d5 0 |
{7} | a2 0 0 d5 |
{7} | 0 -b3 -c4 0 |
{8} | 0 a2 0 -c4 |
{9} | 0 0 a2 b3 |
6 4
o5 : Matrix S <--- S
|
i6 : EG = evansGriffith(f,2) -- notice that we have a matrix with one less row, as described in elementary, and the target module rank is one less.
o6 = {5} | c4 d5 0
{6} | -b3 0 d5
{7} | 0 -b3 5205a4+3078a3b+3345a2b2-5299a3c+3576a2bc-5917a2c2-c4
{7} | a2 0 4061a4-7354a3b+13533a2b2-9692a3c-10793a2bc+7817a2c2
{8} | 0 a2 14014a3-4242a2b-563a2c
------------------------------------------------------------------------
0 |
0 |
5205a2b3+3078ab4+3345b5-5299ab3c+3576b4c-5917b3c2 |
4061a2b3-7354ab4+13533b5-9692ab3c-10793b4c+7817b3c2+d5 |
14014ab3-4242b4-563b3c-c4 |
5 4
o6 : Matrix S <--- S
|
i7 : isSyzygy(coker EG,2) o7 = true |