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 1590a4+545a3b-15029a2b2+11327a3c+2279a2bc+2641a2c2-c4
{7} | a2 0 -2846a4-8919a3b-13427a2b2-449a3c+10590a2bc-12962a2c2
{8} | 0 a2 -9384a3-14184a2b+12276a2c
------------------------------------------------------------------------
0 |
0 |
1590a2b3+545ab4-15029b5+11327ab3c+2279b4c+2641b3c2 |
-2846a2b3-8919ab4-13427b5-449ab3c+10590b4c-12962b3c2+d5 |
-9384ab3-14184b4+12276b3c-c4 |
5 4
o6 : Matrix S <--- S
|
i7 : isSyzygy(coker EG,2) o7 = true |