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 6391a4+13366a3b+14248a2b2-3114a3c+4182a2bc-12538a2c2-c4 {7} | a2 0 -285a4-3027a3b-2025a2b2+13314a3c+14258a2bc-12179a2c2 {8} | 0 a2 2332a3+10501a2b+474a2c ------------------------------------------------------------------------ 0 | 0 | 6391a2b3+13366ab4+14248b5-3114ab3c+4182b4c-12538b3c2 | -285a2b3-3027ab4-2025b5+13314ab3c+14258b4c-12179b3c2+d5 | 2332ab3+10501b4+474b3c-c4 | 5 4 o6 : Matrix S <--- S |
i7 : isSyzygy(coker EG,2) o7 = true |