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 -7377a4+2158a3b+2560a2b2+2169a3c+6270a2bc-15584a2c2-c4 {7} | a2 0 -447a4+14033a3b-3852a2b2+6911a3c+1285a2bc+4536a2c2 {8} | 0 a2 12346a3+5388a2b+3073a2c ------------------------------------------------------------------------ 0 | 0 | -7377a2b3+2158ab4+2560b5+2169ab3c+6270b4c-15584b3c2 | -447a2b3+14033ab4-3852b5+6911ab3c+1285b4c+4536b3c2+d5 | 12346ab3+5388b4+3073b3c-c4 | 5 4 o6 : Matrix S <--- S |
i7 : isSyzygy(coker EG,2) o7 = true |