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 4576a4-12517a3b+10910a2b2-703a3c-10341a2bc+8834a2c2-c4 {7} | a2 0 -10320a4-9987a3b+13331a2b2+14913a3c+2776a2bc-6421a2c2 {8} | 0 a2 7732a3+10971a2b-3380a2c ------------------------------------------------------------------------ 0 | 0 | 4576a2b3-12517ab4+10910b5-703ab3c-10341b4c+8834b3c2 | -10320a2b3-9987ab4+13331b5+14913ab3c+2776b4c-6421b3c2+d5 | 7732ab3+10971b4-3380b3c-c4 | 5 4 o6 : Matrix S <--- S |
i7 : isSyzygy(coker EG,2) o7 = true |