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 1115a4-13313a3b+14438a2b2-14000a3c-9318a2bc-14346a2c2-c4 {7} | a2 0 -10476a4-5054a3b-6482a2b2-4755a3c+3079a2bc+12401a2c2 {8} | 0 a2 7259a3-13038a2b-11061a2c ------------------------------------------------------------------------ 0 | 0 | 1115a2b3-13313ab4+14438b5-14000ab3c-9318b4c-14346b3c2 | -10476a2b3-5054ab4-6482b5-4755ab3c+3079b4c+12401b3c2+d5 | 7259ab3-13038b4-11061b3c-c4 | 5 4 o6 : Matrix S <--- S |
i7 : isSyzygy(coker EG,2) o7 = true |