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 7431a4-6442a3b+11967a2b2+6213a3c-11414a2bc+14536a2c2-c4 {7} | a2 0 -14467a4+15916a3b+714a2b2+14196a3c-14361a2bc-14879a2c2 {8} | 0 a2 -5552a3-4588a2b+10552a2c ------------------------------------------------------------------------ 0 | 0 | 7431a2b3-6442ab4+11967b5+6213ab3c-11414b4c+14536b3c2 | -14467a2b3+15916ab4+714b5+14196ab3c-14361b4c-14879b3c2+d5 | -5552ab3-4588b4+10552b3c-c4 | 5 4 o6 : Matrix S <--- S |
i7 : isSyzygy(coker EG,2) o7 = true |