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 15179a4+4249a3b+13214a2b2-12572a3c+15665a2bc-1588a2c2-c4 {7} | a2 0 -5297a4-11229a3b-8252a2b2+4861a3c+12429a2bc-682a2c2 {8} | 0 a2 -14142a3-15067a2b+6894a2c ------------------------------------------------------------------------ 0 | 0 | 15179a2b3+4249ab4+13214b5-12572ab3c+15665b4c-1588b3c2 | -5297a2b3-11229ab4-8252b5+4861ab3c+12429b4c-682b3c2+d5 | -14142ab3-15067b4+6894b3c-c4 | 5 4 o6 : Matrix S <--- S |
i7 : isSyzygy(coker EG,2) o7 = true |