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.
See the book of Evans and Griffith (Syzygies. London Mathematical Society Lecture Note Series, 106. Cambridge University Press, Cambridge, 1985.)
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 0 {6} | -b3 0 d5 0 {7} | 0 -b3 -8251a4+5071a3b-9480a2b2+12365a3c+8231a2bc+5026a2c2-c4 -8251a2b3+5071ab4-9480b5+12365ab3c+8231b4c+5026b3c2 {7} | a2 0 2653a4-6203a3b-11950a2b2-13508a3c+5864a2bc+10259a2c2 2653a2b3-6203ab4-11950b5-13508ab3c+5864b4c+10259b3c2+d5 {8} | 0 a2 -7501a3+9534a2b-7216a2c -7501ab3+9534b4-7216b3c-c4 ---------------------------------------------------------------------------------------------------------------------------- | | | | | 5 4 o6 : Matrix S <--- S |
i7 : isSyzygy(coker EG,2) o7 = true |
This is called within bruns.
The object evansGriffith is a method function.