A complex is homogeneous (graded) if the base ring is graded, all of the component objects are graded, and all the component maps are graded of degree zero.
i1 : S = ZZ/101[a,b,c,d]; |
i2 : I = minors(2, matrix{{a,b,c},{b,c,d}})
2 2
o2 = ideal (- b + a*c, - b*c + a*d, - c + b*d)
o2 : Ideal of S
|
i3 : C = freeResolution (S^1/I)
1 3 2
o3 = S <-- S <-- S
0 1 2
o3 : Complex
|
i4 : isHomogeneous C o4 = true |
i5 : J = minors(2, matrix{{a,b,c},{b,c,d^2}})
2 2 2 2
o5 = ideal (- b + a*c, a*d - b*c, b*d - c )
o5 : Ideal of S
|
i6 : D = freeResolution (S^1/J)
1 3 2
o6 = S <-- S <-- S
0 1 2
o6 : Complex
|
i7 : isHomogeneous D o7 = false |