ring(Complex) -- access the ring of a complex or a complex map

i1 : S = ZZ/101[a,b,c,d];

i2 : C = freeResolution coker vars S

      1      4      6      4      1
o2 = S  <-- S  <-- S  <-- S  <-- S
                                  
     0      1      2      3      4

o2 : Complex

i3 : ring C

o3 = S

o3 : PolynomialRing

i4 : assert(ring C === S)

i5 : ring id_C

o5 = S

o5 : PolynomialRing

i6 : assert(ring id_C === S)