ring(ZZdFactorization) -- access the ring of a ZZ/d-graded factorization or a factorization map

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

i2 : C = koszulMF({a,b,c,d}, a^2+b^2+c^2+d^2)

      8      8      8
o2 = S  <-- S  <-- S
                    
     0      1      0

o2 : ZZdFactorization

i3 : C.dd

          8                                  8
o3 = 1 : S  <------------------------------ S  : 0
               | d 0  0  0  c  0  b  a  |
               | 0 d  0  0  0  c  a  -b |
               | 0 0  d  0  b  a  -c 0  |
               | 0 0  0  d  a  -b 0  -c |
               | c 0  b  a  -d 0  0  0  |
               | 0 c  a  -b 0  -d 0  0  |
               | b a  -c 0  0  0  -d 0  |
               | a -b 0  -c 0  0  0  -d |

          8                                  8
     0 : S  <------------------------------ S  : 1
               | d 0  0  0  c  0  b  a  |
               | 0 d  0  0  0  c  a  -b |
               | 0 0  d  0  b  a  -c 0  |
               | 0 0  0  d  a  -b 0  -c |
               | c 0  b  a  -d 0  0  0  |
               | 0 c  a  -b 0  -d 0  0  |
               | b a  -c 0  0  0  -d 0  |
               | a -b 0  -c 0  0  0  -d |

o3 : ZZdFactorizationMap

i4 : ring C

o4 = S

o4 : PolynomialRing

i5 : assert(ring C === S)

i6 : ring id_C

o6 = S

o6 : PolynomialRing

i7 : assert(ring id_C === S)