The base ring of a ring R is the ring from which R was formed. For example, if R is a quotient ring of the form S/I, or if R is a fraction ring of the form frac S, or if R is a polynomial ring over S, then the base ring is S.
i1 : baseRing QQ o1 = ZZ o1 : Ring |
i2 : R = QQ[x,y] o2 = R o2 : PolynomialRing |
i3 : S = R / (x^2 + y^3 - 1) o3 = S o3 : QuotientRing |
i4 : T = frac S o4 = T o4 : FractionField |
i5 : baseRing T o5 = S o5 : QuotientRing |
i6 : baseRing S o6 = R o6 : PolynomialRing |
i7 : baseRing R o7 = QQ o7 : Ring |
The entire chain of base rings can be obtained under the key baseRings.
i8 : T.baseRings o8 = {ZZ, QQ, R, S} o8 : List |
The object baseRing is a method function.