When a ring (or a monoid) is assigned to a global variable, this function is automatically called for it.
It is possible to have several polynomial rings defined, perhaps with a variable belonging to several rings.
i1 : R = QQ[a..d]
o1 = R
o1 : PolynomialRing

i2 : S = QQ[b,c,d,e]
o2 = S
o2 : PolynomialRing

i3 : b
o3 = b
o3 : S

At this point, b is thought to be a variable of S. If one typed
a+b, an error would occur, since Macaulay2 doesn't know how to add elements of R and S together. This is fixed via:
i4 : use R
o4 = R
o4 : PolynomialRing

i5 : b
o5 = b
o5 : R

i6 : a+b
o6 = a + b
o6 : R

There are several functions that create rings for you. Generally, their variables are not globally visible. However, once you 'use' the ring, the variables are available.For example, the numerator of the Hilbert function is a polynomial in a ring with a variable T.
i7 : T
o7 = T
o7 : Symbol

i8 : hf = poincare ideal vars S
2 3 4
o8 = 1  4T + 6T  4T + T
o8 : ZZ[T]

i9 : T
o9 = T
o9 : Symbol

i10 : use ring hf
o10 = ZZ[T]
o10 : PolynomialRing

i11 : T
o11 = T
o11 : ZZ[T]
