use(Ring) -- install ring variables and ring operations

Synopsis

• Usage:
use R
• Function: use
• Inputs:
• Consequences:
• All variables of R are set to global variables. Additionally, certain operations creating elements of R are installed globally.

Description

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]```

Caveat

Any values stored in the variables that have been assigned to are lost, hence this operation should not be used by code in a package.