# Singular Book 1.1.9 -- computation in polynomial rings

Create a polynomial ring using reasonably standard notation.
 i1 : A = QQ[x,y,z]; i2 : f = x^3+y^2+z^2 3 2 2 o2 = x + y + z o2 : A i3 : f^2-f 6 3 2 3 2 4 2 2 4 3 2 2 o3 = x + 2x y + 2x z + y + 2y z + z - x - y - z o3 : A
Here are several more examples.
 i4 : B = ZZ/32003[x,y,z]; i5 : C = GF(8)[x,y,z]; i6 : D = ZZ[x,y,z]; i7 : E = (frac(ZZ[a,b,c]))[x,y,z];
In Macaulay2, there is no concept of current ring. When you assign a ring to a variable, the variables in the ring are made global variables. To get the variables in a previous ring to be available, use use(Ring).
 i8 : x o8 = x o8 : E i9 : use D o9 = D o9 : PolynomialRing i10 : x o10 = x o10 : D
Now x is an element of the ring D.
 i11 : describe D o11 = ZZ[x..z, Degrees => {3:1}, Heft => {1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 1] {GRevLex => {3:1} } {Position => Up }