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Macaulay2Doc > basic commutative algebra > M2SingularBook > Singular Book 1.1.9

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    }