basic rings

The following rings are initially present in every session with Macaulay 2.
  • ZZ, the ring of integers.
  • QQ, the field of rational numbers.
  • RR, the field of real (floating point) numbers.
  • CC, the field of complex (floating point) numbers.
  • (The names of these rings are double letters so the corresponding symbols with single letters can be used as variables in rings.) Entries of these rings are constructed as follows, and the usual arithmetic operations apply.

    i1 : 1234

    o1 = 1234
    i2 : 123/4

         123
    o2 = ---
          4

    o2 : QQ
    i3 : 123.4

    o3 = 123.4

    o3 : RR
    i4 : 123+4*ii

    o4 = 123 + 4ii

    o4 : CC

    The usual arithmetic operations are available.

    i5 : 4/5 + 2/3

         22
    o5 = --
         15

    o5 : QQ
    i6 : 10^20

    o6 = 100000000000000000000
    i7 : 3*5*7

    o7 = 105
    i8 : 5!

    o8 = 120

    An additional pair of division operations which produce integral quotients and remainders is available.

    i9 : 1234//100

    o9 = 12
    i10 : 1234%100

    o10 = 34


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