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Macaulay2Doc :: random(Type)

random(Type) -- random element of a type

Synopsis

Description

Synopsis

  • Usage:
    random T
  • Inputs:
  • Outputs:
    • a random instance of the type T. If the Height option specifies a number h and T is ZZ and , then the integers returned are in the range 0 .. h-1; for QQ the numerator and denominator are in the range 1 .. h.
i1 : random RR

o1 = .59593398259744

o1 : RR (of precision 53)
i2 : random CC_100

o2 = .232240779018955935435647144971+.640584291292569989979538933958*ii

o2 : CC (of precision 100)
i3 : tally for i to 100 list random GF 11

o3 = Tally{-1 => 8 }
           -2 => 13
           -3 => 9
           -4 => 17
           -5 => 6
           0 => 9
           1 => 8
           2 => 8
           3 => 9
           4 => 5
           5 => 9

o3 : Tally
i4 : random GF(2,40)

      38    37    33    32    29    27    24    23    22    21    19    17  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      14    13    12    11    7    2
     a   + a   + a   + a   + a  + a  + a + 1

o4 : GF 1099511627776

Synopsis

  • Usage:
    random(d,R)
  • Inputs:
  • Outputs:
    • a random homogeneous element of the ring R of degree d
i5 : R = ZZ[x,y];
i6 : random(5,R)

       5     4      3 2     2 3       4     5
o6 = 5x  + 5x y + 4x y  + 8x y  + 2x*y  + 9y

o6 : R
i7 : R = GF(25,Variable=>a)[x,y];
i8 : VerticalList for i to 6 list random(3,R)

     {   3       2               2    3                      }
o8 = {a*x  + 2a*x y + (2a + 1)x*y  + y                       }
     {    3     2        2              3                    }
     {- 2x  + 2x y + 2x*y  + (- 2a - 2)y                     }
     {  3            2        2       3                      }
     {2x  + (2a + 1)x y - 2x*y  - 2a*y                       }
     {   3      2              2    3                        }
     {a*x  - a*x y + (a - 2)x*y  - y                         }
     {          3             2                2            3}
     {(- a - 1)x  + (- a + 2)x y + (- a + 2)x*y  + (2a - 1)y }
     {      3      2          2    3                         }
     {- 2a*x  - a*x y + 2a*x*y  + y                          }
     {   3              2         2      3                   }
     {a*x  + (- 2a + 1)x y + a*x*y  - a*y                    }

o8 : VerticalList
The length of d, if it's a list, should be the same as degreeLength R.

See also