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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 = .527716319202807

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

o2 = .570973635649099514671159453526+.72043948901115446726697754123*ii

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

o3 = Tally{-1 => 8 }
           -2 => 8
           -3 => 12
           -4 => 14
           -5 => 8
           0 => 9
           1 => 5
           2 => 9
           3 => 14
           4 => 5
           5 => 9

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

      39    32    30    27    25    24    23    22    21    18    15    14  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      13    9    7    5    3
     a   + a  + a  + a  + a

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 = 7x  + x y + 5x y  + 2x y  + 8x*y  + 8y

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

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

See also