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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 = .358887685011094

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

o2 = .230341860618709561026850669021+.067536978318266314187907518673*ii

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

o3 = Tally{-1 => 12}
           -2 => 11
           -3 => 14
           -4 => 18
           -5 => 7
           0 => 2
           1 => 6
           2 => 9
           3 => 8
           4 => 7
           5 => 7

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

      36    33    28    25    24    23    18    17    14    13    12    11  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      7    6    4    3    2
     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
o6 = 2x  + 5x y + 6x y  + 8x y  + 9x*y

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

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

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

See also