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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 = .970360088545553

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

o2 = .345919252561423168835439594836+.00384863297404823671079538436211*ii

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

o3 = Tally{-1 => 6 }
           -2 => 15
           -3 => 4
           -4 => 9
           -5 => 12
           0 => 9
           1 => 9
           2 => 5
           3 => 14
           4 => 13
           5 => 5

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

      39    37    33    32    31    27    26    25    24    22    20    19  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      14    13    11    6    3
     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  + 4x y + 7x y  + 4x y  + 7x*y  + 6y

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

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

See also