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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 = .988218074783266

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

o2 = .221508117830771442743669085262+.9202800496479011501617325379*ii

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

o3 = Tally{-1 => 10}
           -2 => 7
           -3 => 7
           -4 => 9
           -5 => 4
           0 => 13
           1 => 11
           2 => 8
           3 => 8
           4 => 7
           5 => 17

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

      39    38    37    36    35    33    32    30    28    27    26    25  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      24    23    22    20    19    18    17    16    14    13    9    8    4
     a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a  + a  + a 
     ------------------------------------------------------------------------
        3    2
     + 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 = 2x  + 5x y + 2x y  + 5x y  + 7x*y  + y

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

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

See also