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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 = .153597551735792

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

o2 = .214021707504346674365414977446+.913196770351618251946357644107*ii

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

o3 = Tally{-1 => 10}
           -2 => 6
           -3 => 12
           -4 => 6
           -5 => 5
           0 => 7
           1 => 8
           2 => 8
           3 => 13
           4 => 14
           5 => 12

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

      37    36    35    33    31    30    29    28    27    26    25    24  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      23    21    19    15    14    12    11    10    8    7    5    4    3  
     a   + a   + a   + a   + a   + a   + a   + a   + a  + a  + a  + a  + a  +
     ------------------------------------------------------------------------
      2
     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)

       4      3 2     2 3       4    5
o6 = 6x y + 4x y  + 4x y  + 6x*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 = {x  + 2x y + (2a - 1)x*y  + (- a - 2)y        }
     {         3             2         2    3      }
     {(2a + 2)x  + (- a - 2)x y + a*x*y  + y       }
     {           3            2       2      3     }
     {(- 2a - 1)x  + (2a + 2)x y + x*y  + a*y      }
     {    3              2                 2      3}
     {- 2x  + (- 2a - 1)x y + (- 2a + 2)x*y  - a*y }
     {        3    2       2             3         }
     {(a - 2)x  - x y + x*y  + (- a - 1)y          }
     {   2                2    3                   }
     {a*x y + (- a - 1)x*y  + y                    }
     {     3              2        2     3         }
     {- a*x  + (- 2a - 1)x y - 2x*y  + 2y          }

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

See also