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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 = .60462392808151

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

o2 = .822693488174118279197089681138+.580871634378341172029954602657*ii

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

o3 = Tally{-1 => 13}
           -2 => 9
           -3 => 7
           -4 => 11
           -5 => 5
           0 => 14
           1 => 7
           2 => 7
           3 => 5
           4 => 12
           5 => 11

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

      38    35    34    32    31    30    29    27    25    24    23    22  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      20    18    17    16    15    13    11    10    9    6    3
     a   + a   + a   + a   + a   + 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  + 8x y + 4x y  + 4x y  + 5x*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 = {(a + 1)x  + 2x y - a*x*y  + (a - 2)y                     }
     {  3           2                 2                        }
     {2x  + (a + 2)x y + (- 2a - 2)x*y                         }
     {         3              2               2            3   }
     {(2a - 1)x  + (- 2a - 1)x y + (2a + 1)x*y  + (2a - 2)y    }
     {          3              2               2              3}
     {(- a + 2)x  + (- 2a - 1)x y + (2a - 1)x*y  + (- 2a - 2)y }
     {           3            2               3                }
     {(- 2a - 1)x  + (2a + 2)x y + (- 2a - 2)y                 }
     {    3           2              3                         }
     {2a*x  + (a - 1)x y + (- a + 2)y                          }
     {        3             2                 2       3        }
     {(a - 1)x  + (- a - 1)x y + (- 2a - 2)x*y  - 2a*y         }

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

See also