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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 = .143148067704005

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

o2 = .350747659336578577203061761544+.363943062082721632259869745*ii

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

o3 = Tally{-1 => 8 }
           -2 => 13
           -3 => 11
           -4 => 11
           -5 => 8
           0 => 10
           1 => 4
           2 => 9
           3 => 8
           4 => 12
           5 => 7

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

      38    37    36    35    34    33    30    28    25    21    17    15  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      14    13    12    10    5    3
     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 = 8x  + 3x y + 5x y  + 6x y  + 6x*y  + 5y

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