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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 = .012076463749391

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

o2 = .809316917249454786526641670338+.630234257935574368673566176686*ii

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

o3 = Tally{-1 => 5 }
           -2 => 8
           -3 => 6
           -4 => 13
           -5 => 17
           0 => 8
           1 => 11
           2 => 12
           3 => 10
           4 => 5
           5 => 6

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

      39    32    31    30    23    22    21    19    18    12    11    7  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a  +
     ------------------------------------------------------------------------
      5    4    3
     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 = 6x  + 5x y + 2x y  + 6x y  + 8x*y  + 9y

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