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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 = .68628282708965

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

o2 = .278484852345358256591881528155+.286962866250356863724447972901*ii

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

o3 = Tally{-1 => 14}
           -2 => 7
           -3 => 12
           -4 => 4
           -5 => 8
           0 => 6
           1 => 10
           2 => 12
           3 => 10
           4 => 7
           5 => 11

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

      38    36    35    34    33    30    28    26    24    23    22    21  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      20    19    18    16    15    14    13    11    9    2
     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     3 2    2 3       4     5
o6 = 7x  + 5x y  + x y  + 3x*y  + 2y

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