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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 = .847560702065222

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

o2 = .647546977185684098805139357664+.14063019510221549969698403186*ii

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

o3 = Tally{-1 => 9 }
           -2 => 8
           -3 => 7
           -4 => 10
           -5 => 11
           0 => 8
           1 => 9
           2 => 8
           3 => 10
           4 => 14
           5 => 7

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

      39    38    36    33    29    28    27    26    25    20    18    14  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      11    10    6    5    4    3
     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)

       4      3 2     2 3       4     5
o6 = 2x y + 3x y  + 9x y  + 6x*y  + 7y

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

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

See also