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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 = .902282452699957

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

o2 = .547491168601894631347279860066+.846448804701059638211333427777*ii

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

o3 = Tally{-1 => 9 }
           -2 => 7
           -3 => 5
           -4 => 7
           -5 => 12
           0 => 8
           1 => 18
           2 => 8
           3 => 9
           4 => 7
           5 => 11

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

      39    37    36    35    30    29    28    26    24    16    13    12  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      9    8    5    4
     a  + a  + a  + a  + a

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 = x  + 9x y + 7x y  + 9x y  + x*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 - 1)x  + x y + 2a*x*y  + (- a - 1)y          }
     {   3           2               2    3             }
     {a*x  + (a - 1)x y + (2a - 2)x*y  - y              }
     {           3    2                 2       3       }
     {(- 2a - 2)x  - x y + (- 2a - 2)x*y  + 2a*y        }
     {  3     2              2                          }
     {2x  + 2x y + (a + 2)x*y                           }
     {      3              2                 2     3    }
     {- 2a*x  + (- 2a + 1)x y + (- 2a + 1)x*y  - 2y     }
     {           3      2               2            3  }
     {(- 2a - 1)x  + a*x y + (2a + 2)x*y  + (2a - 2)y   }
     {           3              2               2      3}
     {(- 2a + 1)x  + (- 2a + 1)x y + (2a - 2)x*y  - a*y }

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

See also