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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 = .735960520559775

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

o2 = .862815234551484611559649172703+.156204193304093503288459926146*ii

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

o3 = Tally{-1 => 12}
           -2 => 10
           -3 => 6
           -4 => 3
           -5 => 9
           0 => 12
           1 => 8
           2 => 12
           3 => 8
           4 => 9
           5 => 12

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

      39    38    35    34    28    26    25    24    23    22    21    15  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      13    9    7    5
     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      2 3       4     5
o6 = 3x  + 2x y + 2x y  + 7x*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 = {- 2a*x  + (a - 2)x y + (a + 2)x*y  + y            }
     {          3       2       2            3          }
     {(- a - 2)x  + 2a*x y + x*y  + (2a + 1)y           }
     {        3       2               2             3   }
     {(a - 2)x  - 2a*x y + (2a + 1)x*y  + (- a + 2)y    }
     {         3    2               2           3       }
     {(2a - 1)x  + x y + (2a - 2)x*y  + (a + 2)y        }
     {        3    2         2       3                  }
     {(a - 1)x  + x y - a*x*y  - 2a*y                   }
     {          3    2         2             3          }
     {(- a + 1)x  + x y - a*x*y  + (- a - 1)y           }
     {           3             2        2              3}
     {(- 2a + 2)x  + (- a - 2)x y + 2x*y  + (- 2a + 2)y }

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

See also