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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 = .0447273218537463

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

o2 = .507378543215778430103665672598+.323167966802742914230339036767*ii

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

o3 = Tally{-1 => 10}
           -2 => 9
           -3 => 10
           -4 => 7
           -5 => 11
           0 => 5
           1 => 8
           2 => 7
           3 => 6
           4 => 15
           5 => 13

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

      39    37    35    33    28    26    25    21    19    18    17    13  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      11    10    9    8    2
     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 = x  + 6x y + 7x y  + 6x*y  + 8y

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

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

See also