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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 = .877375206329896

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

o2 = .857516836235018281449851477382+.408687714299446628035336181915*ii

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

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

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

      39    38    37    34    33    32    29    25    24    23    22    20  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      18    15    14    12    4
     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)

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

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