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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 = .245600383416702

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

o2 = .806357253741775684985725808832+.935762538593725379196737991294*ii

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

o3 = Tally{-1 => 8 }
           -2 => 12
           -3 => 8
           -4 => 8
           -5 => 8
           0 => 10
           1 => 9
           2 => 8
           3 => 7
           4 => 15
           5 => 8

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

      38    35    34    30    29    26    24    19    18    17    14    13  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      11    9    8    5    4    2
     a   + 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 = 8x  + 9x y + 2x y  + 4x y  + x*y  + 4y

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