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Macaulay2Doc :: random(Type)

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 = .516475812081347

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

o2 = .980905726836456971449989587938+.690873568575421292696765555828*ii

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

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

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

      39    38    35    31    30    26    23    22    20    18    17    16  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      15    14    12    11    10    9    8    6    5    4    3
     a   + a   + a   + a   + a   + a  + a  + 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)

       5     4      3 2     2 3       4     5
o6 = 9x  + 3x y + 3x y  + 5x y  + 5x*y  + 6y

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

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

See also