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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 = .00103016502229669

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

o2 = .847630959376723263247390230883+.626602472657466552764440583349*ii

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

o3 = Tally{-1 => 8 }
           -2 => 11
           -3 => 9
           -4 => 6
           -5 => 5
           0 => 10
           1 => 14
           2 => 11
           3 => 9
           4 => 11
           5 => 7

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

      39    38    37    36    35    32    31    29    23    20    17    16  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      15    14    12    11    7    6    5    4    3
     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 = 5x  + 5x y + 9x y  + 4x y  + 9x*y  + 7y

o6 : R
i7 : R = GF(25,Variable=>a)[x,y];
i8 : VerticalList for i to 6 list random(3,R)

     {  3               2            3                    }
o8 = {2x  + (- a + 1)x*y  + (2a - 1)y                     }
     {   3         2             3                        }
     {a*x  + 2a*x*y  + (- a + 2)y                         }
     {        3           2       2             3         }
     {(a + 2)x  + (a + 2)x y + x*y  + (- a - 2)y          }
     {      3              2               2      3       }
     {- 2a*x  + (- 2a - 2)x y + (2a - 1)x*y  - a*y        }
     {    3              2                 2             3}
     {2a*x  + (- 2a + 1)x y + (- 2a + 2)x*y  + (- a - 2)y }
     {    3      2       3                                }
     {- 2x  - a*x y + a*y                                 }
     {      3            2        2    3                  }
     {- 2a*x  + (2a + 2)x y - 2x*y  - y                   }

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

See also