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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 = .472920014876514

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

o2 = .57667949204864623102946658012+.558186147049429915045062066902*ii

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

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

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

      39    36    34    32    29    28    27    26    24    23    19    17  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      16    13    12    11    10    9    8    7    6    4
     a   + a   + a   + a   + 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 = 4x  + 7x y + x y  + 3x y  + 7x*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  + x y - 2a*x*y  - 2a*y                       }
     {  2                 2           3                       }
     {2x y + (- 2a + 2)x*y  + (a - 2)y                        }
     {           3           2              2            3    }
     {(- 2a - 1)x  + (a - 2)x y + (a + 2)x*y  + (2a - 2)y     }
     {        3     2          2              3               }
     {(a - 1)x  + 2x y + 2a*x*y  + (- 2a + 2)y                }
     {  3            2          2           3                 }
     {2x  + (2a - 1)x y + 2a*x*y  + (a - 2)y                  }
     {           3           2        2     3                 }
     {(- 2a + 1)x  + (a - 2)x y - 2x*y  - 2y                  }
     {         3             2                2              3}
     {(2a - 1)x  + (- a - 1)x y + (- a + 2)x*y  + (- 2a + 1)y }

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

See also