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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 = .425303184624877

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

o2 = .441322484115900824796287265844+.753911319772752650790883702946*ii

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

o3 = Tally{-1 => 1}
           -1 => 1
           -1 => 1
           -1 => 1
           -1 => 1
           -1 => 1
           -2 => 1
           -2 => 1
           -2 => 1
           -2 => 1
           -2 => 1
           -2 => 1
           -2 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -3 => 1
           -4 => 1
           -4 => 1
           -4 => 1
           -4 => 1
           -4 => 1
           -4 => 1
           -4 => 1
           -4 => 1
           -4 => 1
           -4 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           -5 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           1 => 1
           1 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           2 => 1
           3 => 1
           3 => 1
           3 => 1
           3 => 1
           3 => 1
           3 => 1
           3 => 1
           3 => 1
           3 => 1
           4 => 1
           4 => 1
           4 => 1
           4 => 1
           4 => 1
           4 => 1
           4 => 1
           4 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1
           5 => 1

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

      36    35    34    32    31    29    28    27    24    21    20    19  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      17    16    11    10    8    5    4    3    2
     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     2 3       4     5
o6 = 3x  + 8x y  + 7x*y  + 8y

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