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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 = .187364973676902

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

o2 = .170199887883966356964660378229+.0120186969951980338564747681866*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
           -1 => 1
           -1 => 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
           -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
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           0 => 1
           1 => 1
           1 => 1
           1 => 1
           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
           2 => 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
           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

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

      38    33    31    24    23    22    21    18    17    13    12    10  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      9    8    5    3    2
     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  + 2x y + 9x y  + 5x y  + 5x*y  + 9y

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

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

See also