next | previous | forward | backward | up | top | index | toc | Macaulay2 web site

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 = .753276088263001

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

o2 = .805533580343320393391082353451+.292562114779475286910740803742*ii

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

o3 = Tally{-1 => 10}
           -2 => 11
           -3 => 12
           -4 => 5
           -5 => 8
           0 => 8
           1 => 14
           2 => 10
           3 => 8
           4 => 8
           5 => 7

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

      38    37    36    34    30    29    25    24    23    22    18    16  
o4 = a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   + a   +
     ------------------------------------------------------------------------
      15    14    13    11    9    6    5    3    2
     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 = 2x  + 9x y + 6x y  + 9x y  + 3x*y  + 5y

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

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