randomBinaryForm -- random homogeneous polynomial in two variables

Usage:

randomBinaryForm d

randomBinaryForm(d,r,c)

randomBinaryForm(d,r,)

randomBinaryForm(d,,c)
Inputs:
- d, an integer
- r, an integer
- c, an integer
Optional inputs:
- Variable => ..., default value "t", specify a name for a variable
Outputs:
- a ring element, a random binary form of degree d, real rank r and complex rank c

Description

i1 : setRandomSeed 2
 -- setting random seed to 2

o1 = 2

i2 : F = randomBinaryForm 5

         5      4        3 2       2 3        4      5
o2 = 240t  + 72t t  + 84t t  + 288t t  + 80t t  + 45t
         0      0 1      0 1       0 1      0 1      1

o2 : QQ[t ..t ]
         0   1

i3 : F = randomBinaryForm(5,4,3)

                         5                        4    
o3 = 3632847812679562677t  + 64366001823879435600t t  -
                         0                        0 1  
     ------------------------------------------------------------------------
                           3 2                        2 3  
     106392032652111552000t t  - 39170346880997376000t t  +
                           0 1                        0 1  
     ------------------------------------------------------------------------
                            4                        5
     14107325283586560000t t  + 98119710255335593600t
                          0 1                        1

o3 : QQ[t ..t ]
         0   1

i4 : (realrank F,complexrank F)

o4 = (4, 3)

o4 : Sequence

i5 : F = randomBinaryForm(6,4,4)

                           6                          5    
o5 = 300520202301371515365t  - 2069614352168054125560t t  +
                           0                          0 1  
     ------------------------------------------------------------------------
                            4 2                          3 3  
     5985932490977412481200t t  - 9195475372651897862400t t  +
                            0 1                          0 1  
     ------------------------------------------------------------------------
                            2 4                            5  
     8133439679423489491200t t  - 4300375337403805900800t t  +
                            0 1                          0 1  
     ------------------------------------------------------------------------
                            6
     1252983305456129492992t
                            1

o5 : QQ[t ..t ]
         0   1

i6 : (realrank F,complexrank F)

o6 = (4, 4)

o6 : Sequence

Ways to use randomBinaryForm:

randomBinaryForm(ZZ)
randomBinaryForm(ZZ,Ring)
randomBinaryForm(ZZ,Thing,Thing)
randomBinaryForm(ZZ,Thing,Thing,Ring)

For the programmer

The object randomBinaryForm is a method function with options.

The source of this document is in CoincidentRootLoci/documentation.m2:335:0.

randomBinaryForm -- random homogeneous polynomial in two variables

Description

See also

Ways to use randomBinaryForm:

For the programmer