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ExampleSystems :: virasoro

virasoro -- the construction of Virasoro algebras

Synopsis

Description

This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-5250U CPU at 1.60GHz.

There were 256 solutions found in 0.356 seconds (with a Bezout bound of 256).

Reference: "Generalized Virasoro Constructions for SU(3)" by S. Schrans and W. Troost (pages 584-606).

See also: http://homepages.math.uic.edu/~jan/Demo/virasoro.html.

i1 : virasoro(QQ)

        2                                                                  
o1 = {8x  + 8x x  + 8x x  - 8x x  + 2x x  + 2x x  + 2x x  - 2x x  + 2x x  -
        1     1 2     1 3     2 3     1 4     1 5     1 6     5 6     1 7  
     ------------------------------------------------------------------------
                           2                                                
     2x x  - x , 8x x  + 8x  - 8x x  + 8x x  + 2x x  + 2x x  + 2x x  - 2x x 
       4 7    1    1 2     2     1 3     2 3     2 4     2 5     2 6     4 6
     ------------------------------------------------------------------------
                                                       2                  
     + 2x x  - 2x x  - x , - 8x x  + 8x x  + 8x x  + 8x  + 2x x  + 2x x  -
         2 7     5 7    2      1 2     1 3     2 3     3     3 4     3 5  
     ------------------------------------------------------------------------
                                                                   2        
     2x x  + 2x x  + 2x x  - 2x x  - x , 2x x  + 2x x  + 2x x  + 8x  - 2x x 
       4 5     3 6     3 7     6 7    3    1 4     2 4     3 4     4     3 5
     ------------------------------------------------------------------------
                                                                            
     + 8x x  - 2x x  + 2x x  - 2x x  + 2x x  + 6x x  - 6x x  - x , - 2x x  +
         4 5     2 6     4 6     1 7     4 7     4 8     5 8    4      3 4  
     ------------------------------------------------------------------------
                                       2                                  
     2x x  + 2x x  + 2x x  + 8x x  + 8x  - 2x x  + 2x x  - 2x x  + 2x x  -
       1 5     2 5     3 5     4 5     5     1 6     5 6     2 7     5 7  
     ------------------------------------------------------------------------
                                                                          
     6x x  + 6x x  - x , - 2x x  - 2x x  + 2x x  + 2x x  + 2x x  + 2x x  +
       4 8     5 8    5      2 4     1 5     1 6     2 6     3 6     4 6  
     ------------------------------------------------------------------------
               2                                                        
     2x x  + 8x  - 2x x  + 8x x  + 6x x  - 6x x  - x , - 2x x  - 2x x  -
       5 6     6     3 7     6 7     6 8     7 8    6      1 4     2 5  
     ------------------------------------------------------------------------
                                                               2          
     2x x  + 2x x  + 2x x  + 2x x  + 2x x  + 2x x  + 8x x  + 8x  - 6x x  +
       3 6     1 7     2 7     3 7     4 7     5 7     6 7     7     6 8  
     ------------------------------------------------------------------------
                                                                     2
     6x x  - x , - 6x x  - 6x x  + 6x x  + 6x x  + 6x x  + 6x x  + 8x  - x }
       7 8    7      4 5     6 7     4 8     5 8     6 8     7 8     8    8

o1 : List

Ways to use virasoro :

For the programmer

The object virasoro is a method function.