virasoro -- the construction of Virasoro algebras

Synopsis

• Usage:
virasoro(kk)
• Inputs:
• kk, a ring, the coefficient ring
• Outputs:
• a list, of the polynomials in the system

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).

 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