This optional argument decides between two ways to calculate higherSpechtPolynomials. If it is set to to true then a calculation involving the row and column stabilizers is used. If it is set to false then another strategy is used. This strategy is based on a representation of higher specht polynomials as a multiplication of simpler Specht polynomials and Schur polynomials.
i1 : R = QQ[x_1..x_4] o1 = R o1 : PolynomialRing |
i2 : p = new Partition from {2,2}
o2 = Partition{2, 2}
o2 : Partition
|
i3 : S = youngTableau(p,{0,2,1,3})
o3 = | 0 2 |
| 1 3 |
o3 : YoungTableau
|
i4 : T = youngTableau(p,{0,1,2,3})
o4 = | 0 1 |
| 2 3 |
o4 : YoungTableau
|
i5 : higherSpechtPolynomial(S,T,R,Robust => true)
2 2 2 2 2 2 2 2
o5 = x x x - x x x + x x x - x x x - x x x + x x x - x x x + x x x
1 2 3 1 2 3 1 2 4 1 3 4 2 3 4 1 3 4 1 2 4 2 3 4
o5 : R
|
i6 : higherSpechtPolynomial(S,T,R,Robust => false)
2 2 2 2 2 2 2 2
o6 = x x x - x x x + x x x - x x x - x x x + x x x - x x x + x x x
1 2 3 1 2 3 1 2 4 1 3 4 2 3 4 1 3 4 1 2 4 2 3 4
o6 : R
|
This option is used mainly to check that the alternative algorithm proposed was correct.