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Robust -- an optional argument for specifying the algorithm for calculating higherSpechtPolynomials

Description

This optional argument decides between two ways to calculate higherSpechtPolynomials. If it is set 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.

See also

Functions with optional argument named Robust :

For the programmer

The object Robust is a symbol.