schurPolynomial(List,Partition,PolynomialRing) -- a method for constructing Schur polynomials

Synopsis

• Function: schurPolynomial

• Usage:

  schurPolynomial(indices,parti,R)

• Inputs:
  • indices, a list, a list of the variables that appear in each column of the matrix
  • parti, an instance of the type Partition, a partition that indexes the Schur polynomial
  • R, a polynomial ring,
• Optional inputs:
  • AsExpression => ..., default value false, an optional argument that returns polynomials as expressions
  • Strategy (missing documentation) => ..., default value "semistandard_tableaux",
• Outputs:
  • a matrix,

Description

i1 : R = QQ[x_0..x_4]

o1 = R

o1 : PolynomialRing

i2 : M = generalizedVandermondeMatrix({0,2,3},{1,3,5},R)

o2 = | x_0   x_2   x_3   |
     | x_0^3 x_2^3 x_3^3 |
     | x_0^5 x_2^5 x_3^5 |

             3      3
o2 : Matrix R  <-- R

i3 : (determinant M)//vandermondeDeterminant({0,2,3},R)

      3 2      2 3      3   2     2 2 2      3 2    2   3      2 3
o3 = x x x  + x x x  + x x x  + 2x x x  + x x x  + x x x  + x x x
      0 2 3    0 2 3    0 2 3     0 2 3    0 2 3    0 2 3    0 2 3

o3 : R