class DiagonalPolynomialRing:
"""
The ring of diagonal polynomials in n x r variables + n x inert variables
EXAMPLES::
sage: DiagonalPolynomialRing(QQ, n, r, inert=0)
"""
def young_idempotent(self, p, mu):
def polarization(self, p, ...):
...
class DiagonalAntisymmetricPolynomials:
"""
The subspace of diagonal polynomials that are antisymmetric w.r.t. certain variables
Polynomials are represented by picking within each orbit of monomials a canonical one.
"""
def from_polynomial(self, p):
'''Create an element from a fully expanded antisymmetric polynomial'''
def young_idempotent(self, p):
''''''
def polarization()
'''compute usual polarization and renormalize'''
def PolarizationSpace(P, generators, mu, r, use_symmetry=, verbose=, use_lie, use_commutativity???=):
"""
Starting from polynomials in the mu-isotypic component of the polynomial ring in one set of variables (possibly with additional inert variables), construct the space obtained by polarization.
P: a diagonal polynomial ring (or assymmetric version)
generators: polynomials in one set of variables (+inert) in the image of b_mu
"""
def harmonic_XXX(mu, n):
'''construct a basis of the mu-isotypic component of harmonic polynomials in n variables through higher specht polynomials'''
def YYY(mu, nu, n):
'''The analogue for Pauline's case'''