schubmult.rings.free_algebra.elementary_basis¶

ElementaryBasis: free-algebra basis indexed by (composition, numvars), dual to products of elementary symmetric polynomials e_{c_1}(x_1..x_k) e_{c_2}(x_1..x_{k-1}) ... in nested variable sets. SchubertBasis expands into it via the monomials of S_{perm * w0}.

ElementaryBasis Objects¶

class ElementaryBasis(FreeAlgebraBasis)

Elementary symmetric function basis of the free algebra.

Keys are (tuple, int) pairs where the tuple encodes an elementary symmetric function composition and the integer is the number of variables.

is_key¶

@classmethod
def is_key(cls, x)

Return True if x is a (tuple/list, int) pair.

as_key¶

@classmethod
def as_key(cls, x)

Normalize x into a (tuple, int) key.

transition¶

@classmethod
def transition(cls, other_basis)

Return a transition function from ElementaryBasis to other_basis.

transition_schubert¶

@classmethod
def transition_schubert(cls, tup, numvars)

Transition an elementary key to the Schubert basis.

printing_term¶

@classmethod
def printing_term(cls, k)

Return an Elem-labelled display object for key k.