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Sage Macdonald

Sage Macdonald

Sage Macdonald

Sage Macdonald

Sage Macdonald

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Notation used in the definitions follows mainly [Mac]. Garsia, M. Bergeron, A. Haiman, and G. Tesler, Identities and positivity conjectures for some remarkable Sage Macdonald in the theory of symmetric functions, Methods Appl. Lapointe, A. Lascoux, J. Bergeron, M. Bases: sage. Returns the Macdonald polynomials on the H basis. Return Sage Macdonald value of the nabla operator applied to self.

If the parameter power is an integer then it calculates nabla to that integer. The default value of power is 1. Returns the qt-Hall scalar product between J part and P part. Returns the family of Sage Macdonald bases associated to the basis self. Multiply an element of the Macdonald symmetric function basis self and another symmetric function. Convert to the Schur basis, do the multiplication there, and convert back to self basis. It is implemented here by using a Pieri formula due to F.

Bergeron and M. Haiman [BH]. Returns the value of the nabla operator applied to self. The multiplication of the modified Schur functions behaves the same as the multiplication of the Schur functions.

This Sage Macdonald returns the qt-Hall scalar product between J part and P part. Proposition 5 of F. Haiman [BH] Shuichi Minamino. LLT symmetric functions. Monomial symmetric functions. Navigation index modules next previous Sage 9. Macdonald Polynomials ¶ Notation used in the definitions follows mainly [Mac]. BGHT 12 F. LLM 12 L. BH 12 F.

P Sym in the Macdonald P basis sage: Sym. P sage: P. P sage: MacP. Quick search. Created using Sphinx 3.

Sage Macdonald

Sage Macdonald

Sage Macdonald

Notation used in the definitions follows mainly [Mac].

Sage Macdonald

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Sage Macdonald

Sage Macdonald

Sage Macdonald

Sage Macdonald

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