Half_Idempotent.hpp File Reference

Contains the methods and classes for symmetric polynomials with half idempotent variables. More...

#include "Symmetric_Basis.hpp"
#include <sstream>
#include "impl/Half_Idempotent.ipp"

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Classes
struct	HalfIdempotentVariables< T, _deg, N >
	Variables \(x_1,...,x_n,y_1,...,y_n\) with \(y_i^2=y_i\) and \(|x_i|=1\), \(|y_i|=0\). More...
struct	TwistedChernVariables< T, _deg >
	The twisted Chern generators as variables \(\gamma_{s,j}\). More...
class	TwistedChernBasis< xy_poly_t, chern_poly_t >
	Class for half-idempotent symmetric polynomials. More...

Namespaces
	symmp
	The namespace which contains every method and class in the library.

Functions
template<class xy_poly_t , class chern_poly_t >
void	print_half_idempotent_relations (int n, bool print=1, bool verify=1, bool verify_verbose=1)
	Prints the relations of \(\Big(\mathbf Z[x_1,...,x_n,y_1,...,y_n]/(y_i^2=y_i)\Big)^{\Sigma_n}\). More...

Detailed Description

Contains the methods and classes for symmetric polynomials with half idempotent variables.

The goal is to solve the following problem: If

\[R=\mathbf Z[x_1,...,x_n,y_1,...,y_n]/(y_i^2=y_i)\]

produce minimal algebra generators for the fixed points of \(R\) under the \(\Sigma_n\) action (permuting the \(x_i,y_i\) separately), give an algorithm for writing a fixed point in terms of the generators and an algorithm for producing the relations of those generators.