116 lines
3.2 KiB
C
116 lines
3.2 KiB
C
#ifndef WEYL_H
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#define WEYL_H
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#include <inttypes.h>
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struct _simple_type;
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struct _semisimple_type;
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struct _weylgroup_element;
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struct _weylgroup;
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struct _doublecoset;
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struct _doublecoset_list;
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struct _doublequotient;
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typedef uint64_t weylid_t;
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typedef struct _simple_type simple_type_t;
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typedef struct _semisimple_type semisimple_type_t;
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typedef struct _weylgroup_element weylgroup_element_t;
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typedef struct _weylgroup weylgroup_t;
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typedef struct _doublecoset doublecoset_t;
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typedef struct _doublecoset_list doublecoset_list_t;
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typedef struct _doublequotient doublequotient_t;
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/***************************** structures *******************************/
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struct _simple_type {
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char series;
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int rank;
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};
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struct _semisimple_type {
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int n;
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simple_type_t *factors;
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};
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struct _weylgroup_element {
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int *word;
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int wordlength;
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weylgroup_element_t **left;
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weylgroup_element_t **right;
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weylgroup_element_t *opposite;
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int is_root_reflection; // boolean value
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weylid_t id; // a unique id
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int index;
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// only set if quotient is generated
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doublecoset_t *coset;
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};
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struct _weylgroup {
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semisimple_type_t type;
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weylgroup_element_t *elements;
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weylgroup_element_t **lists;
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int *letters;
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};
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struct _doublecoset {
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doublecoset_list_t *bruhat_lower;
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doublecoset_list_t *bruhat_higher;
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doublecoset_t *opposite;
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weylgroup_element_t *max;
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weylgroup_element_t *min;
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int index;
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};
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struct _doublecoset_list {
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doublecoset_t *to;
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doublecoset_list_t *next;
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};
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struct _doublequotient {
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semisimple_type_t type;
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int left_invariance; // bitmask with rank bits
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int right_invariance;
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int count; // number of double cosets
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doublecoset_t *cosets;
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weylgroup_element_t *group;
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doublecoset_list_t *lists; // only for memory allocation / freeing
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weylgroup_element_t **grouplists; // only for memory allocation / freeing
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int *groupletters; // only for memory allocation / freeing
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};
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/***************************** functions **************************************/
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/* query some basic information on root systems / Weyl groups */
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// the rank
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int weyl_rank(semisimple_type_t type);
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// the order of the weyl group
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int weyl_order(semisimple_type_t type);
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// the number of reduced positive roots
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int weyl_positive(semisimple_type_t type);
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// the Cartan matrix (has rank columns and rank rows)
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void weyl_cartan_matrix(semisimple_type_t type, int *m);
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// the opposition involution as a map from simple roots to simple roots (indexed from 0 to rank-1)
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int weyl_opposition(semisimple_type_t type, int simple_root);
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/* generate the Weyl group:
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weyl_destroy() has to be used to free memory
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*/
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weylgroup_t *weyl_generate(semisimple_type_t type);
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void weyl_destroy(weylgroup_t *group);
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/* generate a double quotient of the Weyl group and its Bruhat order:
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left_invariance and right_invariance are bitmaps specifying a subset of the simple roots
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The Weyl group will be quotiented from the left and right by the subgroups generated by these simple root reflections
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weyl_destroy_bruhat() has to be used to free memory
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*/
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doublequotient_t *weyl_generate_bruhat(semisimple_type_t type, int left_invariance, int right_invariance);
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void weyl_destroy_bruhat(doublequotient_t *dq);
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#endif
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