.. _weyl_character_formula.at_ref:

weyl_character_formula.at Function References
=======================================================
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.. _find_ratvec_mod_vec_[ratvec]_v,_ratvec_w->int1:

find_ratvec_mod_vec
-------------------------------------------------
| ``find_ratvec_mod_vec:[ratvec] v, ratvec w->int`` Defined in line number 33.
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.. _reduce_ratvecs_mod_lattice_[ratvec]_s->[ratvec]1:

reduce_ratvecs_mod_lattice
-------------------------------------------------
| ``reduce_ratvecs_mod_lattice:[ratvec] S->[ratvec]`` Defined in line number 37.
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.. _w_orbit_torus_element_rootdatum_rd,ratvec_v->[ratvec]1:

W_orbit_torus_element
-------------------------------------------------
| ``W_orbit_torus_element:RootDatum rd,ratvec v->[ratvec]`` Defined in line number 44.
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.. _centralizer_rootdatum_rd,ratvec_v->rootdatum1:

centralizer
-------------------------------------------------
| ``centralizer:RootDatum rd,ratvec v->RootDatum`` Defined in line number 50.
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.. _qmodz_order_ratvec_v->int1:

QmodZ_order
-------------------------------------------------
| ``QmodZ_order:ratvec v->int`` Defined in line number 56.
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| Order of element of Q/Z
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.. _eval_char_t_vec_lambda,_ratvec_v,cyclotomicfield_f->cyclotomicfieldelement1:

eval_char_T
-------------------------------------------------
| ``eval_char_T:vec lambda, ratvec v,cyclotomicField F->cyclotomicFieldElement`` Defined in line number 60.
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.. _weyl_denominator_quotient_rootdatum_rd,_ratvec_v,cyclotomicfield_f->cyclotomicfieldelement1:

weyl_denominator_quotient
-------------------------------------------------
| ``weyl_denominator_quotient:RootDatum rd, ratvec v,cyclotomicField F->cyclotomicFieldElement`` Defined in line number 64.
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| Product of :math:`1-\exp(-alpha)(t)`  over all posroots :math:`\alpha`  making it nonzero
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.. _wcf_semisimple_simply_connected_rootdatum_rd,_vec_lambda,ratvec_v,cyclotomicfield_f->cyclotomicfieldelement1:

wcf_semisimple_simply_connected
-------------------------------------------------
| ``wcf_semisimple_simply_connected:RootDatum rd, vec lambda,ratvec v,cyclotomicField F->cyclotomicFieldElement`` Defined in line number 75.
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| Weyl character formula for finite dimensional with extremal weight lambda   at t=exp_1(v), in the semisimple simply connected case
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.. _wcf_rootdatum_rd,_vec_lambda,_ratvec_t,_cyclotomicfield_f->cyclotomicfieldelement1:

wcf
-------------------------------------------------
| ``wcf:RootDatum rd, vec lambda, ratvec t, cyclotomicField F->cyclotomicFieldElement`` Defined in line number 100.
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| Weyl character formula for finite dimensional with extremal weight lambda exp_1(v)
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.. _wcf_long_rootdatum_rd,_vec_lambda,ratvec_v,cyclotomicfield_f->(cyclotomicfieldelement,[cyclotomicfieldelement])1:

wcf_long
-------------------------------------------------
| ``wcf_long:RootDatum rd, vec lambda,ratvec v,cyclotomicField F->(cyclotomicFieldElement,[cyclotomicFieldElement])`` Defined in line number 110.
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| 

.. _wcf_rootdatum_rd,_vec_lambda,ratvec_v->cyclotomicfieldelement1:

wcf
-------------------------------------------------
| ``wcf:RootDatum rd, vec lambda,ratvec v->cyclotomicFieldElement`` Defined in line number 133.
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| 

.. _wcf_vec_lambda,(rootdatum_rd,ratvec_v)->cyclotomicfieldelement1:

wcf
-------------------------------------------------
| ``wcf:vec lambda,(RootDatum rd,ratvec v)->cyclotomicFieldElement`` Defined in line number 135.
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| 

.. _wcf_param_p,_ratvec_v->cyclotomicfieldelement1:

wcf
-------------------------------------------------
| ``wcf:Param p, ratvec v->cyclotomicFieldElement`` Defined in line number 137.
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.. _wcf_long_rootdatum_rd,_vec_lambda,ratvec_v->(cyclotomicfieldelement,[cyclotomicfieldelement])1:

wcf_long
-------------------------------------------------
| ``wcf_long:RootDatum rd, vec lambda,ratvec v->(cyclotomicFieldElement,[cyclotomicFieldElement])`` Defined in line number 140.
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| 

.. _wcf_long_vec_lambda,(rootdatum_rd,ratvec_v)->(cyclotomicfieldelement,[cyclotomicfieldelement])1:

wcf_long
-------------------------------------------------
| ``wcf_long:vec lambda,(RootDatum rd,ratvec v)->(cyclotomicFieldElement,[cyclotomicFieldElement])`` Defined in line number 143.
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| 

.. _wcf_strong_real_rootdatum_rd,_ratvec_lambda,ratvec_v->(rat,rat)1:

wcf_strong_real
-------------------------------------------------
| ``wcf_strong_real:RootDatum rd, ratvec lambda,ratvec v->(rat,rat)`` Defined in line number 161.
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| Weyl character formula for highest weight lambda evaluated on an element x   in T with x^2 in Z
| 

.. _wcf_strong_real_param_p,ratvec_v->(rat,rat)1:

wcf_strong_real
-------------------------------------------------
| ``wcf_strong_real:Param p,ratvec v->(rat,rat)`` Defined in line number 179.
| 
| Weyl character formula for finite dimensional p evaluated on an element x  in T with x^2 in Z
| 

.. _wcf_[vec]_weights,ratvec_v->cyclotomicfieldelement1:

wcf
-------------------------------------------------
| ``wcf:[vec] weights,ratvec v->cyclotomicFieldElement`` Defined in line number 185.
| 
| Evaluate sum of weights at t
| 

.. _torus_factor_x_realform_g->(rootdatum,ratvec)1:

torus_factor_x
-------------------------------------------------
| ``torus_factor_x:RealForm G->(RootDatum,ratvec)`` Defined in line number 194.
| 
| Torus factor of strong real form of x
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.. _wcf_report_realform_g,_vec_lambda,_ratvec_t->void1:

wcf_report
-------------------------------------------------
| ``wcf_report:RealForm G, vec lambda, ratvec t->void`` Defined in line number 198.
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| Output of Weyl character formula
| 

.. _wcf_report_param_p,ratvec_t->void1:

wcf_report
-------------------------------------------------
| ``wcf_report:Param p,ratvec t->void`` Defined in line number 203.
| 
| 

.. _wcf_report_realform_g,_int_height_bound,_ratvec_t->void1:

wcf_report
-------------------------------------------------
| ``wcf_report:RealForm G, int height_bound, ratvec t->void`` Defined in line number 207.
| 
| Run over all finite dimensionals up to height bound
|