Atlas of Lie Groups and Representations

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atlas Library · Script File

laurentPolynomial.at

laurent polynomial in indeterminate v with integer coefficients

([a_0,...,a_{m-1}],n) <-> v^n(a_0+a_1v + ...a_{m-1} v^{m-1})
Source
atlas-scripts/laurentPolynomial.at (102 lines)
Definitions
36
Loads
Loaded by
jantzen.at hodgeParamLaurentPol.at

Definitions in source order

i_laurent_poly type

L6
set_type i_laurent_poly = (vec w,int n)

Fields: w, n

( [0,a_0,...,a_m],n) = ([a_0,...,a_m],n+1)
 ([0^r,a_0,...,a_m],n) = ([a_0,...,a_m],n+r)  (cut off r leading zeros; n -> n+r)
 ([a_0,...,a_m],n) = ([0,a_0,...,a_m],n-1)
 ([a_0,...,a_m],n) = ([0^r,a_0,...,a_m],n-r)       (add r leading zeros; n -> n-r)
L8

normalize

L16normalize(i_laurent_poly (f,n)) = i_laurent_poly
normalize: a_0\ne 0

also defined in combinatorics.at

degree

L20degree(i_laurent_poly (f,n)) = int

also defined in cyclotomic.at, polynomial.at, character_tables.at

lowest_power

L21lowest_power(i_laurent_poly (f,n))

=

L23=(i_laurent_poly f,i_laurent_poly g) = bool

also defined in basic.at, combinatorics.at, modules.at, parabolics.at, synthetic.at, hash.at, tits.at, K_highest_weights.at, nilpotent_orbits.at, cyclotomic.at, polynomial.at, W_reps_type_BC.at, hodgeParamLaurentPol.at, hodgeParamPol.at, extended.at, disconnected.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at

poly_as_laurent_poly

L26poly_as_laurent_poly(i_poly f) = i_laurent_poly

laurent_poly_as_poly

L28laurent_poly_as_poly(i_laurent_poly f) = i_poly

constant_laurent_poly

L33constant_laurent_poly (int n) = i_laurent_poly

zero_laurent_poly

L34zero_laurent_poly = i_laurent_poly

v_laurent_power

L36v_laurent_power(int i) = i_laurent_poly
i can be negative

v_laurent

L37v_laurent = i_laurent_poly
v^1 as Laurent polynomial

v_minus_power

L39v_minus_power(int k) = i_laurent_poly

v_inverse

L41v_inverse = i_laurent_poly
1/v

v_laurent_squared

L42v_laurent_squared = v_laurent_power(2)
v^2

v_minus_two

L43v_minus_two = v_laurent_power(-2)
v^{-2}

poly

L47poly(i_laurent_poly (w,)) = i_poly
ignore the integer (shift) factor

shift

L49shift(i_laurent_poly (f,n),int shift) = i_laurent_poly

also defined in hodge_tensor.at, hodgeParamPol.at, lazy_lists.at

* 4 overloads

L53*(int c,i_laurent_poly f) = i_laurent_poly
L55*(i_laurent_poly f,i_laurent_poly g) = i_laurent_poly
L58*(i_poly f,i_laurent_poly g)
L59*(i_laurent_poly f,i_poly g)

also defined in basic.at, extParamPol.at, complex.at, modules.at, hodge_tensor.at, tits_centralizer.at, stable.at, synthetic.at, Weylgroup.at, group_operations.at, ratmat.at, tits.at, twisted_root_datum.at, cyclotomic.at, polynomial.at, hodgeParamLaurentPol.at, hodgeParamPol.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, hodge_functions.at, sparse.at, lazy_lists.at

+ 3 overloads

L61+(i_laurent_poly f,i_laurent_poly g) = i_laurent_poly
L67+(i_poly f,i_laurent_poly g)
L68+(i_laurent_poly f,i_poly g)

also in this file at line 71; also defined in basic.at, extParamPol.at, modules.at, ratmat.at, cyclotomic.at, polynomial.at, hodgeParamLaurentPol.at, hodgeParamPol.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, hodge_functions.at, lazy_lists.at

-

L69-(i_laurent_poly f,i_laurent_poly g) = i_laurent_poly

also in this file at line 72; also defined in basic.at, extParamPol.at, modules.at, ratmat.at, cyclotomic.at, polynomial.at, hodgeParamLaurentPol.at, hodgeParamPol.at, cyclotomicMat.at, hodge_functions.at, lazy_lists.at

+

L71+(i_laurent_poly f,int i) = i_laurent_poly

also in this file at line 61, line 67, line 68; also defined in basic.at, extParamPol.at, modules.at, ratmat.at, cyclotomic.at, polynomial.at, hodgeParamLaurentPol.at, hodgeParamPol.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, hodge_functions.at, lazy_lists.at

-

L72-(i_laurent_poly f,int i) = i_laurent_poly

also in this file at line 69; also defined in basic.at, extParamPol.at, modules.at, ratmat.at, cyclotomic.at, polynomial.at, hodgeParamLaurentPol.at, hodgeParamPol.at, cyclotomicMat.at, hodge_functions.at, lazy_lists.at

v_sum

L73v_sum = i_laurent_poly
v+1/v

at_q_inverse

L75at_q_inverse(i_laurent_poly (w,n)) = i_laurent_poly

laurent_poly_format

L77laurent_poly_format (i_laurent_poly (v,n), string q) = string

show

L94show(i_laurent_poly f) = void

also defined in modules.at, K_Nilpotent.at, good_W_representatives.at, arthur_parameters.at, sub_cells.at, associated_variety_annihilator.at, geck_generic.at, L_packet.at, ratmat.at, Levi_subgroups.at, nilpotent_orbits.at, subgroups.at, poset.at, cyclotomic.at, polynomial.at, character_tables.at, springer_tables.at, hodgeParamLaurentPol.at, hodgeParamPol.at, weak_packets.at, cyclotomic_Lie_algebra.at, cyclotomicMat.at, bracket.at, exceptional.at, nilpotent_posets.at, lazy_lists.at

g

L97g = (vec:[0,0,3,4,-2,4,0],-5)

also defined in nilpotent_posets.at

h

L98h = (vec:[0,0,3,4,-2,4,0],-8)

a

L100a = (vec:[1,1],0)

b

L101b = (vec:[1,1],-1)

c

L102c = (vec:[1,1],1)

Generated from atlas-scripts at commit 648506c (2026-10-13).