Atlas of Lie Groups and Representations

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atlas Library · Script File

extended_types.at

types of extended parameters:
1C+,1C-,1i1,1i2f,1i2s,1ic,1r1f,1r1s,1r2,1rn
2C+,2C-,2Ci,2Cr,2i11,2i12,2i22,2r22,2r21,2r11,2rn,2rc
3C+,3C-,3Ci,3Cr,3i,3r,3rn,3ic

In this module no effort is done to handle cases more efficiently by numeric
encoding, so types are simply short strings. Similarly we use |status_text|
from basic.at rather than the numeric codes from built-in |status|, for
readability.
Source
atlas-scripts/extended_types.at (104 lines)
Definitions
8
Loads
Loaded by
extended.at

Definitions in source order

ext_length 2 overloads

L17ext_length (RootDatum rd,mat delta, int j) = int
ext_length(rd,delta,j)=1,2,3
L22ext_length(int j, ExtParam E) = int
E=extended parameter, ext_length(j,E) = ext_length(ic(E),delta(E),j)

ext_type_1

L28ext_type_1(mat delta,int j,Param p) = string
ext_type has many cases, split cases by length
ext_type_1(delta,j,p)=1C+,1C-,1i1,1i2f,1i2s,1ic,1r1f,1r1s,1r2,1rn
j=index of root in integral-simple roots (not all simple roots)

ext_type_2

L38ext_type_2 (mat delta,int j,Param p) = string
ext_type_2(delta,j,p)=2C+,2C-,2Ci,2Cr,2i11,2i12,2i22,2r22,2r21,2r11,2rn,2rc
j=index of root in integral-simple roots (not in all simple roots)

ext_type_3

L63ext_type_3 (mat delta,int j,Param p) = string
ext_type_e(delta,j,p)=3C+3C-,3Ci,3Cr,3i,3r,3rn,3ic
j=index of root in integral-simple roots (not all simple roots)

ext_type 2 overloads

L83ext_type (mat delta,int j,Param p) = string
ext_type(delta,j,p)=ext_type_i(delta,j,p) where i=ext_length(G,delta,j)
j=index of root in integral-simple roots (not in all simple roots)
L98ext_type(int j,ExtParam E) = string
E=extended parameter, ext_type(j,E)=ext_type(delta,j,parameter(E))
j=index of root in integral-simple roots (not in all simple roots)

ext_types

L102ext_types(ExtParam (ic,delta,,,,,,,,):E) = [string]
E=extended parameter, ext_types=[ext_type(j,E)]

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