View 20220504-extended-dynkin-diagrams.tex
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\documentclass[10pt,a4paper]{article} % -*- coding: utf-8 -*- | |
\usepackage[a4paper,margin=1.5cm]{geometry} | |
\usepackage[english]{babel} | |
\usepackage[utf8]{inputenc} | |
\usepackage[T1]{fontenc} | |
\usepackage{times} | |
\usepackage{amsmath} | |
\usepackage{amsfonts} | |
\usepackage{amssymb} | |
\usepackage{amsthm} |
View shape-of-c3.sage
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C = CartanType("C3") | |
rk = C.rank() | |
detcmat = C.cartan_matrix().det() | |
invcmat = C.cartan_matrix().inverse() | |
WCR = WeylCharacterRing(C) | |
WR = WeightRing(WCR) | |
# Fundamental coweights: | |
fundcoweights = dict([(i+1, sum([invcmat[i][j]*WCR.simple_coroots()[j+1] for j in range(rk)])) for i in range(rk)]) | |
# Coefficients of highest root: | |
hwcf = [WCR.highest_root().scalar(fundcoweights[j]) for j in range(1,rk+1)] |
View OrbitControls.js
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console.warn( "THREE.OrbitControls: As part of the transition to ES6 Modules, the files in 'examples/js' were deprecated in May 2020 (r117) and will be deleted in December 2020 (r124). You can find more information about developing using ES6 Modules in https://threejs.org/docs/index.html#manual/en/introduction/Import-via-modules." ); | |
/** | |
* @author qiao / https://github.com/qiao | |
* @author mrdoob / http://mrdoob.com | |
* @author alteredq / http://alteredqualia.com/ | |
* @author WestLangley / http://github.com/WestLangley | |
* @author erich666 / http://erichaines.com | |
* @author ScieCode / http://github.com/sciecode | |
*/ |
View example.vote
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A>B>C>D: 00.00% | |
A>B>D>C: 05.60% | |
A>C>B>D: 06.80% | |
A>C>D>B: 07.00% | |
A>D>B>C: 01.50% | |
A>D>C>B: 06.30% | |
B>A>C>D: 04.40% | |
B>A>D>C: 06.70% | |
B>C>A>D: 02.30% | |
B>C>D>A: 06.60% |
View perlscoping.pl
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#! /usr/local/bin/perl -w | |
use strict; | |
use warnings; | |
for ( my $i=0 ; $i<5 ; $i++ ) { | |
my $var; | |
sub returnvar { return $var; } | |
$var = $i; | |
print "\$i=$i, \$var=$var, returnvar returns ", returnvar, "\n"; | |
} |
View thornify.js
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// JavaScript functions to replace "th" by the letter thorn throughout | |
// a document. Use this with `thornifyDoc(window.document)`. | |
// Written by David A. Madore, 2022-04-02. Public Domain. | |
function thornifyString(s) { | |
return s.replace(/T[Hh]/g, "\u00DE").replace(/th/g, "\u00FE"); | |
} | |
function thornifyDoc(doc) { |
View q-analog-plots-on-unit-circle.sage
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### The case of E_6 | |
WCR = WeylCharacterRing("E6", style="coroots") | |
weylcovec = sum([rt.associated_coroot() for rt in WCR.positive_roots()])/2 | |
R.<t> = QQ['t'] | |
weyldenom = prod([t^rt.scalar(weylcovec)-1 for rt in WCR.positive_roots()]) | |
weylnumertab = [None] + [prod([t^(rt.scalar(weylcovec)+(1 if WCR.fundamental_weights()[i].scalar(rt.associated_coroot())>0 else 0))-1 for rt in WCR.positive_roots()]) for i in range(1,6+1)] | |
counttab = [None] + [R(weylnumertab[i]/weyldenom) for i in range(1,6+1)] | |
def realize(pol): | |
d = pol.degree() | |
def v(x): |
View gamma-ticks.pl
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#! /usr/local/bin/perl -w | |
# Generate a ticking sound where the intervals between ticks are | |
# distributed following a Gamma distribution. | |
# Produces raw 48k 16-bit signed single channel audio. So pipe this to: | |
# sox -t raw -r 48k -c 1 -e signed -b 16 -L - -t wav ticks.wav | |
# Command-line parameters are: | |
# -r <number>: the average tick rate in ticks per second (defaults to 2) |
View tileable-fractals.sage
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# Base 3-w where w is a 6-th root of unity | |
w = N(exp(I*pi/3)) | |
def dragonpoints(depth): | |
if depth <= 0: | |
return [(1+w)/3] | |
else: | |
parta = [z+1 for z in dragonpoints(depth-1)] | |
partb = [z/w+w for z in dragonpoints(depth-1)] | |
partc = [z+w for z in dragonpoints(depth-1)] | |
return [z/(3-w) for z in parta+partb+partc] |
View stoermers-problem.sage
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# Return cnt solutions of the Pell-Fermat equation x^2 - d*y^2 = 1 | |
def pell_equation(d, cnt): | |
if cnt < 1: | |
return [] | |
# First, find the "fundamental" solution | |
cf = continued_fraction(QQbar(sqrt(d))) | |
i = 0 | |
(xfun,yfun) = (None,None) | |
while True: | |
r = cf.convergent(i) |
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