Gro-Tsen

#! /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";
}

Gro-Tsen

// 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) {

Gro-Tsen

### 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):

Gro-Tsen

#! /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)

Gro-Tsen

# 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]

Gro-Tsen

# 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)

Gro-Tsen

# Try to find an approximate pentagon in a square lattice:

# For this, we use LLL to try to find (v_0,v_1,v_2,v_3) four
# integer-valued vectors of size 2 such that v_1 is close to R(v_0),
# v_2 is close to R^2(v_0) and v_3 is close to R^3(v_0), where R is
# rotation by 2*pi/5, and v_0 is not too large.

# How much weight to give to the size of the approximation:
weight = 1/200

Gro-Tsen

size = 4
valtab = []
for n in range(2^(size*size)):
    m = Matrix(QQ,size,size,[(n>>i)&1 for i in range(size*size)])
    for v in m.eigenvalues():
        valtab.append(v)
numtab = [N(v) for v in valtab]

numdict = {}
for v in numtab:

Gro-Tsen

*** 2022-01-21
2022-01-14,545,2190
2022-01-15,473,2157
2022-01-16,436,2088
2022-01-17,528,2420
2022-01-18,437,2325
2022-01-19,437,2321
2022-01-20,338,1780
*** 2022-01-22
2022-01-14,545,2188

Gro-Tsen

#! /usr/local/bin/perl -w

# Find auto-descriptive sentences in English, such as the following:

# To do this, we iterate replacing a sentence by its description
# until, hopefully, we reach a fixed point.  Generally this won't
# happen (we hit a loop instead).  When this happens, we randomly
# change the initial blurb and try iterating again with this new blurb
# to break out of the loop.