Basic abstract temperament translation code - Revision history

Fredg999 category edits: Moving from Category:EA to Category:Exterior algebra using Cat-a-lot

2023-03-05T05:52:56Z

Moving from Category:EA to Category:Exterior algebra using Cat-a-lot

← Older revision		Revision as of 05:52, 5 March 2023
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	[[Category:code]]		[[Category:code]]
	[[Category:maple]]		[[Category:maple]]
	[[Category:EA]]		[[Category:Exterior algebra]]

Fredg999 category edits: Removing from Category:Algorithm using Cat-a-lot

2023-03-02T03:57:25Z

Removing from Category:Algorithm using Cat-a-lot

← Older revision		Revision as of 03:57, 2 March 2023
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	</pre>		</pre>

	~~[[Category:algorithm]]~~
	[[Category:code]]		[[Category:code]]
	[[Category:maple]]		[[Category:maple]]
	[[Category:EA]]		[[Category:EA]]

Cmloegcmluin: VEA → EA

2021-11-13T02:12:20Z

VEA → EA

← Older revision		Revision as of 02:12, 13 November 2021
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	[[Category:code]]		[[Category:code]]
	[[Category:maple]]		[[Category:maple]]
	[[Category:~~VEA~~]]		[[Category:EA]]

Cmloegcmluin: add VEA category

2021-10-11T17:33:59Z

add VEA category

← Older revision		Revision as of 17:33, 11 October 2021
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	[[Category:code]]		[[Category:code]]
	[[Category:maple]]		[[Category:maple]]
			[[Category:VEA]]

Xenwolf: fixed maple code

2020-05-28T20:57:50Z

fixed maple code

Show changes

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>spt3125: Imported revision 505938090 - Original comment:

2014-05-01T22:30:57Z

**Imported revision 505938090 - Original comment: **

← Older revision		Revision as of 22:30, 1 May 2014
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	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:~~genewardsmith~~\|~~genewardsmith~~]] and made on <tt>~~2011~~-06-~~18 21~~:05:50 UTC</tt>.<br>		: This revision was by author [[User:spt3125\|spt3125]] and made on <tt>2014-05-01 22:30:57 UTC</tt>.<br>
	: The original revision id was <tt>~~237496955~~</tt>.<br>		: The original revision id was <tt>505938090</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
	<h4>Original Wikitext content:</h4>		<h4>Original Wikitext content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">(code language: [[http://en.wikipedia.org/wiki/Maple_%28software%29\|Maple]])

			----


	ech := proc(l)		ech := proc(l)
	# reduced row echelon form of listlist l		# reduced row echelon form of listlist l
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	convert(LinearAlgebra[ReducedRowEchelonForm](M), listlist) end:		convert(LinearAlgebra[ReducedRowEchelonForm](M), listlist) end:

	relpar := proc(u, v)		relpar := proc(u, v)
	# relative parity of two permutations		# relative parity of two permutations
	local t;		local t;
Line 127:		Line 131:
	N := Matrix(N);		N := Matrix(N);
	N := LinearAlgebra[Transpose](N);		N := LinearAlgebra[Transpose](N);
	ech(convert(N, listlist)) end:		ech(convert(N, listlist)) end:</pre></div>
	</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Basic abstract temperament translation code</title></head><body><br />		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Basic abstract temperament translation code</title></head><body>(code language: <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Maple_%28software%29" rel="nofollow">Maple</a>)<br />
			<br />
			<hr />
			<br />
			<br />
	ech := proc(l)<br />		ech := proc(l)<br />
	<ol><li>reduced row echelon form of listlist l</li></ol>local M;<br />		<ol><li>reduced row echelon form of listlist l</li></ol>local M;<br />
Line 136:		Line 143:
	convert(LinearAlgebra[ReducedRowEchelonForm](M), listlist) end:<br />		convert(LinearAlgebra[ReducedRowEchelonForm](M), listlist) end:<br />
	<br />		<br />
	relpar := proc(u, v)<br />		relpar := proc(u, v)<br />
	<ol><li>relative parity of two permutations</li></ol>local t;<br />		<ol><li>relative parity of two permutations</li></ol>local t;<br />
	t := table('antisymmetric');<br />		t := table('antisymmetric');<br />

Wikispaces>genewardsmith: Imported revision 237496955 - Original comment:

2011-06-18T21:05:50Z

**Imported revision 237496955 - Original comment: **

← Older revision		Revision as of 21:05, 18 June 2011
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-06-18 18:04:39 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-06-18 21:05:50 UTC</tt>.<br>
	: The original revision id was <tt>~~237481247~~</tt>.<br>		: The original revision id was <tt>237496955</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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	dualproj := proc(w)		dualproj := proc(w)
	# dual projection map		# dual projection map
	convert(LinearAlgebra[IdentityMatrix](nops(w[1])), listlist)-w end:</pre></div>		convert(LinearAlgebra[IdentityMatrix](nops(w[1])), listlist)-w end:

			norc2e := proc(l)
			# normal comma list to rref
			local M, N;
			M := Matrix(l);
			N := LinearAlgebra[NullSpace](M);
			N := convert(N, list);
			N := Matrix(N);
			N := LinearAlgebra[Transpose](N);
			ech(convert(N, listlist)) end:
			</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Basic abstract temperament translation code</title></head><body><br />		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Basic abstract temperament translation code</title></head><body><br />
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	<br />		<br />
	dualproj := proc(w)<br />		dualproj := proc(w)<br />
	<ol><li>dual projection map</li></ol>convert(LinearAlgebra[IdentityMatrix](nops(w[1])), listlist)-w end:</body></html></pre></div>		<ol><li>dual projection map</li></ol>convert(LinearAlgebra[IdentityMatrix](nops(w[1])), listlist)-w end:<br />
			<br />
			norc2e := proc(l)<br />
			<ol><li>normal comma list to rref</li></ol>local M, N;<br />
			M := Matrix(l);<br />
			N := LinearAlgebra[NullSpace](M);<br />
			N := convert(N, list);<br />
			N := Matrix(N);<br />
			N := LinearAlgebra[Transpose](N);<br />
			ech(convert(N, listlist)) end:</body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 237481247 - Original comment:

2011-06-18T18:04:39Z

**Imported revision 237481247 - Original comment: **

New page

<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference: 
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-18 18:04:39 UTC</tt>. 
: The original revision id was <tt>237481247</tt>. 
: The revision comment was: <tt></tt> 
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it. 
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">
ech := proc(l)
# reduced row echelon form of listlist l
local M;
M := Matrix(l);
convert(LinearAlgebra[ReducedRowEchelonForm](M), listlist) end:

relpar := proc(u, v)
# relative parity of two permutations
local t;
t := table('antisymmetric');
t[op(u)] := 1;
t[op(v)];
end:

pari := proc(u)
# parity of permutation u
local v;
v := sort(u);
relpar(u, v) end:

zerlist := proc(n)
# list of n 0s
local i, u;
u := NULL;
for i from 1 to n do
u := u,0 od;
[u] end:

denomlist := proc(w)
map(denom, w) end:

cleardenom := proc(w)
local n;
n := ilcm(op(denomlist(w)));
n * w end:

vec2e := proc(w)
# rref temperament identifier from val list or projection matrix w
local i, u, v, z;
u := ech(w);
z := NULL;
for i from 1 to nops(u) do
v := u[i];
if not convert(v, set)={0} then
z := z,v fi od:
[z] end:

wedgie := proc(w)
# reduction of multivector w to wedgie
local i, n, u;
u := cleardenom(w);
n := igcd(op(u));
if n=0 then RETURN(w) fi;
u := u/n;
for i from 1 to nops(w) do
if not u[i]=0 then
if u[i]>0 then RETURN(u) fi;
RETURN(-u) fi od end:

mvec := proc(l)
# multivector wedge product of vector list l
local c, i, j, k, q, r, t, u, v, w;
u := combinat[permute](nops(l));
c := combinat[choose](nops(l[1]), nops(l));
w := zerlist(nops(c));
for i from 1 to nops(c) do
t := c[i];
r := 0;
for j from 1 to nops(u) do
v := u[j];
q := pari(v);
for k from 1 to nops(v) do
q := q * l[v[k], t[k]] od;
r := r+q od;
w[i] := w[i]+r od;
w end:

wedgie2e := proc(w, n, p)
# rank n p-limit multival to rref
local b, c, i, j, k, m, u, v, x, y, z;
m := numtheory[pi](p);
b := combinat[choose](m, n);
c := combinat[choose](m, n-1);
z := NULL;
for i from 1 to nops(c) do
u := c[i];
v := NULL;
for j from 1 to m do
y := [op(u), j];
if nops(convert(y, set))<n then v:=v,0 fi;
x := sort(y);
for k from 1 to nops(b) do
if x=b[k] then v := v,relpar(b[k], y)*w[k] fi od od;
v := [v];
z := z,v od;
vec2e([z]) end:

e2wedgie := proc(l)
# rref l to wedgie
wedgie(mvec(l)) end:

e2frob := proc(l)
# rref or normal val list to Frobenius projection map
local U, V;
U := Matrix(l);
V := LinearAlgebra[Transpose](U);
convert(V.(U.V)^(-1).U, listlist) end:

dualproj := proc(w)
# dual projection map
convert(LinearAlgebra[IdentityMatrix](nops(w[1])), listlist)-w end:</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Basic abstract temperament translation code</title></head><body> 
ech := proc(l) 
<ol><li>reduced row echelon form of listlist l</li></ol>local M; 
M := Matrix(l); 
convert(LinearAlgebra[ReducedRowEchelonForm](M), listlist) end: 
 
relpar := proc(u, v) 
<ol><li>relative parity of two permutations</li></ol>local t; 
t := table('antisymmetric'); 
t[op(u)] := 1; 
t[op(v)]; 
end: 
 
pari := proc(u) 
<ol><li>parity of permutation u</li></ol>local v; 
v := sort(u); 
relpar(u, v) end: 
 
zerlist := proc(n) 
<ol><li>list of n 0s</li></ol>local i, u; 
u := NULL; 
for i from 1 to n do 
u := u,0 od; 
[u] end: 
 
denomlist := proc(w) 
map(denom, w) end: 
 
cleardenom := proc(w) 
local n; 
n := ilcm(op(denomlist(w))); 
n * w end: 
 
vec2e := proc(w) 
<ol><li>rref temperament identifier from val list or projection matrix w</li></ol>local i, u, v, z; 
u := ech(w); 
z := NULL; 
for i from 1 to nops(u) do 
v := u[i]; 
if not convert(v, set)={0} then 
z := z,v fi od: 
[z] end: 
 
wedgie := proc(w) 
<ol><li>reduction of multivector w to wedgie</li></ol>local i, n, u; 
u := cleardenom(w); 
n := igcd(op(u)); 
if n=0 then RETURN(w) fi; 
u := u/n; 
for i from 1 to nops(w) do 
if not u[i]=0 then 
if u[i]&gt;0 then RETURN(u) fi; 
RETURN(-u) fi od end: 
 
mvec := proc(l) 
<ol><li>multivector wedge product of vector list l</li></ol>local c, i, j, k, q, r, t, u, v, w; 
u := combinat[permute](nops(l)); 
c := combinat[choose](nops(l[1]), nops(l)); 
w := zerlist(nops(c)); 
for i from 1 to nops(c) do 
t := c[i]; 
r := 0; 
for j from 1 to nops(u) do 
v := u[j]; 
q := pari(v); 
for k from 1 to nops(v) do 
q := q * l[v[k], t[k]] od; 
r := r+q od; 
w[i] := w[i]+r od; 
w end: 
 
wedgie2e := proc(w, n, p) 
<ol><li>rank n p-limit multival to rref</li></ol>local b, c, i, j, k, m, u, v, x, y, z; 
m := numtheory[pi](p); 
b := combinat[choose](m, n); 
c := combinat[choose](m, n-1); 
z := NULL; 
for i from 1 to nops(c) do 
u := c[i]; 
v := NULL; 
for j from 1 to m do 
y := [op(u), j]; 
if nops(convert(y, set))&lt;n then v:=v,0 fi; 
x := sort(y); 
for k from 1 to nops(b) do 
if x=b[k] then v := v,relpar(b[k], y)*w[k] fi od od; 
v := [v]; 
z := z,v od; 
vec2e([z]) end: 
 
e2wedgie := proc(l) 
<ol><li>rref l to wedgie</li></ol>wedgie(mvec(l)) end: 
 
e2frob := proc(l) 
<ol><li>rref or normal val list to Frobenius projection map</li></ol>local U, V; 
U := Matrix(l); 
V := LinearAlgebra[Transpose](U); 
convert(V.(U.V)^(-1).U, listlist) end: 
 
dualproj := proc(w) 
<ol><li>dual projection map</li></ol>convert(LinearAlgebra[IdentityMatrix](nops(w[1])), listlist)-w end:</body></html></pre></div>