@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2010-05-15 02:14:23 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-22 03:16:05 UTC</tt>.<br>
-: The original revision id was <tt>142172981</tt>.<br>
+: The original revision id was <tt>143888077</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>
@@ Line 67: / Line 67: @@
 The point of steps three and four is that now the vals on the list correspond to a list of generators which are all positive (written additively) or equivalently greater than 1 (written multiplicatively.) Just as a normal comma list can be used to classify an abstract regular temperament, so can a normal val list. The val list is what on [[Graham Breed]]'s [[http://x31eq.com/temper/|web site]]  is called a "mapping", put into a canonical form.
+==Maple code==
+Below is Maple code for finding the normal interval and val list, given an interval list or a val list.
+with(padic, ordp):
+with(LinearAlgebra):
+log2 := proc(x) evalf(ln(x)/ln(2)) end:
+pril := proc(n)
+ # log2 of first n primes
+local i, u;
+u := NULL;
+for i from 1 to n do
+u := u,log2(ithprime(i)) od;
+[u] end:
+revlist := proc(l)
+ # reverse of list
+local i, v, e;
+e := nops(l);
+for i from 1 to e do
+v[i] := l[e-i+1] od;
+convert(convert(v,array),list) end:
+plim := proc(q)
+ # prime limit of rational number q
+local r, i, p;
+r := 1;
+i := 0;
+while not (r=q) do
+i := i+1;
+p := ithprime(i);
+r := r*p^ordp(q, p) od;
+i end:
+rat2monz := proc(q, n)
+ # converts rational number q to monzo of length n
+local v, i;
+for i from 1 to n do
+v[i] := ordp(q, ithprime(i)) od;
+convert(convert(v, array), list) end:
+monz2rat := proc(m)
+ # converts monzo to rational number
+local i, t;
+t := 1;
+for i from 1 to nops(m) do
+t := t * ithprime(i)^m[i] od;
+t end:
+herm := proc(l)
+ # hermite normal form of listlist l
+local M;
+M := Matrix(l);
+convert(convert(HermiteForm[Z](M), array), listlist) end:
+nori := proc(l)
+ # normal interval list from list of intervals l
+local i, p, u, v, w;
+p := 1;
+for i from 1 to nops(l) do
+p := max(p, plim(l[i])) od;
+u := [];
+for i from 1 to nops(l) do
+u := [op(u), revlist(rat2monz(l[i], p))] od;
+v := herm(u);
+for i from 1 to nops(l) do
+u := revlist(v[i]);
+u := monz2rat(u);
+w[i] := u od;
+u := [];
+for i from 1 to nops(l) do
+v := w[i];
+if v&lt;1 then v:=1/v fi;
+if not v=1 then u := [op(u), v] fi od;
+revlist(u) end:
+norv := proc(l)
+ # normal val list from list of vals l
+local M, N, u, v, i, j, a;
+u := herm(l);
+j := Rank(Matrix(u));
+v := NULL:
+for i from 1 to j do
+v := v,u[i] od;
+v := [v];
+M := Matrix(v);
+N := SubMatrix(M, 1..j, 1..j);
+N := N^(-1);
+a := Vector[row](pril(j));
+a := a.N;
+u := NULL;
+for i from 1 to j do
+if a[i] &lt; 0 then u := u,-v[i] fi;
+if a[i] &gt;= 0 then u := u,v[i] fi od;
+[u] end:
 </pre></div>
 <h4>Original HTML content:</h4>
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 [1 log2(3) log2(5) ... log2(p)]. If the ith entry in the result is negative, multiply the corresponding val by -1. Return the result as the normalized val list.&lt;br /&gt;
 &lt;br /&gt;
-The point of steps three and four is that now the vals on the list correspond to a list of generators which are all positive (written additively) or equivalently greater than 1 (written multiplicatively.) Just as a normal comma list can be used to classify an abstract regular temperament, so can a normal val list. The val list is what on &lt;a class="wiki_link" href="/Graham%20Breed"&gt;Graham Breed&lt;/a&gt;'s &lt;a class="wiki_link_ext" href="http://x31eq.com/temper/" rel="nofollow"&gt;web site&lt;/a&gt;  is called a &amp;quot;mapping&amp;quot;, put into a canonical form.&lt;/body&gt;&lt;/html&gt;</pre></div>
+The point of steps three and four is that now the vals on the list correspond to a list of generators which are all positive (written additively) or equivalently greater than 1 (written multiplicatively.) Just as a normal comma list can be used to classify an abstract regular temperament, so can a normal val list. The val list is what on &lt;a class="wiki_link" href="/Graham%20Breed"&gt;Graham Breed&lt;/a&gt;'s &lt;a class="wiki_link_ext" href="http://x31eq.com/temper/" rel="nofollow"&gt;web site&lt;/a&gt;  is called a &amp;quot;mapping&amp;quot;, put into a canonical form.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Maple code"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Maple code&lt;/h2&gt;
+Below is Maple code for finding the normal interval and val list, given an interval list or a val list.&lt;br /&gt;
+&lt;br /&gt;
+with(padic, ordp):&lt;br /&gt;
+with(LinearAlgebra):&lt;br /&gt;
+&lt;br /&gt;
+log2 := proc(x) evalf(ln(x)/ln(2)) end:&lt;br /&gt;
+&lt;br /&gt;
+pril := proc(n)&lt;br /&gt;
+ # log2 of first n primes&lt;br /&gt;
+local i, u;&lt;br /&gt;
+u := NULL;&lt;br /&gt;
+for i from 1 to n do&lt;br /&gt;
+u := u,log2(ithprime(i)) od;&lt;br /&gt;
+[u] end:&lt;br /&gt;
+&lt;br /&gt;
+revlist := proc(l)&lt;br /&gt;
+ # reverse of list&lt;br /&gt;
+local i, v, e;&lt;br /&gt;
+e := nops(l);&lt;br /&gt;
+for i from 1 to e do&lt;br /&gt;
+v[i] := l[e-i+1] od;&lt;br /&gt;
+convert(convert(v,array),list) end:&lt;br /&gt;
+&lt;br /&gt;
+plim := proc(q)&lt;br /&gt;
+ # prime limit of rational number q&lt;br /&gt;
+local r, i, p;&lt;br /&gt;
+r := 1;&lt;br /&gt;
+i := 0;&lt;br /&gt;
+while not (r=q) do&lt;br /&gt;
+i := i+1;&lt;br /&gt;
+p := ithprime(i);&lt;br /&gt;
+r := r*p^ordp(q, p) od;&lt;br /&gt;
+i end:&lt;br /&gt;
+&lt;br /&gt;
+rat2monz := proc(q, n)&lt;br /&gt;
+ # converts rational number q to monzo of length n&lt;br /&gt;
+local v, i;&lt;br /&gt;
+for i from 1 to n do&lt;br /&gt;
+v[i] := ordp(q, ithprime(i)) od;&lt;br /&gt;
+convert(convert(v, array), list) end:&lt;br /&gt;
+&lt;br /&gt;
+monz2rat := proc(m)&lt;br /&gt;
+ # converts monzo to rational number&lt;br /&gt;
+local i, t;&lt;br /&gt;
+t := 1;&lt;br /&gt;
+for i from 1 to nops(m) do&lt;br /&gt;
+t := t * ithprime(i)^m[i] od;&lt;br /&gt;
+t end:&lt;br /&gt;
+&lt;br /&gt;
+herm := proc(l)&lt;br /&gt;
+ # hermite normal form of listlist l&lt;br /&gt;
+local M;&lt;br /&gt;
+M := Matrix(l);&lt;br /&gt;
+convert(convert(HermiteForm[Z](M), array), listlist) end:&lt;br /&gt;
+&lt;br /&gt;
+nori := proc(l)&lt;br /&gt;
+ # normal interval list from list of intervals l&lt;br /&gt;
+local i, p, u, v, w;&lt;br /&gt;
+p := 1;&lt;br /&gt;
+for i from 1 to nops(l) do&lt;br /&gt;
+p := max(p, plim(l[i])) od;&lt;br /&gt;
+u := [];&lt;br /&gt;
+for i from 1 to nops(l) do&lt;br /&gt;
+u := [op(u), revlist(rat2monz(l[i], p))] od;&lt;br /&gt;
+v := herm(u);&lt;br /&gt;
+for i from 1 to nops(l) do&lt;br /&gt;
+u := revlist(v[i]);&lt;br /&gt;
+u := monz2rat(u);&lt;br /&gt;
+w[i] := u od;&lt;br /&gt;
+u := [];&lt;br /&gt;
+for i from 1 to nops(l) do&lt;br /&gt;
+v := w[i];&lt;br /&gt;
+if v&amp;lt;1 then v:=1/v fi;&lt;br /&gt;
+if not v=1 then u := [op(u), v] fi od;&lt;br /&gt;
+revlist(u) end:&lt;br /&gt;
+&lt;br /&gt;
+norv := proc(l)&lt;br /&gt;
+ # normal val list from list of vals l&lt;br /&gt;
+local M, N, u, v, i, j, a;&lt;br /&gt;
+u := herm(l);&lt;br /&gt;
+j := Rank(Matrix(u));&lt;br /&gt;
+v := NULL:&lt;br /&gt;
+for i from 1 to j do&lt;br /&gt;
+v := v,u[i] od;&lt;br /&gt;
+v := [v];&lt;br /&gt;
+M := Matrix(v);&lt;br /&gt;
+N := SubMatrix(M, 1..j, 1..j);&lt;br /&gt;
+N := N^(-1);&lt;br /&gt;
+a := Vector[row](pril(j));&lt;br /&gt;
+a := a.N;&lt;br /&gt;
+u := NULL;&lt;br /&gt;
+for i from 1 to j do&lt;br /&gt;
+if a[i] &amp;lt; 0 then u := u,-v[i] fi;&lt;br /&gt;
+if a[i] &amp;gt;= 0 then u := u,v[i] fi od;&lt;br /&gt;
+[u] end:&lt;/body&gt;&lt;/html&gt;</pre></div>

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