Fokker block: Difference between revisions

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<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>2012-03-~~09 17~~:57:21 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-03-11 22:20:18 UTC</tt>.<br>

: The original revision id was <tt>~~309555482~~</tt>.<br>

: The original revision id was <tt>309917852</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>

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=First definition of a Fokker block=

Let us set ei = vi(2), and also P = e1 = v1(2), and choose n ~~positive~~ integers a1, ...., an with ak < P. Let ti = log2(ci), so that e1*t1+e2*t2+...+en*tn=1. Now define a function on the integers by

Let us set ei = vi(2), and also P = e1 = v1(2), and choose n non-negative integers a1, ...., an with 0 ≤ ak < P. Let ti = log2(ci), so that e1*t1+e2*t2+...+en*tn=1. Now define a function on the integers by

S[i] = floor((e1*i + a1)/P)*t1 + ... + floor((en*i + an)/P)*tn

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<br />

<h1 id="toc1"><a name="First definition of a Fokker block"></a>First definition of a Fokker block</h1>

Let us set ei = vi(2), and also P = e1 = v1(2), and choose n ~~positive~~ integers a1, ...., an with ak &lt; P. Let ti = log2(ci), so that e1*t1+e2*t2+...+en*tn=1. Now define a function on the integers by<br />

Let us set ei = vi(2), and also P = e1 = v1(2), and choose n non-negative integers a1, ...., an with 0 ≤ ak &lt; P. Let ti = log2(ci), so that e1*t1+e2*t2+...+en*tn=1. Now define a function on the integers by<br />

<br />

S[i] = floor((e1*i + a1)/P)*t1 + ... + floor((en*i + an)/P)*tn<br />

@@ 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>2012-03-09 17:57:21 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-03-11 22:20:18 UTC</tt>.<br>
-: The original revision id was <tt>309555482</tt>.<br>
+: The original revision id was <tt>309917852</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 21: / Line 21: @@
 =First definition of a Fokker block=
-Let us set ei = vi(2), and also P = e1 = v1(2), and choose n positive integers a1, ...., an with ak &lt; P. Let ti = log2(ci), so that e1*t1+e2*t2+...+en*tn=1. Now define a function on the integers by
+Let us set ei = vi(2), and also P = e1 = v1(2), and choose n non-negative integers a1, ...., an with 0 ≤ ak &lt; P. Let ti = log2(ci), so that e1*t1+e2*t2+...+en*tn=1. Now define a function on the integers by
 S[i] = floor((e1*i + a1)/P)*t1 + ... + floor((en*i + an)/P)*tn
@@ Line 89: / Line 89: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="First definition of a Fokker block"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;First definition of a Fokker block&lt;/h1&gt;
-Let us set ei = vi(2), and also P = e1 = v1(2), and choose n positive integers a1, ...., an with ak &amp;lt; P. Let ti = log2(ci), so that e1*t1+e2*t2+...+en*tn=1. Now define a function on the integers by&lt;br /&gt;
+Let us set ei = vi(2), and also P = e1 = v1(2), and choose n non-negative integers a1, ...., an with 0 ≤ ak &amp;lt; P. Let ti = log2(ci), so that e1*t1+e2*t2+...+en*tn=1. Now define a function on the integers by&lt;br /&gt;
 &lt;br /&gt;
 S[i] = floor((e1*i + a1)/P)*t1 + ... + floor((en*i + an)/P)*tn&lt;br /&gt;