Monzos and interval space
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2010-05-11 18:36:20 UTC.
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Original Wikitext content:
A [[Harmonic Limit|p-limit]] rational number q can by definition be factored into primes of size less than or equal to p, giving q = 2^e2 3^e3 ... p^ep, where the exponents are integers (positive, negative, or zero.) This is often written in [[http://mathworld.wolfram.com/Bra.html|bra vector]] notation as <e2 e3 ... ep|, in which case it is called a **monzo**, whee the name refers to the enthusiastic advocacy of [[Joe Monzo]]. The [[Tenney Height|Tenney height]] of this monzo is given by || <e2 e3 ... ep| || = |e2| + log2(3)|e3| + ... + log2(p) |ep| which is a [[http://en.wikipedia.org/wiki/Normed_vector_space|vector space norm]]. The monzos with this norm now define a [[http://en.wikipedia.org/wiki/Lattice_%28group%29|lattice]], which is a discrete subgroup spanning a finite dimensional real normed vector space.
Original HTML content:
<html><head><title>Monzos and Interval Space</title></head><body>A <a class="wiki_link" href="/Harmonic%20Limit">p-limit</a> rational number q can by definition be factored into primes of size less than or equal to p, giving q = 2^e2 3^e3 ... p^ep, where the exponents are integers (positive, negative, or zero.) This is often written in <a class="wiki_link_ext" href="http://mathworld.wolfram.com/Bra.html" rel="nofollow">bra vector</a> notation as <e2 e3 ... ep|, in which case it is called a <strong>monzo</strong>, whee the name refers to the enthusiastic advocacy of <a class="wiki_link" href="/Joe%20Monzo">Joe Monzo</a>.<br /> <br /> The <a class="wiki_link" href="/Tenney%20Height">Tenney height</a> of this monzo is given by<br /> <br /> || <e2 e3 ... ep| || = |e2| + log2(3)|e3| + ... + log2(p) |ep|<br /> <br /> which is a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Normed_vector_space" rel="nofollow">vector space norm</a>. The monzos with this norm now define a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lattice_%28group%29" rel="nofollow">lattice</a>, which is a discrete subgroup spanning a finite dimensional real normed vector space.</body></html>