/usr/share/doc/axiom-doc/hypertex/numromannumerals.xhtml

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  <div align="center"><img align="middle" src="doctitle.png"/></div>
  <hr/>
  <div align="center">Roman Numerals</div>
  <hr/>
The Roman numeral package was added to Axiom in MCMLXXXVI for use in
denoting higher order derivatives.

For example, let f be a symbolic operator.
<ul>
 <li>
  <input type="submit" id="p1" class="subbut" onclick="makeRequest('p1');"
    value="f:=operator 'f" />
  <div id="ansp1"><div></div></div>
 </li>
</ul>
This is the seventh derivative of f with respect to x
<ul>
 <li>
  <input type="submit" id="p2" class="subbut" onclick="makeRequest('p2');"
    value="D(f x,x,7)" />
  <div id="ansp2"><div></div></div>
 </li>
</ul>
You can have integers printed as Roman numerals by declaring variables
to be of type 
<a href="db.xhtml?RomanNumeral">RomanNumeral</a> 
(abbreviation <a href="db.xhtml?RomanNumeral">ROMAN</a>).
<ul>
 <li>
  <input type="submit" id="p3" class="subbut" onclick="makeRequest('p3');"
    value="a:=roman(1978-1965)" />
  <div id="ansp3"><div></div></div>
 </li>
</ul>
This package now has a small but devoted group of followers that claim
this domain has shown its efficacy in many other contexts. They claim
that Roman numerals are every bit as useful as ordinary integers.
In a sense, they are correct, because Roman numerals form a ring and
you can therefore construct polynomials with Roman numeral 
coefficients, matrices over Roman numerals,etc..
<ul>
 <li>
  <input type="submit" id="p4" class="subbut" onclick="makeRequest('p4');"
    value="x:UTS(ROMAN,'x,0):=x" />
  <div id="ansp4"><div></div></div>
 </li>
</ul>
Was Fibonacci Italian or ROMAN?
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 <li>
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    value="recip(1-x-x^2)" />
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 </li>
</ul>
You can also construct fractions with Roman numeral numerators and 
denominators, as this matrix Hilberticus illustrates.
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 <li>
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    value="m:MATRIX FRAC ROMAN" />
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 </li>
</ul>
Note that the inverse of the matrix has integral 
<a href="db.xhtml?RomanNumeral">ROMAN</a> entries.
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 <li>
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    onclick="handleFree(['p6','p7','p8']);"
    value="inverse m" />
  <div id="ansp8"><div></div></div>
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</ul>
Unfortunately, the spoil-sports say that the fun stops when the
numbers get big -- mostly because the Romans didn't establish
conventions about representing very large numbers.
<ul>
 <li>
  <input type="submit" id="p9" class="subbut" onclick="makeRequest('p9');"
    value="y:=factorial 10" />
  <div id="ansp9"><div></div></div>
 </li>
</ul>
You work it out!
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 <li>
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    value="roman y" />
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Issue the system command
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 <li>
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   value=")show RomanNumeral"/>
  <div id="ansp11"><div></div></div>
 </li>
</ul>
to display the full list of operations defined by 
<a href="db.xhtml?RomanNumeral">RomanNumeral</a>).
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axiom-hypertex-data 20120501-8 / usr / share / doc / axiom-doc / hypertex / numromannumerals.xhtml
