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<div class="document" id="package-polexpr-documentation">
<h1 class="title">Package polexpr documentation</h1>

<!-- comment: -*- fill-column: 72; mode: rst; -*- -->
<div class="section" id="first-examples">
<h1>First Examples</h1>
<p>The syntax is:</p>
<pre class="literal-block">
\poldef &lt;name&gt;(x):=&lt;expression in variable x&gt;;
</pre>
<p>where in place of <tt class="docutils literal">x</tt> an arbitrary <em>dummy variable</em> is authorized
(i.e. per default any of <tt class="docutils literal"><span class="pre">[a..z|A..Z]</span></tt>; more letters can be declared
under Unicode engines.) One can also issue:</p>
<pre class="literal-block">
\PolDef{name}{expression in variable x}
</pre>
<p>which admits an optional first argument to modify the variable letter
from its default <tt class="docutils literal">x</tt>.</p>
<dl class="docutils">
<dt><tt class="docutils literal">\poldef <span class="pre">f(x):=</span> <span class="pre">1-x+x^2;</span></tt></dt>
<dd>defines polynomial <tt class="docutils literal">f</tt>. Polynomial names must start with a letter
and may contain letters, digits, and underscores. The variable must
be a single letter. The colon character is optional. The semi-colon
at end of expression is mandatory.</dd>
<dt><tt class="docutils literal"><span class="pre">\PolDef{f}{1-x+x^2}</span></tt></dt>
<dd>does the same as <tt class="docutils literal">\poldef <span class="pre">f(x):=</span> <span class="pre">1-x+x^2;</span></tt> To use another letter
than <tt class="docutils literal">x</tt> in the expression, one must pass it as an extra optional
argument to <tt class="docutils literal">\PolDef</tt>. Useful if the semi-colon has been assigned
some non-standard catcode by some package.</dd>
<dt><tt class="docutils literal"><span class="pre">\PolLet{g}{f}</span></tt></dt>
<dd>saves a copy of <tt class="docutils literal">f</tt> under name <tt class="docutils literal">g</tt>.</dd>
<dt><tt class="docutils literal">\poldef <span class="pre">f(z):=</span> <span class="pre">f(z)^2;</span></tt></dt>
<dd>redefines <tt class="docutils literal">f</tt> in terms of itself.</dd>
<dt><tt class="docutils literal">\poldef <span class="pre">f(T):=</span> <span class="pre">f(f(T));</span></tt></dt>
<dd>again redefines <tt class="docutils literal">f</tt> in terms of its (new) self.</dd>
<dt><tt class="docutils literal">\poldef <span class="pre">k(z):=</span> <span class="pre">f(z)-g(g(z)^2)^2;</span></tt></dt>
<dd>should now define the zero polynomial... Let's check:
<tt class="docutils literal">\[ k(z) = <span class="pre">\PolTypeset[z]{k}</span> \]</tt></dd>
<dt><tt class="docutils literal"><span class="pre">\PolDiff{f}{df_dx}</span></tt></dt>
<dd>sets <tt class="docutils literal">df_dx</tt> to the derivative of <tt class="docutils literal">f</tt>.</dd>
<dt><tt class="docutils literal"><span class="pre">\PolDiff{df_dx}{f_xx}</span></tt></dt>
<dd>obtains second derivative.</dd>
<dt><tt class="docutils literal"><span class="pre">\PolDiff[3]{f}{d3f_dx3}</span></tt></dt>
<dd>computes directly the third derivative. Its name does not have to be
chosen so complicated <tt class="docutils literal">:)</tt>, but the right quote <tt class="docutils literal">'</tt> is not
allowed in polynomial names (currently).</dd>
</dl>
<pre class="literal-block">
$f(z)   = \PolTypeset[z]{f}    $\newline
$f'(z)  = \PolTypeset[z]{df_dx}$\newline
$f''(z) = \PolTypeset[z]{f_xx}$\newline
$f'''(z)= \PolTypeset[z]{d3f_dx3}$\par
</pre>
<div class="admonition important">
<p class="first admonition-title">Important</p>
<p>The package does not currently know rational functions: <tt class="docutils literal">/</tt> in
a parsed polynomial expression does the Euclidean quotient:</p>
<pre class="literal-block">
(1-x^2)/(1-x)
</pre>
<p>does give <tt class="docutils literal">1+x</tt> but</p>
<pre class="literal-block">
(1/(1-x))*(1-x^2)
</pre>
<p>evaluates to zero. This will work as expected:</p>
<pre class="last literal-block">
\poldef k(x):= (x-1)(x-2)(x-3)(x-4)/(x^2-5x+4);
</pre>
</div>
<div class="admonition attention">
<p class="first admonition-title">Attention!</p>
<p class="last"><tt class="docutils literal">1/2 x</tt> skips the space and is treated like <tt class="docutils literal"><span class="pre">1/(2x)</span></tt> because of
the tacit multiplication rules of xintexpr. But this means it gives
zero! Thus one must use <tt class="docutils literal">(1/2)x</tt> or <tt class="docutils literal">1/2*x</tt> or <tt class="docutils literal"><span class="pre">(1/2)*x</span></tt> for
disambiguation: <tt class="docutils literal"><span class="pre">x-1/2*x^2+1/3*x^3...</span></tt></p>
</div>
<p>After:</p>
<pre class="literal-block">
\poldef f1(x):= 25(x-1)(x^2-2)(x-3)(x-4)(x-5);%
\poldef f2(x):= 37(x-1)(x^2-2)(x-6)(x-7)(x-8);%
</pre>
<p>the macro call <tt class="docutils literal"><span class="pre">\PolGCD{f1}{f2}{k}</span></tt> sets <tt class="docutils literal">k</tt> to the (unitary) GCD of
<tt class="docutils literal">f1</tt> and <tt class="docutils literal">f2</tt>.</p>
<dl class="docutils">
<dt><tt class="docutils literal">\PolToExpr{k}</tt></dt>
<dd>will thus (expandably) give in this case <tt class="docutils literal"><span class="pre">2-2*x^1-1*x^2+1*x^3</span></tt>.
This is useful for console or file output (the syntax is Maple- and
PSTricks-compatible; currently the letter <tt class="docutils literal">x</tt> in output is not
customizable, but this can easily be added if requested from author.)</dd>
</dl>
</div>
<div class="section" id="non-expandable-macros">
<h1>Non-expandable macros</h1>
<dl class="docutils">
<dt><tt class="docutils literal">\poldef <span class="pre">name(letter):=</span> polynomial expression using letter;</tt></dt>
<dd><p class="first">This evaluates the polynomial expression and stores the coefficients
in a private structure accessible later via other package macros,
under the user-chosen <tt class="docutils literal">name</tt>. Of course previously defined
polynomials are allowed in a new expression. Names must start with a
letter and are constituted of letters, digits and underscore
characters. See Examples above.</p>
<p>As a side effect the function <tt class="docutils literal">name()</tt> is recognized as a genuine
<tt class="docutils literal"><span class="pre">\xintexpr...\relax</span></tt> function for (exact) numerical evaluation. It
computes values not according to the original expression but via
the Horner scheme corresponding to the polynomial coefficients.</p>
<p class="last">The original expression is lost after parsing, and in particular
the package provides no way to typeset it. This has to be done
manually, if needed.</p>
</dd>
<dt><tt class="docutils literal"><span class="pre">\PolDef{name}{P(x)}</span></tt></dt>
<dd>Does the same but the variable is assumed to be <tt class="docutils literal">x</tt>. To use
another letter, pass it as first optional argument:
<tt class="docutils literal"><span class="pre">\PolDef[X]{name}{P(X)}</span></tt>.</dd>
<dt><tt class="docutils literal"><span class="pre">\PolLet{g}{f}</span></tt></dt>
<dd>Makes a copy of already defined polynomial f to new one g. Same
effect as <tt class="docutils literal"><span class="pre">\PolDef{g}{f(x)}</span></tt> but faster.</dd>
<dt><tt class="docutils literal"><span class="pre">\PolAssign{f}\toarray\Array</span></tt></dt>
<dd><p class="first">Defines a one-argument expandable macro <tt class="docutils literal"><span class="pre">\Array{#1}</span></tt> which expands
to the (raw) #1th polynomial coefficient.</p>
<ul class="last simple">
<li>Attention, coefficients here are indexed starting at 1.</li>
<li>With #1=-1, -2, ..., <tt class="docutils literal"><span class="pre">\Array{#1}</span></tt> returns leading coefficients.</li>
<li>With #1=0, returns the number of coefficients, i.e. <tt class="docutils literal">1 + deg f</tt>
for non-zero polynomials.</li>
<li>Out-of-range #1's return <tt class="docutils literal">0/1[0]</tt>.</li>
</ul>
</dd>
<dt><tt class="docutils literal"><span class="pre">\PolGet{f}\fromarray\Array</span></tt></dt>
<dd><p class="first">Does the converse operation to <tt class="docutils literal"><span class="pre">\PolAssign{f}\toarray\Array</span></tt>. No
error checks on validity of coefficients as numbers. Each
<tt class="docutils literal">\Array{index}</tt> is expanded in an <tt class="docutils literal">\edef</tt> before being assigned
to a coefficient. Leading zero coefficients are removed from the
polynomial.</p>
<p>(contrived) Example:</p>
<pre class="literal-block">
\xintAssignArray{1}{-2}{5}{-3}\to\foo
\PolGet{f}\fromarray\foo
</pre>
<p class="last">This will define <tt class="docutils literal">f</tt> as would have <tt class="docutils literal">\poldef <span class="pre">f(x):=1-2x+5x^2-3x^3;</span></tt>.
However the coefficients are still in their original form (i.e.
they were not subjected to <tt class="docutils literal">\xintRaw</tt> or similar xintfrac macro.)</p>
</dd>
<dt><tt class="docutils literal"><span class="pre">\PolFromCSV{f}{comma</span> separated coefficients}</tt></dt>
<dd><p class="first">Defines a polynomial directly from the comma separated list (or a
macro expanding to such a list) of its coefficients, the constant
term being the first item. No validity checks. Spaces from the list
argument are trimmed. List items are expanded in an <tt class="docutils literal">\edef</tt>, but
currently left in their original form like e.g. <tt class="docutils literal">1.5e3</tt> which is
not converted to <tt class="docutils literal">15/1[2]</tt> <em>raw</em> xintfrac format (this may
change).</p>
<p>Leading zero coefficients are removed:</p>
<pre class="literal-block">
\PolFromCSV{J}{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
</pre>
<p>defines the zero polynomial, which has only one (zero) coefficient.</p>
<p class="last">See also expandable macro <tt class="docutils literal">\PolToCSV</tt>.</p>
</dd>
<dt><tt class="docutils literal">\PolTypeset{name}</tt></dt>
<dd><p class="first">Typesets in descending powers in math mode. It uses letter <tt class="docutils literal">x</tt> but
this can be changed via an optional argument:</p>
<pre class="literal-block">
\PolTypeset[z]{name}
</pre>
<p>By default zero coefficients are skipped (issue <tt class="docutils literal">\poltypesetalltrue</tt>
to get all of them in output).</p>
<p class="last">Macros <tt class="docutils literal">\PolTypesetCmd</tt>, <tt class="docutils literal">\PolTypesetPlus</tt>, <tt class="docutils literal">\PolTypesetMonomial</tt>
can help configure the output. See the package code.</p>
</dd>
<dt><tt class="docutils literal"><span class="pre">\PolTypeset*{name}</span></tt></dt>
<dd>Typesets in ascending powers. Change the letter from its default
<tt class="docutils literal">x</tt> by optional argument.</dd>
<dt><tt class="docutils literal"><span class="pre">\PolDiff{f1}{f2}</span></tt></dt>
<dd><p class="first">This sets f2 to the first derivative of <tt class="docutils literal">f1</tt>. It is allowed to
issue <tt class="docutils literal"><span class="pre">\PolDiff{f}{f}</span></tt>, effectively replacing <tt class="docutils literal">f</tt> by <tt class="docutils literal">f'</tt>.</p>
<p class="last">Coefficients of the result <tt class="docutils literal">f2</tt> are irreducible fractions
(see <a class="reference internal" href="#technicalities">Technicalities</a> for the whole story.)</p>
</dd>
<dt><tt class="docutils literal"><span class="pre">\PolDiff[N]{f1}{f2}</span></tt></dt>
<dd>This sets <tt class="docutils literal">f2</tt> to the <tt class="docutils literal">N</tt>-th derivative of <tt class="docutils literal">f1</tt>. Identical
arguments is allowed. With <tt class="docutils literal">N=0</tt>, same effect as
<tt class="docutils literal"><span class="pre">\PolLet{f2}{f1}</span></tt>. With negative <tt class="docutils literal">N</tt>, switches to using
<tt class="docutils literal">\PolAntiDiff</tt>.</dd>
<dt><tt class="docutils literal"><span class="pre">\PolAntiDiff{f1}{f2}</span></tt></dt>
<dd><p class="first">This sets <tt class="docutils literal">f2</tt> to the primitive of <tt class="docutils literal">f1</tt> vanishing at zero.</p>
<p class="last">Coefficients of the result <tt class="docutils literal">f2</tt> are irreducible fractions
(see <a class="reference internal" href="#technicalities">Technicalities</a> for the whole story.)</p>
</dd>
<dt><tt class="docutils literal"><span class="pre">\PolAntiDiff[N]{f1}{f2}</span></tt></dt>
<dd>This sets <tt class="docutils literal">f2</tt> to the result of <tt class="docutils literal">N</tt> successive integrations on
<tt class="docutils literal">f1</tt>. With negative <tt class="docutils literal">N</tt>, it switches to using <tt class="docutils literal">\PolDiff</tt>.</dd>
<dt><tt class="docutils literal"><span class="pre">\PolDivide{f1}{f2}{Q}{R}</span></tt></dt>
<dd>This sets <tt class="docutils literal">Q</tt> and <tt class="docutils literal">R</tt> to be the quotient and remainder in the
Euclidean division of <tt class="docutils literal">f1</tt> by <tt class="docutils literal">f2</tt>.</dd>
<dt><tt class="docutils literal"><span class="pre">\PolGCD{f}{g}{k}</span></tt></dt>
<dd>This sets <tt class="docutils literal">k</tt> to be the G.C.D. It is a unitary polynomial except
if both <tt class="docutils literal">f</tt> and <tt class="docutils literal">g</tt> vanish, then <tt class="docutils literal">k</tt> is the zero polynomial.</dd>
<dt><tt class="docutils literal"><span class="pre">\PolMapCoeffs{\macro}{name}</span></tt></dt>
<dd><p class="first">It modifies each coefficient of the defined polynomial via the
<em>expandable</em> macro <tt class="docutils literal">\macro</tt>. The degree is adjusted as necessary
if some leading coefficients vanish after the operation. In
replacement text of <tt class="docutils literal">\macro</tt>, <tt class="docutils literal">\index</tt> expands to the
coefficient index (which is defined to be zero for the constant
term).</p>
<p>Notice that <tt class="docutils literal">\macro</tt> will have to handle inputs of the shape
<tt class="docutils literal">A/B[N]</tt> (xintfrac internal notation). This means that it probably
will have to be expressed in terms of macros from xintfrac package.</p>
<p>Example:</p>
<pre class="literal-block">
\def\foo#1{\xintMul{#1}{\the\numexpr\index*\index\relax}}
</pre>
<p class="last">(or with <tt class="docutils literal"><span class="pre">\xintSqr{\xindex}</span></tt>) to replace <tt class="docutils literal">n</tt>-th coefficient
<tt class="docutils literal">f_n</tt> by <tt class="docutils literal">f_n*n^2</tt>.</p>
</dd>
<dt><tt class="docutils literal">\PolReduceCoeffs{name}</tt></dt>
<dd>About the same as <tt class="docutils literal"><span class="pre">\PolMapCoeffs{\xintIrr}{name}</span></tt> (but adds
<tt class="docutils literal">[0]</tt> postfix which speeds up xintfrac operations when
evaluating.)</dd>
</dl>
</div>
<div class="section" id="expandable-macros">
<h1>Expandable macros</h1>
<p>All these macros expand completely in two steps except <tt class="docutils literal">\PolToExpr</tt>
which needs a <tt class="docutils literal">\write</tt>, <tt class="docutils literal">\edef</tt> or a <tt class="docutils literal"><span class="pre">\csname...\endcsname</span></tt> context.</p>
<dl class="docutils">
<dt><tt class="docutils literal"><span class="pre">\PolEval{name}\At{value}</span></tt></dt>
<dd>It boils down to <tt class="docutils literal">\xinttheexpr <span class="pre">reduce(name(value))\relax</span></tt>.</dd>
<dt><tt class="docutils literal"><span class="pre">\PolNthCoeff{name}{N}</span></tt></dt>
<dd>It expands to the raw <tt class="docutils literal">N</tt>-th coefficient (<tt class="docutils literal">0/1[0]</tt> if index is
out of range). With <tt class="docutils literal"><span class="pre">N=-1</span></tt>, <tt class="docutils literal"><span class="pre">-2</span></tt>, ... expands to the leading
coefficients.</dd>
<dt><tt class="docutils literal">\PolDegree{name}</tt></dt>
<dd>It expands to the degree. This is <tt class="docutils literal"><span class="pre">-1</span></tt> if zero polynomial but this
may change in future. Should it then expand to <tt class="docutils literal"><span class="pre">-\infty</span></tt> ?</dd>
<dt><tt class="docutils literal">\PolToExpr{f}</tt></dt>
<dd><p class="first">Expands to <tt class="docutils literal">f_0 + f_1*x + f_2*x^2 + ...</tt> (ascending powers). <a class="footnote-reference" href="#id3" id="id1">[1]</a>,
<a class="footnote-reference" href="#id4" id="id2">[2]</a></p>
<table class="docutils footnote" frame="void" id="id3" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id1">[1]</a></td><td>in a <tt class="docutils literal">\write</tt>, <tt class="docutils literal">\edef</tt>, or <tt class="docutils literal"><span class="pre">\csname...\endcsname</span></tt>, but
not under <tt class="docutils literal"><span class="pre">\romannumeral-`0</span></tt>.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="id4" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id2">[2]</a></td><td>the letter <tt class="docutils literal">x</tt> is (in this release) not customizable.</td></tr>
</tbody>
</table>
<p>By default zero coefficients are skipped (issue <tt class="docutils literal">\poltoexprtrue</tt> to
get all of them in output).</p>
<p>No <tt class="docutils literal">+</tt> sign before negative coefficients, for compliance with Maple
input format. This means though that parsing the result back via
naive delimited macros is difficult, see <tt class="docutils literal">\PolToList</tt> and <tt class="docutils literal">\PolToCSV</tt>
for more low-level formats making it easier to get expandably some
output of one's choice, which may possibly be parsed later on by
other macros of one's design, or from other packages.</p>
<p>Of course <tt class="docutils literal">\PolToExpr{f}</tt> can be inserted in a poldef, as the
latter expands token by token, hence will force complete expansion
of <tt class="docutils literal">\PolToExpr{f}</tt>, but simply <tt class="docutils literal">f(x)</tt> will be more efficient for the
identical result.</p>
<p class="last"><tt class="docutils literal">\PolToExprCmd</tt> is the one-argument macro used by <tt class="docutils literal">\PolToExpr</tt> for the
coefficients, it defaults to <tt class="docutils literal"><span class="pre">\xintPRaw{\xintRawWithZeros{#1}}</span></tt>. One
will have to redefine it to use <tt class="docutils literal"><span class="pre">\xintIrr{#1}</span></tt> in place of
<tt class="docutils literal"><span class="pre">\xintRawWithZeros{#1}</span></tt> to get in output reduced coefficients.</p>
</dd>
<dt><tt class="docutils literal">\PolToList{f}</tt></dt>
<dd>Expands to <tt class="docutils literal"><span class="pre">{f_0}{f_1}...{f_N}</span></tt> with <tt class="docutils literal">N</tt> = degree of f (except
zero polynomial which does give <tt class="docutils literal">{0/1[0]}</tt> and not an empty
output.)</dd>
<dt><tt class="docutils literal">\PolToCSV{f}</tt></dt>
<dd>Expands to <tt class="docutils literal">f_0, f_1, f_2, <span class="pre">.....,</span> f_N</tt>. Converse to
<tt class="docutils literal">\PolFromCSV</tt>.</dd>
</dl>
</div>
<div class="section" id="technicalities">
<h1>Technicalities</h1>
<ul>
<li><p class="first">The catcode of the semi-colon is reset temporarily by <tt class="docutils literal">\poldef</tt> macro in
case some other package (for example the French babel module) may have
made it active. This will fail though if the whole thing was already
part of a macro argument, in such cases one can use <tt class="docutils literal">\PolDef</tt> rather.
The colon in <tt class="docutils literal">:=</tt> may be active with no consequences.</p>
</li>
<li><p class="first">Beware the <tt class="docutils literal">1/2 x</tt> problem: as mentioned above, it will be give zero due
to the tacit multiplication rules of <tt class="docutils literal">\xintexpr</tt> and to the fact that
the package will do the Euclidean division of <tt class="docutils literal">1</tt> by polynomial <tt class="docutils literal">2x</tt>.</p>
</li>
<li><p class="first">During execution of polynomial operations by <tt class="docutils literal">\poldef</tt> (but not
during the initial purely numerical parsing of the expression), the
xintfrac macro <tt class="docutils literal">\xintAdd</tt> is temporarily patched to always express
<tt class="docutils literal">a/b + c/d</tt> with <tt class="docutils literal"><span class="pre">l.c.m.(b,d)</span></tt> as denominator. Indeed the current
(xint 1.2p) <tt class="docutils literal">\xintAdd</tt> uses <tt class="docutils literal"><span class="pre">(ad+bc)/bd</span></tt> formula except if <tt class="docutils literal">b</tt>
divides <tt class="docutils literal">d</tt> or <tt class="docutils literal">d</tt> divides <tt class="docutils literal">b</tt>, which quickly leads in real life
to big denominators.</p>
<p>It is probable that this convention will be backported as default
behaviour of xintfrac's <tt class="docutils literal">\xintAdd</tt> in a future xint release. When this
change is merged, there will be an impact on coefficients computed by
<tt class="docutils literal">\poldef</tt> because the change will apply even to the pure numerical
evaluations arising during the initial stage of the parsing. Of course
the coefficients are still the same rational numbers, only
representation as fractions may change.</p>
</li>
<li><p class="first">As a consequence of previous rule, user-chosen common denominators
survive addition and multiplications:</p>
<pre class="literal-block">
\poldef P(x):= 1/2 + 2/2*x + 3/2*x^3 + 4/2*x^4;
\poldef Q(x):= 1/3 + (2/3)x + (3/3)x^3 + (4/3)x^4;
\poldef PQ(x):= P(x)Q(x);
</pre>
<p>gives the polynomial:</p>
<pre class="literal-block">
1/6+4/6*x^1+4/6*x^2+6/6*x^3+20/6*x^4+16/6*x^5+9/6*x^6+24/6*x^7+16/6*x^8
</pre>
<p>where all coefficients have the same denominator 6 (which in this
example is the <tt class="docutils literal">l.c.m</tt> of the denominators of the reduced coefficients.)</p>
</li>
<li><p class="first"><tt class="docutils literal">\PolDiff</tt> always applies <tt class="docutils literal">\xintIrr</tt> to the resulting coefficients, except
that the <em>power of ten</em> part <tt class="docutils literal">[N]</tt> (for example an input in scientific
notation such as <tt class="docutils literal">1.23e5</tt> gives <tt class="docutils literal">123/1[3]</tt> internally in xintfrac) is not
taken into account in the reduction of the fraction. This is tentative
and may change.</p>
<p>Same remark for <tt class="docutils literal">\PolAntiDiff</tt>.</p>
</li>
<li><p class="first">If <tt class="docutils literal">f</tt> was created from comma separated values by macro PolFromCSV,
then the coefficients will be in the output of <tt class="docutils literal">\PolToList</tt> and
<tt class="docutils literal">\PolToCSV</tt> in the same format as originally in input: a <tt class="docutils literal">1.3e2</tt>
will again be a <tt class="docutils literal">1.3e2</tt>.</p>
<p>In contrast when such coefficients are used in a <tt class="docutils literal">\poldef</tt> (or
<tt class="docutils literal">\PolDef</tt>) expression, they get transformed during the parsing to
the xintfrac <em>raw</em> format. This is an unavoidable consequence of usage
by poldef of <tt class="docutils literal">\xintdeffunc</tt> which itself is based on <tt class="docutils literal">\xintexpr.</tt>
This <em>raw</em> format speeds up expansion of xintfrac macros for numerical
evaluations.</p>
</li>
<li><p class="first">Currently, the package does not as a result of <tt class="docutils literal">\poldef</tt> add to the TeX
memory an already pre-computed <em>array</em> structure for the polynomial
coefficients, as would be constructed by <tt class="docutils literal"><span class="pre">\PolAssign{f}\toarray\macro</span></tt>.
Such structures are used, but for internal calculations in temporarily
restricted scopes. Apart from the function <tt class="docutils literal">f()</tt> known to the
(numerical) <tt class="docutils literal">\xintexpr</tt> parser (whose meaning can be found in the log
file after xintverbosetrue), the data is (currently) stored in a
single other macro encapsulating the degree, and the coefficients as a
list. This may evolve in future.</p>
</li>
<li><p class="first">As is to be expected internal structures of the package are barely
documented and unstable. Don't use them.</p>
</li>
</ul>
</div>
<div class="section" id="releases">
<h1>RELEASES</h1>
<ul class="simple">
<li>0.1 (2018/01/11): initial release (files README, polexpr.sty).</li>
<li>0.2 (2018/01/14): documentation moved to polexpr.{txt,html}.</li>
</ul>
<p>Files of 0.2 release:</p>
<ul class="simple">
<li>README.md,</li>
<li>polexpr.sty (package file),</li>
<li>polexpr.txt (documentation),</li>
<li>polexpr.html (conversion via <a class="reference external" href="http://docutils.sourceforge.net/docs/index.html">DocUtils</a> rst2html.py)</li>
</ul>
<p>See README.md for the License and the change log.</p>
</div>
</div>
</body>
</html>