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<!DOCTYPE html>

<html lang="en">
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  <section id="changes">
<h1>CHANGES</h1>
<section id="v0-1-2018-01-11-initial-release-features">
<span id="firstrelease"></span><h2>v0.1 (2018/01/11): initial release. Features:</h2>
<ul class="simple">
<li><p>The <a class="reference internal" href="polexpr-ref.html#poldef"><span class="std std-ref">\poldef</span></a> parser itself,</p></li>
<li><p>Differentiation and anti-differentiation,</p></li>
<li><p>Euclidean division and GCDs,</p></li>
<li><p>Various utilities such as <a class="reference internal" href="polexpr-ref.html#polfromcsv"><span class="std std-ref">\PolFromCSV</span></a>,
<a class="reference internal" href="polexpr-ref.html#polmapcoeffs"><span class="std std-ref">\PolMapCoeffs</span></a>,
<a class="reference internal" href="polexpr-ref.html#poltocsv"><span class="std std-ref">\PolToCSV</span></a>, <a class="reference internal" href="polexpr-ref.html#poltoexpr"><span class="std std-ref">\PolToExpr</span></a>, …</p></li>
</ul>
<p>Only one-variable polynomials so far.</p>
</section>
<section id="v0-2-2018-01-14">
<h2>v0.2 (2018/01/14)</h2>
<ul class="simple">
<li><p>Fix: <code class="docutils literal notranslate"><span class="pre">&quot;README</span> <span class="pre">thinks</span> <span class="pre">\numexpr</span> <span class="pre">recognizes</span> <span class="pre">^</span> <span class="pre">operator&quot;</span></code>.</p></li>
<li><p>Convert README to reStructuredText markup.</p></li>
<li><p>Move main documentation from README to separate <code class="docutils literal notranslate"><span class="pre">polexpr.txt</span></code> file.</p></li>
<li><p>Provide <code class="docutils literal notranslate"><span class="pre">polexpr.html</span></code> as obtained via <a class="reference external" href="http://docutils.sourceforge.net/docs/index.html">DocUtils</a> <code class="docutils literal notranslate"><span class="pre">rst2html.py</span></code>.</p></li>
<li><p>Convert README to (CTAN compatible) Markdown markup.</p></li>
</ul>
<p>Due to lack of available time the test suite might not be extensive
enough. Bug reports are very welcome!</p>
</section>
<section id="v0-3-2018-01-17">
<h2>v0.3 (2018/01/17)</h2>
<ul>
<li><p>bug fixes:</p>
<ul>
<li><p>the <code class="docutils literal notranslate"><span class="pre">0.1</span></code> <a class="reference internal" href="polexpr-ref.html#polevalat"><span class="std std-ref">\PolEval</span></a> accepted expressions for its
second argument, but this was removed by mistake at <code class="docutils literal notranslate"><span class="pre">0.2</span></code>. Restored.</p>
<p><strong>Attention</strong>: at <code class="docutils literal notranslate"><span class="pre">0.4</span></code> this has been reverted again, and
<a class="reference internal" href="polexpr-ref.html#polevalatexpr"><span class="std std-ref">\PolEval{P}\AtExpr{foo}</span></a> syntax is needed for
using expressions in the second argument.</p>
</li>
</ul>
</li>
<li><p>incompatible or breaking changes:</p>
<ul class="simple">
<li><p><a class="reference internal" href="polexpr-ref.html#poltoexpr"><span class="std std-ref">\PolToExpr</span></a> now by default uses <em>descending</em>
powers (it also treats differently coefficients equal to 1 or -1.)
Use <a class="reference internal" href="polexpr-ref.html#id78"><span class="std std-ref">\PolToExpr*</span></a> for <em>ascending</em> powers.</p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polevalat"><span class="std std-ref">\PolEval</span></a> reduced the output to smallest terms,
but as this is costly with big fractions and not needed if e.g.
wrapped in an <code class="docutils literal notranslate"><span class="pre">\xintRound</span></code> or <code class="docutils literal notranslate"><span class="pre">\xintFloat</span></code>, this step has been
removed; the former meaning is available as
<a class="reference internal" href="polexpr-ref.html#polevalreducedat"><span class="std std-ref">\PolEvalReduced</span></a>.</p></li>
</ul>
</li>
<li><p>new (or newly documented) macros:</p>
<ul class="simple">
<li><p><a class="reference internal" href="polexpr-ref.html#poltypesetcmd"><span class="std std-ref">\PolTypesetCmd</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltypesetcmdprefix"><span class="std std-ref">\PolTypesetCmdPrefix</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltypesetmonomialcmd"><span class="std std-ref">\PolTypesetMonomialCmd</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polevalreducedat"><span class="std std-ref">\PolEvalReducedAt</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltofloatexpr"><span class="std std-ref">\PolToFloatExpr</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltoexproneterm"><span class="std std-ref">\PolToExprOneTerm</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltofloatexproneterm"><span class="std std-ref">\PolToFloatExprOneTerm</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltoexprcmd"><span class="std std-ref">\PolToExprCmd</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltofloatexprcmd"><span class="std std-ref">\PolToFloatExprCmd</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltoexprtermprefix"><span class="std std-ref">\PolToExprTermPrefix</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltoexprvar"><span class="std std-ref">\PolToExprVar</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltoexprtimes"><span class="std std-ref">\PolToExprTimes</span></a></p></li>
</ul>
</li>
<li><p>improvements:</p>
<ul>
<li><p>documentation has a table of contents, internal hyperlinks,
standardized signature notations and added explanations.</p></li>
<li><p>one can do <code class="docutils literal notranslate"><span class="pre">\PolLet{g}={f}</span></code> or <code class="docutils literal notranslate"><span class="pre">\PolLet{g}{f}</span></code>.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">\PolToExpr{f}</span></code> is highly customizable.</p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poldef"><span class="std std-ref">\poldef</span></a> and other defining macros prepare the
polynomial functions for usage within <code class="docutils literal notranslate"><span class="pre">\xintthefloatexpr</span></code> (or
<code class="docutils literal notranslate"><span class="pre">\xintdeffloatvar</span></code>). Coefficients are pre-rounded to the floating
point precision. Indispensible for numerical algorithms, as exact
fractions, even reduced, quickly become very big. See the documentation
about how to use the exact polynomials also in floating point context.</p>
<p><strong>Attention</strong>: this has been reverted at <code class="docutils literal notranslate"><span class="pre">0.4</span></code>. The macro
<a class="reference internal" href="polexpr-ref.html#polgenfloatvariant"><span class="std std-ref">\PolGenFloatVariant</span></a> must be used for
generation floating point polynomial functions.</p>
</li>
</ul>
</li>
</ul>
</section>
<section id="v0-3-1-2018-01-18">
<h2>v0.3.1 (2018/01/18)</h2>
<p>Fixes two typos in example code included in the documentation.</p>
</section>
<section id="v0-4-2018-02-16">
<h2>v0.4 (2018/02/16)</h2>
<ul>
<li><p>bug fixes:</p>
<ul class="simple">
<li><p>when Euclidean division gave a zero remainder, the internal
representation of this zero polynomial could be faulty; this
could cause mysterious bugs in conjunction with other package
macros such as <a class="reference internal" href="polexpr-ref.html#polmapcoeffs"><span class="std std-ref">\PolMapCoeffs</span></a>.</p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polgcd"><span class="std std-ref">\PolGCD</span></a> was buggy in case of first polynomial being
of lesser degree than the second one.</p></li>
</ul>
</li>
<li><p>breaking changes:</p>
<ul>
<li><p>formerly <a class="reference internal" href="polexpr-ref.html#polevalat"><span class="std std-ref">\PolEval{P}\At{foo}</span></a> allowed <code class="docutils literal notranslate"><span class="pre">foo</span></code> to
be an expression, which was transparently handled via
<code class="docutils literal notranslate"><span class="pre">\xinttheexpr</span></code>. Now, <code class="docutils literal notranslate"><span class="pre">foo</span></code> must be a fraction (or a macro
expanding to such) in the format acceptable by <code class="docutils literal notranslate"><span class="pre">xintfrac.sty</span></code>
macros. Use <a class="reference internal" href="polexpr-ref.html#polevalatexpr"><span class="std std-ref">\PolEval{P}\AtExpr{foo}</span></a> for more
general arguments using expression syntax. E.g., if <code class="docutils literal notranslate"><span class="pre">foo</span></code> is the
name of a variable known to <code class="docutils literal notranslate"><span class="pre">\xintexpr</span></code>.</p>
<p>The same holds for <a class="reference internal" href="polexpr-ref.html#polevalreducedat"><span class="std std-ref">\PolEvalReduced</span></a>
and <a class="reference internal" href="polexpr-ref.html#polfloatevalat"><span class="std std-ref">\PolFloatEval</span></a>.</p>
</li>
<li><p>the <code class="docutils literal notranslate"><span class="pre">3.0</span></code> automatic generation of floating point variants has
been reverted. Not only do <em>not</em> the package macros automatically
generate floating point variants of newly created polynomials,
they actually make pre-existing such variant undefined.</p>
<p>See <a class="reference internal" href="polexpr-ref.html#polgenfloatvariant"><span class="std std-ref">\PolGenFloatVariant</span></a>.</p>
</li>
</ul>
</li>
<li><p>new non-expandable macros:</p>
<ul class="simple">
<li><p><a class="reference internal" href="polexpr-ref.html#polgenfloatvariant"><span class="std std-ref">\PolGenFloatVariant</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polgloballet"><span class="std std-ref">\PolGlobalLet</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltypesetone"><span class="std std-ref">\PolTypesetOne</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polquo"><span class="std std-ref">\PolQuo</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polrem"><span class="std std-ref">\PolRem</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltosturm"><span class="std std-ref">\PolToSturm</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#id35"><span class="std std-ref">\PolToSturm*</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsettosturmchainsignchangesat"><span class="std std-ref">\PolSetToSturmChainSignChangesAt</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsettonbofzeroswithin"><span class="std std-ref">\PolSetToNbOfZerosWithin</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmisolatezeros"><span class="std std-ref">\PolSturmIsolateZeros</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polrefineinterval"><span class="std std-ref">\PolRefineInterval*</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#id46"><span class="std std-ref">\PolRefineInterval[N]</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polensureintervallength"><span class="std std-ref">\PolEnsureIntervalLength</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polensureintervallengths"><span class="std std-ref">\PolEnsureIntervalLengths</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervals"><span class="std std-ref">\PolPrintIntervals</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervalsprintexactzero"><span class="std std-ref">\PolPrintIntervalsPrintExactZero</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervalsprintleftendpoint"><span class="std std-ref">\PolPrintIntervalsPrintLeftEndPoint</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervalsprintrightendpoint"><span class="std std-ref">\PolPrintIntervalsPrintRightEndPoint</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#id20"><span class="std std-ref">\PolReduceCoeffs*</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polmakemonic"><span class="std std-ref">\PolMakeMonic</span></a></p></li>
</ul>
</li>
<li><p>new expandable macros:</p>
<ul class="simple">
<li><p><a class="reference internal" href="polexpr-ref.html#poltoexpronetermstylea"><span class="std std-ref">\PolToExprOneTermStyleA</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polifcoeffisplusorminusone"><span class="std std-ref">\PolIfCoeffIsPlusOrMinusOne</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polleadingcoeff"><span class="std std-ref">\PolLeadingCoeff</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmchainlength"><span class="std std-ref">\PolSturmChainLength</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmnbofisolatedzeros"><span class="std std-ref">\PolSturmNbOfIsolatedZeros</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmifzeroexactlyknown"><span class="std std-ref">\PolSturmIfZeroExactlyKnown</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmisolatedzeroleft"><span class="std std-ref">\PolSturmIsolatedZeroLeft</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmisolatedzeroright"><span class="std std-ref">\PolSturmIsolatedZeroRight</span></a></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">\PolPrintIntervalsTheEndPoint</span></code> (removed at 0.7)</p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervalstheindex"><span class="std std-ref">\PolPrintIntervalsTheIndex</span></a></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">\PolIfEndPointIsPositive</span></code> (removed at 0.7)</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">\PolIfEndPointIsNegative</span></code> (removed at 0.7)</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">\PolIfEndPointIsZero</span></code> (removed at 0.7)</p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polintervalwidth"><span class="std std-ref">\PolIntervalWidth</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poldectostring"><span class="std std-ref">\PolDecToString</span></a></p></li>
</ul>
</li>
<li><p>improvements:</p>
<p>The main new feature is implementation of the <a class="reference external" href="https://en.wikipedia.org/wiki/Sturm%27s_theorem">Sturm algorithm</a>
for localization of the real roots of polynomials.</p>
</li>
</ul>
</section>
<section id="v0-4-1-2018-03-01">
<h2>v0.4.1 (2018/03/01)</h2>
<p>Synced with xint 1.3.</p>
</section>
<section id="v0-4-2-2018-03-03">
<h2>v0.4.2 (2018/03/03)</h2>
<p>Documentation fix.</p>
</section>
<section id="v0-5-2018-04-08">
<h2>v0.5 (2018/04/08)</h2>
<ul class="simple">
<li><p>bug fixes:</p>
<ul>
<li><p><a class="reference internal" href="polexpr-ref.html#polget"><span class="std std-ref">\PolGet{polname}\fromarray\macro</span></a>
crashed when <code class="docutils literal notranslate"><span class="pre">\macro</span></code> was
an <a class="reference external" href="https://www.ctan.org/pkg/xint">xinttools</a> array macro with no items. It now produces the zero
polynomial.</p></li>
</ul>
</li>
<li><p>breaking changes:</p>
<ul>
<li><p><a class="reference internal" href="polexpr-ref.html#poltosturm"><span class="std std-ref">\PolToSturm</span></a> creates primitive integer coefficients
polynomials. This speeds up localization of roots via
<a class="reference internal" href="polexpr-ref.html#polsturmisolatezeros"><span class="std std-ref">\PolSturmIsolateZeros</span></a>. In case of user
protests the author will make available again the code producing the
bona fide Sturm polynomials as used formerly.</p></li>
<li><p>polynomials created from <a class="reference internal" href="polexpr-ref.html#polfromcsv"><span class="std std-ref">\PolFromCSV</span></a> or
<a class="reference internal" href="polexpr-ref.html#polget"><span class="std std-ref">\PolGet</span></a>
get their coefficients normalized via <a class="reference external" href="https://www.ctan.org/pkg/xint">xintfrac</a>‘s <code class="docutils literal notranslate"><span class="pre">\xintRaw</span></code>.</p></li>
</ul>
</li>
<li><p>experimental change:</p>
<ul>
<li><p>optional argument to <a class="reference internal" href="polexpr-ref.html#polsturmisolatezeros"><span class="std std-ref">\PolSturmIsolateZeros</span></a>
(see <code class="docutils literal notranslate"><span class="pre">The</span> <span class="pre">degree</span> <span class="pre">41</span> <span class="pre">polynomial</span> <span class="pre">with</span> <span class="pre">-2,</span> <span class="pre">-1.9,</span> <span class="pre">-1.8,</span> <span class="pre">...,</span> <span class="pre">0,</span> <span class="pre">0.1,</span> <span class="pre">...,</span>
<span class="pre">1.9,</span> <span class="pre">2</span> <span class="pre">as</span> <span class="pre">roots</span></code> in <code class="docutils literal notranslate"><span class="pre">polexpr-examples.pdf</span></code>). It will presumably be
replaced in future by an interval specification.</p></li>
</ul>
</li>
<li><p>new non-expandable macro:</p>
<ul>
<li><p><a class="reference internal" href="polexpr-ref.html#polmakeprimitive"><span class="std std-ref">\PolMakePrimitive</span></a></p></li>
</ul>
</li>
<li><p>new expandable macro:</p>
<ul>
<li><p><a class="reference internal" href="polexpr-ref.html#policontent"><span class="std std-ref">\PolIContent</span></a></p></li>
</ul>
</li>
</ul>
</section>
<section id="v0-5-1-2018-04-22">
<h2>v0.5.1 (2018/04/22)</h2>
<ul class="simple">
<li><p>new feature:</p>
<ul>
<li><p>the character <code class="docutils literal notranslate"><span class="pre">'</span></code> can be used in polynomial names.</p></li>
</ul>
</li>
</ul>
</section>
<section id="v0-6-2018-11-20">
<h2>v0.6 (2018/11/20)</h2>
<ul class="simple">
<li><p>bugfix:</p>
<ul>
<li><p>the starred variant
<a class="reference internal" href="polexpr-ref.html#id35"><span class="std std-ref">\PolToSturm*{&lt;polname&gt;}{&lt;sturmname&gt;}</span></a>
was broken. On the occasion of the fix, its meaning has
been modified, see its documentation.</p></li>
<li><p>using <a class="reference internal" href="polexpr-ref.html#poltosturm"><span class="std std-ref">\PolToSturm</span></a> with a constant polynomial
caused a division by zero error.</p></li>
</ul>
</li>
<li><p>new macro:</p>
<ul>
<li><p><a class="reference internal" href="polexpr-ref.html#id38"><span class="std std-ref">\PolSturmIsolateZeros*</span></a>
acts like the <a class="reference internal" href="polexpr-ref.html#polsturmisolatezeros"><span class="std std-ref">non-starred variant</span></a> then computes all the multiplicities.</p></li>
</ul>
</li>
<li><p>new expandable macros:</p>
<ul>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmisolatedzeromultiplicity"><span class="std std-ref">\PolSturmIsolatedZeroMultiplicity{&lt;sturmname&gt;}{&lt;index&gt;}</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmnbofrootsoflessthanorequalto"><span class="std std-ref">\PolSturmNbOfRootsOf{&lt;sturmname&gt;}\LessThanOrEqualTo{&lt;value&gt;}</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmnbofrootsoflessthanorequaltoexpr"><span class="std std-ref">\PolSturmNbOfRootsOf{&lt;sturmname&gt;}\LessThanOrEqualToExpr{&lt;num. expr.&gt;}</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmnbwithmultofrootsoflessthanorequalto"><span class="std std-ref">\PolSturmNbWithMultOfRootsOf{&lt;sturmname&gt;}\LessThanOrEqualTo{&lt;value&gt;}</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmnbwithmultofrootsoflessthanorequaltoexpr"><span class="std std-ref">\PolSturmNbWithMultOfRootsOf{&lt;sturmname&gt;}\LessThanOrEqualToExpr{&lt;num. expr.&gt;}</span></a></p></li>
</ul>
</li>
</ul>
</section>
<section id="v0-7-2018-12-08-v0-7-1-bugfix-v0-7-2-2nd-bugfix-2018-12-09">
<h2>v0.7 (2018/12/08), v0.7.1 (bugfix), v0.7.2 (2nd bugfix) (2018/12/09)</h2>
<ul class="simple">
<li><p>breaking changes:</p>
<ul>
<li><p>although <a class="reference internal" href="polexpr-ref.html#polprintintervals"><span class="std std-ref">\PolPrintIntervals[&lt;varname&gt;]{&lt;sturmname&gt;}</span></a> default output
remains the same, some auxiliary macros for user-customization
have been removed: <code class="docutils literal notranslate"><span class="pre">\PolPrintIntervalsTheEndPoint</span></code>,
<code class="docutils literal notranslate"><span class="pre">\PolIfEndPointIsPositive{T}{F}</span></code>,
<code class="docutils literal notranslate"><span class="pre">\PolIfEndPointIsNegative{T}{F}</span></code>, and
<code class="docutils literal notranslate"><span class="pre">\PolIfEndPointIsZero{T}{F}</span></code>.</p></li>
</ul>
</li>
<li><p>bugfix:</p>
<ul>
<li><p>it could happen that, contrarily to documentation, an interval computed
by <a class="reference internal" href="polexpr-ref.html#polsturmisolatezeros"><span class="std std-ref">\PolSturmIsolateZeros{&lt;sturmname&gt;}</span></a> had
zero as an endpoint,</p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polensureintervallength"><span class="std std-ref">\PolEnsureIntervalLength{&lt;sturmname&gt;}{&lt;index&gt;}{&lt;exponent&gt;}</span></a> could under certain circumstances erroneously
replace a non-zero root by zero,</p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polensureintervallengths"><span class="std std-ref">\PolEnsureIntervalLengths{&lt;sturmname&gt;}{&lt;exponent&gt;}</span></a> crashed when used with a polynomial with no
real roots, hence for which no isolation intervals existed (thanks to
Thomas Söll for report).</p></li>
</ul>
</li>
<li><p>new macros:</p>
<ul>
<li><p><a class="reference internal" href="polexpr-ref.html#id41"><span class="std std-ref">\PolSturmIsolateZeros**{&lt;sturmname&gt;}</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmisolatezerosgetmultiplicitiesandrationalroots"><span class="std std-ref">\PolSturmIsolateZerosGetMultiplicitiesAndRationalRoots{&lt;sturmname&gt;}</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmisolatezerosandfindrationalroots"><span class="std std-ref">\PolSturmIsolateZerosAndFindRationalRoots{&lt;sturmname&gt;}</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polexprsetup"><span class="std std-ref">\polexprsetup</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#id61"><span class="std std-ref">\PolPrintIntervals*</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervalsnorealroots"><span class="std std-ref">\PolPrintIntervalsNoRealRoots</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervalsbeginenv"><span class="std std-ref">\PolPrintIntervalsBeginEnv</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervalsendenv"><span class="std std-ref">\PolPrintIntervalsEndEnv</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervalsknownroot"><span class="std std-ref">\PolPrintIntervalsKnownRoot</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervalsunknownroot"><span class="std std-ref">\PolPrintIntervalsUnknownRoot</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervalsprintmultiplicity"><span class="std std-ref">\PolPrintIntervalsPrintMultiplicity</span></a></p></li>
</ul>
</li>
<li><p>new expandable macros:</p>
<ul>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmnbofrationalroots"><span class="std std-ref">\PolSturmNbOfRationalRoots{&lt;sturmname&gt;}</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmnbofrationalrootswithmultiplicities"><span class="std std-ref">\PolSturmNbOfRationalRootsWithMultiplicities{&lt;sturmname&gt;}</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmrationalroot"><span class="std std-ref">\PolSturmRationalRoot{&lt;sturmname&gt;}{&lt;k&gt;}</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmrationalrootindex"><span class="std std-ref">\PolSturmRationalRootIndex{&lt;sturmname&gt;}{&lt;k&gt;}</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polsturmrationalrootmultiplicity"><span class="std std-ref">\PolSturmRationalRootMultiplicity{&lt;sturmname&gt;}{&lt;k&gt;}</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervalsthevar"><span class="std std-ref">\PolPrintIntervalsTheVar</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervalsthesturmname"><span class="std std-ref">\PolPrintIntervalsTheSturmName</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervalsthemultiplicity"><span class="std std-ref">\PolPrintIntervalsTheMultiplicity</span></a></p></li>
</ul>
</li>
</ul>
</section>
<section id="v0-7-3-2019-02-04">
<h2>v0.7.3 (2019/02/04)</h2>
<ul class="simple">
<li><p>bugfix:</p>
<ul>
<li><p>Debugging information not destined to user showed in log if root
finding was done under <code class="docutils literal notranslate"><span class="pre">\xintverbosetrue</span></code> regime.</p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#polprintintervalsthevar"><span class="std std-ref">\PolPrintIntervalsTheVar</span></a> remained
defined after <a class="reference internal" href="polexpr-ref.html#polprintintervals"><span class="std std-ref">\PolPrintIntervals</span></a> but was
left undefined after <a class="reference internal" href="polexpr-ref.html#id61"><span class="std std-ref">\PolPrintIntervals*</span></a>
(reported by Jürgen Gilg). Now remains defined in both cases, and
<a class="reference internal" href="polexpr-ref.html#polprintintervalsthesturmname"><span class="std std-ref">\PolPrintIntervalsTheSturmName</span></a>
also.</p></li>
<li><p>Polynomial names ending in digits caused errors (reported by Thomas
Söll).</p></li>
</ul>
</li>
</ul>
</section>
<section id="v0-7-4-2019-02-12">
<h2>v0.7.4 (2019/02/12)</h2>
<ul class="simple">
<li><p>bugfix:</p>
<ul>
<li><p>20000000000 is too big for <code class="docutils literal notranslate"><span class="pre">\numexpr</span></code>, shouldn’t I know that?
Thanks to Jürgen Gilg for report.</p></li>
</ul>
</li>
</ul>
</section>
<section id="v0-7-5-2020-01-31">
<h2>v0.7.5 (2020/01/31)</h2>
<p>Synced with xintexpr 1.4. Requires it.</p>
</section>
<section id="v0-8-2021-03-29">
<span id="polexpr08release"></span><h2>v0.8 (2021/03/29)</h2>
<p>Synced with xintexpr 1.4d. Requires it.</p>
<ul class="simple">
<li><p>breaking changes:</p>
<ul>
<li><p>As the usability of character <code class="docutils literal notranslate"><span class="pre">'</span></code> in names has been extended
from <code class="docutils literal notranslate"><span class="pre">\poldef</span></code> to also generally <code class="docutils literal notranslate"><span class="pre">\xintexpr</span></code>, <code class="docutils literal notranslate"><span class="pre">\xintdefvar</span></code>,
and <code class="docutils literal notranslate"><span class="pre">\xintdeffunc</span></code>, it means that the infix operators
<code class="docutils literal notranslate"><span class="pre">'and'</span></code>, <code class="docutils literal notranslate"><span class="pre">'or'</span></code>, and <code class="docutils literal notranslate"><span class="pre">'mod'</span></code> must be replaced
by <code class="docutils literal notranslate"><span class="pre">&amp;&amp;</span></code>, <code class="docutils literal notranslate"><span class="pre">||</span></code>, and <code class="docutils literal notranslate"><span class="pre">/:</span></code> if they
follow immediately a variable name (similarly <code class="docutils literal notranslate"><span class="pre">'xor'</span></code> must
be replaced by the <code class="docutils literal notranslate"><span class="pre">xor()</span></code> function in such case).</p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltoexpr"><span class="std std-ref">\PolToExpr</span></a> by default uses a catcode 12
<code class="docutils literal notranslate"><span class="pre">^</span></code>. See its documentation and the new configuration
<a class="reference internal" href="polexpr-ref.html#poltoexprcaret"><span class="std std-ref">\PolToExprCaret</span></a>.</p></li>
</ul>
</li>
<li><p>deprecated:</p>
<ul>
<li><p>Usage of <code class="docutils literal notranslate"><span class="pre">P/Q</span></code> for the euclidean quotient of two polynomials is
deprecated.  Start using <code class="docutils literal notranslate"><span class="pre">quo(P,Q)</span></code> in its place.</p></li>
</ul>
</li>
<li><p>bugfix:</p>
<ul>
<li><p>The <code class="docutils literal notranslate"><span class="pre">\xintglobaldefstrue</span></code> setting was obeyed only partially
by the polexpr macros defining polynomials.</p></li>
<li><p>The <code class="docutils literal notranslate"><span class="pre">\xintexpr</span></code> variables storing the values of the extremities of the
intervals as found by <a class="reference internal" href="polexpr-ref.html#polsturmisolatezeros"><span class="std std-ref">\PolSturmIsolateZeros</span></a> were not updated at 0.7.5 to the xintexpr 1.4
format and thus caused low-level TeX errors if used.</p></li>
<li><p>Attempting to use in <code class="docutils literal notranslate"><span class="pre">\poldef</span></code> a function previously declared
via <code class="docutils literal notranslate"><span class="pre">\xintdeffunc</span></code> which made usage of the indexing or slicing
“ople” syntax typically caused <code class="docutils literal notranslate"><span class="pre">TeX</span> <span class="pre">capacity</span> <span class="pre">exceeded</span></code> error.
Indeed 0.7.5 only partially made polexpr able to cope with the
extended possibilities for xintexpr 1.4 user-declared functions.
Hopefully <code class="docutils literal notranslate"><span class="pre">0.8</span></code> achieves full functionality in this context.</p></li>
</ul>
</li>
<li><p>new macros:</p>
<ul>
<li><p><a class="reference internal" href="polexpr-ref.html#polnewpolverbosefalse"><span class="std std-ref">\polnewpolverbosefalse</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltoexprcaret"><span class="std std-ref">\PolToExprCaret</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#poltoexprinvar"><span class="std std-ref">\PolToExprInVar</span></a></p></li>
<li><p>alongside the major new functionalities described in the next item
<a class="reference internal" href="polexpr-ref.html#poltypeset"><span class="std std-ref">\PolTypeset</span></a> and <a class="reference internal" href="polexpr-ref.html#poltoexpr"><span class="std std-ref">\PolToExpr</span></a> have
been enhanced to accept as argument a general expression and not
only a pre-declared polynomial name.</p></li>
</ul>
</li>
<li><p>new features:</p>
<ul>
<li><p>The package is usable under Plain and probably most any TeX format,
and not only under LaTeX.</p></li>
<li><p>The core of the package has been rewritten entirely in order to
start letting <code class="docutils literal notranslate"><span class="pre">\xintexpr</span></code> recognize a polynomial type as a genuine
variable.  This has allowed:</p>
<ul>
<li><p>to solve the reduced inter-operability problems between polexpr
and <a class="reference external" href="https://www.ctan.org/pkg/xintexpr">xintexpr</a> which arose as consequences to the deep <a class="reference external" href="https://www.ctan.org/pkg/xintexpr">xintexpr</a> <code class="docutils literal notranslate"><span class="pre">1.4</span></code>
evolution,</p></li>
<li><p>to make available most of the functionality associated to
expandable macros directly in the <code class="docutils literal notranslate"><span class="pre">\xinteval</span></code> syntax as
operators or functions,</p></li>
<li><p>to provide (expandable) functional interface in <code class="docutils literal notranslate"><span class="pre">\xinteval</span></code> to
features previously available only via (for some, non-expandable)
macro interface such as gcd computations.</p></li>
</ul>
</li>
</ul>
</li>
</ul>
<p>See the updated <a class="reference internal" href="polexpr-ref.html#quick"><span class="std std-ref">Quick syntax overview</span></a> and then
<a class="reference internal" href="polexpr-ref.html#polexpr08"><span class="std std-ref">the extended syntax description</span></a>.</p>
</section>
<section id="v0-8-1-2021-04-12">
<h2>v0.8.1 (2021/04/12)</h2>
<ul class="simple">
<li><p>breaking changes:</p>
<ul>
<li><p>renamed v0.8’s <code class="docutils literal notranslate"><span class="pre">icontent()</span></code> to <a class="reference internal" href="polexpr-ref.html#cont"><span class="std std-ref">cont()</span></a>.</p></li>
<li><p>renamed v0.8’s <code class="docutils literal notranslate"><span class="pre">lcoeff()</span></code> to <a class="reference internal" href="polexpr-ref.html#lc"><span class="std std-ref">lc()</span></a>.</p></li>
</ul>
</li>
<li><p>bugfix:</p>
<ul>
<li><p>Sadly, <code class="docutils literal notranslate"><span class="pre">diff1()</span></code>, <code class="docutils literal notranslate"><span class="pre">diff2()</span></code>,  <code class="docutils literal notranslate"><span class="pre">diffn()</span></code> were broken
for polynomials of degrees 8 or more, due to a typo and
insufficient testing.</p></li>
<li><p>The package should have (as documented) required <a class="reference external" href="https://www.ctan.org/pkg/xintexpr">xintexpr</a> 1.4d
but in practice it accepted to work with <a class="reference external" href="https://www.ctan.org/pkg/xintexpr">xintexpr</a> 1.4c, whose
<code class="docutils literal notranslate"><span class="pre">\xinteval</span></code> does not know how to “output” a polynomial.</p></li>
<li><p>The definition of one of the two variants of
<a class="reference internal" href="polexpr-ref.html#polsturmnbofrootsoflessthanorequalto"><span class="std std-ref">\PolSturmNbOfRootsOf…</span></a>
was broken by an end-of-line space, left-over
from mass conversion from LaTeX to TeX syntax.</p></li>
</ul>
</li>
<li><p>added:</p>
<ul>
<li><p><a class="reference internal" href="polexpr-ref.html#lpol"><span class="std std-ref">lpol()</span></a></p></li>
<li><p><a class="reference internal" href="polexpr-ref.html#lcoeffs"><span class="std std-ref">lcoeffs()</span></a></p></li>
</ul>
</li>
</ul>
</section>
<section id="v0-8-2-2021-05-05">
<h2>v0.8.2 (2021/05/05)</h2>
<ul class="simple">
<li><p>breaking change:</p>
<ul>
<li><p>usage of <code class="docutils literal notranslate"><span class="pre">\xintPFloat</span></code> in place of <code class="docutils literal notranslate"><span class="pre">\xintFloat</span></code> for
<a class="reference internal" href="polexpr-ref.html#poltofloatexprcmd"><span class="std std-ref">\PolToFloatExprCmd</span></a>.</p></li>
</ul>
</li>
<li><p>improved:</p>
<ul>
<li><p>Some <a class="reference external" href="https://www.ctan.org/pkg/xintexpr">xintexpr</a> functions such as <code class="docutils literal notranslate"><span class="pre">rseq()</span></code> use the semi-colon,
and it was mentioned in the documentation that <a class="reference internal" href="polexpr-ref.html#poldef"><span class="std std-ref">\poldef</span></a>
will be confused by this and that inner semi-colons could be
set within braces <code class="docutils literal notranslate"><span class="pre">{;}</span></code> as a work-around.  It was not clear from
this documentation that also <a class="reference internal" href="polexpr-ref.html#id5"><span class="std std-ref">\PolDef</span></a> required
this work-around.  With this relase only <a class="reference internal" href="polexpr-ref.html#poldef"><span class="std std-ref">\poldef</span></a> but
not <a class="reference internal" href="polexpr-ref.html#id5"><span class="std std-ref">\PolDef</span></a> needs the work-around.</p></li>
</ul>
</li>
<li><p>track <a class="reference external" href="https://www.ctan.org/pkg/xintexpr">xintexpr</a> <code class="docutils literal notranslate"><span class="pre">1.4e</span></code> changes relative to powers.</p></li>
</ul>
</section>
<section id="v0-8-3-2021-05-27">
<h2>v0.8.3 (2021/05/27)</h2>
<ul class="simple">
<li><p>small internal update to track an <a class="reference external" href="https://www.ctan.org/pkg/xintexpr">xintexpr</a> <code class="docutils literal notranslate"><span class="pre">1.4h</span></code> change
regarding handling of exceptions.  Will require this version at
least on loading.</p></li>
</ul>
</section>
<section id="v0-8-4-2021-11-01">
<h2>v0.8.4 (2021/11/01)</h2>
<ul class="simple">
<li><p>bugfix: <a class="reference internal" href="polexpr-ref.html#id41"><span class="std std-ref">\PolSturmIsolateZeros**{&lt;sturmname&gt;}</span></a> did not declare the <code class="docutils literal notranslate"><span class="pre">&lt;sturmname&gt;_norr</span></code> and
<code class="docutils literal notranslate"><span class="pre">&lt;sturmname&gt;_sqf_norr</span></code> polynomials if original polynomial had no real
root!</p></li>
</ul>
</section>
<section id="v0-8-5-2021-11-30">
<h2>v0.8.5 (2021/11/30)</h2>
<ul class="simple">
<li><p>bugfix: support for the <code class="docutils literal notranslate"><span class="pre">intfrom()</span></code> function was in the code,
but the declaration to the polynomial parser had not been done.</p></li>
<li><p>track (belatedly) upstream deprecation of <code class="docutils literal notranslate"><span class="pre">\xintSignedFrac</span></code> and
<code class="docutils literal notranslate"><span class="pre">\xintSignedFwOver</span></code> at <a class="reference external" href="https://www.ctan.org/pkg/xintexpr">xintexpr</a> <code class="docutils literal notranslate"><span class="pre">1.4g</span></code></p></li>
</ul>
</section>
<section id="v0-8-6-2022-01-09">
<h2>v0.8.6 (2022/01/09)</h2>
<ul class="simple">
<li><p>provide a separate <code class="docutils literal notranslate"><span class="pre">polexpr-examples.pdf</span></code> with examples formerly
shown as part of the html documentation.</p></li>
<li><p>minor improvement to the computation of a priori bounds on real roots.</p></li>
<li><p>add <a class="reference internal" href="polexpr-ref.html#polprintintervalsrowseparator"><span class="std std-ref">\PolPrintIntervalsRowSeparator</span></a>
and allow usage of <code class="docutils literal notranslate"><span class="pre">amsmath</span></code> environments in custom
<a class="reference internal" href="polexpr-ref.html#polprintintervalsbeginenv"><span class="std std-ref">\PolPrintIntervalsBeginEnv</span></a> and
<a class="reference internal" href="polexpr-ref.html#polprintintervalsendenv"><span class="std std-ref">\PolPrintIntervalsEndEnv</span></a>.</p></li>
</ul>
</section>
<section id="v0-8-7-2022-05-14">
<h2>v0.8.7 (2022/05/14)</h2>
<ul class="simple">
<li><p>bugfix: catcode sanitization by <a class="reference internal" href="polexpr-ref.html#poldef"><span class="std std-ref">\poldef</span></a> was minimal
ever since <code class="docutils literal notranslate"><span class="pre">0.1</span></code> and handled only the semi-colon.  Thus e.g. the
active <code class="docutils literal notranslate"><span class="pre">!</span></code> from babel-french caused errors and <code class="docutils literal notranslate"><span class="pre">\string!</span></code> was
needed as work-around for factorials.  Now the same sanitization as
for <code class="docutils literal notranslate"><span class="pre">\xintdefvar</span></code> and <code class="docutils literal notranslate"><span class="pre">\xintdeffunc</span></code> is applied.  This however can
only work at locations where the catcodes are not yet frozen at the
time <code class="docutils literal notranslate"><span class="pre">\poldef</span></code> expands.</p></li>
<li><p>split the html documentation into three files and enhance it via CSS
styling.</p></li>
</ul>
</section>
</section>


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<ul>
<li><a class="reference internal" href="#">CHANGES</a><ul>
<li><a class="reference internal" href="#v0-1-2018-01-11-initial-release-features">v0.1 (2018/01/11): initial release. Features:</a></li>
<li><a class="reference internal" href="#v0-2-2018-01-14">v0.2 (2018/01/14)</a></li>
<li><a class="reference internal" href="#v0-3-2018-01-17">v0.3 (2018/01/17)</a></li>
<li><a class="reference internal" href="#v0-3-1-2018-01-18">v0.3.1 (2018/01/18)</a></li>
<li><a class="reference internal" href="#v0-4-2018-02-16">v0.4 (2018/02/16)</a></li>
<li><a class="reference internal" href="#v0-4-1-2018-03-01">v0.4.1 (2018/03/01)</a></li>
<li><a class="reference internal" href="#v0-4-2-2018-03-03">v0.4.2 (2018/03/03)</a></li>
<li><a class="reference internal" href="#v0-5-2018-04-08">v0.5 (2018/04/08)</a></li>
<li><a class="reference internal" href="#v0-5-1-2018-04-22">v0.5.1 (2018/04/22)</a></li>
<li><a class="reference internal" href="#v0-6-2018-11-20">v0.6 (2018/11/20)</a></li>
<li><a class="reference internal" href="#v0-7-2018-12-08-v0-7-1-bugfix-v0-7-2-2nd-bugfix-2018-12-09">v0.7 (2018/12/08), v0.7.1 (bugfix), v0.7.2 (2nd bugfix) (2018/12/09)</a></li>
<li><a class="reference internal" href="#v0-7-3-2019-02-04">v0.7.3 (2019/02/04)</a></li>
<li><a class="reference internal" href="#v0-7-4-2019-02-12">v0.7.4 (2019/02/12)</a></li>
<li><a class="reference internal" href="#v0-7-5-2020-01-31">v0.7.5 (2020/01/31)</a></li>
<li><a class="reference internal" href="#v0-8-2021-03-29">v0.8 (2021/03/29)</a></li>
<li><a class="reference internal" href="#v0-8-1-2021-04-12">v0.8.1 (2021/04/12)</a></li>
<li><a class="reference internal" href="#v0-8-2-2021-05-05">v0.8.2 (2021/05/05)</a></li>
<li><a class="reference internal" href="#v0-8-3-2021-05-27">v0.8.3 (2021/05/27)</a></li>
<li><a class="reference internal" href="#v0-8-4-2021-11-01">v0.8.4 (2021/11/01)</a></li>
<li><a class="reference internal" href="#v0-8-5-2021-11-30">v0.8.5 (2021/11/30)</a></li>
<li><a class="reference internal" href="#v0-8-6-2022-01-09">v0.8.6 (2022/01/09)</a></li>
<li><a class="reference internal" href="#v0-8-7-2022-05-14">v0.8.7 (2022/05/14)</a></li>
</ul>
</li>
</ul>

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