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autocomplete="off"> </div> <div class="search-buttons input-group-btn"> <div class="btn-group"> <button class="btn btn-default search" type="submit"><span class="virtual">Search</span> <span class="glyphicon glyphicon-search" style="top: 2px;"></span></button> </div> </div> </span> <span> <div class="search-buttons input-group-btn"> <div class="btn-group"> <div class="btn-group fields"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Fields <i class="caret"></i></button> <ul id="fields" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">any:</span><span>&nbsp;</span>anywhere (default)</a></li> <li><a href="#"><span class="token item">ab:</span><span>&nbsp;&nbsp;</span>description</a></li> <li><a href="#"><span class="token item">au:</span><span>&nbsp;&nbsp;</span>author</a></li> <li><a href="#"><span class="token item">cc:</span><span>&nbsp;&nbsp;</span>msc</a></li> <li><a href="#"><span class="token item">pl:</span><span>&nbsp;&nbsp;</span>programming language</a></li> <li><a href="#"><span class="token item">si:</span><span>&nbsp;&nbsp;</span>software ID</a></li> <li><a href="#"><span class="token item">sw:</span><span>&nbsp;&nbsp;</span>name</a></li> <li><a href="#"><span class="token item">ut:</span><span>&nbsp;&nbsp;</span>keyword</a></li> </ul> </div> <div class="btn-group operators"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Operators <i class="caret"></i></button> <ul id="operators" class="dropdown-menu pull-right"> <li><a href="#"><span class="token">a&nbsp;<span class="item">&</span>&nbsp;b&nbsp;</span><span>&nbsp;</span>logical and (default)</a></li> <li><a href="#"><span class="token">a&nbsp;<span class="item">|</span>&nbsp;b&nbsp;</span><span>&nbsp;</span>logical or</a></li> <li><a href="#"><span class="token"><span class="item">!</span>ab&nbsp;&nbsp;&nbsp;</span><span>&nbsp;</span>logical not</a></li> <li><a href="#"><span class="token">abc<span class="item">*</span>&nbsp;&nbsp;</span><span>&nbsp;</span>right wildcard</a></li> <li><a href="#"><span class="token"><span class="item">"</span>ab&nbsp;c<span class="item">"</span></span><span>&nbsp;</span>phrase</a></li> <li><a href="#"><span class="token"><span class="item">(</span>ab&nbsp;c<span class="item">)</span></span><span>&nbsp;</span>parentheses</a></li> </ul> </div> </div> </div> <div class="special"> <ul class="nav help-button"> <li class="dropdown pull-right"> <a href="#">Help <i class="caret"></i></a> </li> </ul> </div> </span> </div> <div class="help"><h2>Examples</h2> <div id="help-terms" role="table"> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/software/?q=sw%3ASage%2A">sw:Sage*</a></span> <span class="search-explanation" role="cell" role="cell">Search for a specific <strong>s</strong>oft<strong>w</strong>are package containing the sequence <em>Sage</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/software/?q=ab%3Ageometry+%26+ut%3AORMS">ab:geometry &amp; ut:ORMS</a></span> <span class="search-explanation" role="cell" role="cell">Search for software packages with the word <em>geometry</em> in the description(<strong>ab</strong>), and which have the keyword(<strong>ut</strong>) <em>ORMS</em> ( Oberwolfach Registry of Mathematical Software).The operator <strong>&</strong> is the default and may be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/software/?q=cc%3A13+%7C+14">cc:13 | 14</a></span> <span class="search-explanation" role="cell" role="cell">Search for software packages which are cited(<strong>cc</strong>) by articles belonging to the <strong><u>c</u>lassification <u>c</u>ode</strong> sections <em>13</em> and <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/software/?q=GAP+au%3AEick">GAP au:Eick</a></span> <span class="search-explanation" role="cell" role="cell">Search for <em>GAP</em> in the <strong>any</strong> index (which also includes dependencies) and by software <strong><u>au</u>thor</strong> containing the sequence <em>Eick</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/software/?q=pl%3AJava+%26+ab%3AR">pl:Java &amp; ab:R</a></span> <span class="search-explanation" role="cell" role="cell">Search for software package in the <strong><u>p</u>rogramming <u>l</u>anguage</strong> Java whose description text(<strong>ab</strong>) contains <em>R</em></span> </div> </div> <h2>Fields</h2> <div id="help-fields" role="table"> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>ab</strong> </span> <span class="search-explanation" role="cell" role="cell"> Text from the description </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>au</strong> </span> <span class="search-explanation" role="cell" role="cell"> Name(s) of the author(s) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>cc</strong> </span> <span class="search-explanation" role="cell" role="cell"> Main fields of the software (given by first two MSC digits) </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>pl</strong> </span> <span class="search-explanation" role="cell" role="cell"> Programming language the software is written in </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>si</strong> </span> <span class="search-explanation" role="cell" role="cell"> swMATH software ID </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>sw</strong> </span> <span class="search-explanation" role="cell" role="cell"> Software name </span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"> <strong>ut</strong> </span> <span class="search-explanation" role="cell" role="cell"> Keywords </span> </div> </div> <p style="margin-bottom:0.5cm;"></p> <h2>Operators</h2> <div id="operators-fields" role="table"> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>a &amp; b</strong></span> <span class="search-explanation" role="cell" role="cell">logical and</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>a | b</strong></span> <span class="search-explanation" role="cell" role="cell">logical or</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>!ab</strong></span> <span class="search-explanation" role="cell" role="cell">logical not</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>abc*</strong></span> <span class="search-explanation" role="cell" role="cell">right wildcard</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>ab c</strong></span> <span class="search-explanation" role="cell" role="cell">phrase</span> </div> <div class="help-item" role="row"> <span class="search-fields" role="rowheader"><strong>(ab c)</strong></span> <span class="search-explanation" role="cell" role="cell">parentheses</span> </div> </div> <p style="margin-bottom:0.5cm;"></p> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> </div><div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="software"> <div class="content-main"> <article> <div class="head"> <h2>MPI</h2> </div> <div class="text"> <table> <tr> <td>swMATH ID:</td> <td> 6496 </td> </tr> <tr> <td>Software Authors:</td> <td> <div class="author"><a href="/authors/fike.jeffrey-a" title="Author Profile">Fike, Jeffrey A.</a>; <a href="/authors/alonso.juan-j" title="Author Profile">Alonso, Juan J.</a></div> </td> </tr> <tr> <td>Description:</td> <td>Automatic differentiation through the use of hyper-dual numbers for second derivatives. Automatic differentiation techniques are typically derived based on the chain rule of differentiation. Other methods can be derived based on the inherent mathematical properties of generalized complex numbers that enable first-derivative information to be carried in the non-real part of the number. These methods are capable of producing effectively exact derivative values. However, when second-derivative information is desired, generalized complex numbers are not sufficient. Higher-dimensional extensions of generalized complex numbers, with multiple non-real parts, can produce accurate second-derivative information provided that multiplication is commutative. One particular number system is developed, termed hyper-dual numbers, which produces exact first- and second-derivative information. The accuracy of these calculations is demonstrated on an unstructured, parallel, unsteady Reynolds-averaged Navier-Stokes solver.</td> </tr> <tr> <td>Homepage:</td> <td> <a href="http://www.brown.edu/Departments/CCV/doc/mpi-cuda">http://www.brown.edu/Departments/CCV/doc/mpi-cuda</a> </td> </tr> <tr> <td>Keywords:</td> <td> <a href="/software/?q=ut%3Ahyper-dual+numbers">hyper-dual numbers</a>; <a href="/software/?q=ut%3Ageneralized+complex+numbers">generalized complex numbers</a>; <a href="/software/?q=ut%3Aoperator+overloading">operator overloading</a>; <a href="/software/?q=ut%3Asecond+derivatives">second derivatives</a>; <a href="/software/?q=ut%3AHessian">Hessian</a>; <a href="/software/?q=ut%3Aforward+mode">forward mode</a>; <a href="/software/?q=ut%3AC+%2B%2B">C ++</a>; <a href="/software/?q=ut%3ACUDA">CUDA</a>; <a href="/software/?q=ut%3AMPI">MPI</a>; <a href="/software/?q=ut%3Anumerical+examples">numerical examples</a>; <a href="/software/?q=ut%3Aautomatic+differentiation">automatic differentiation</a>; <a href="/software/?q=ut%3Achain+rule+of+differentiation">chain rule of differentiation</a>; <a href="/software/?q=ut%3AReynolds-averaged+Navier-Stokes+solver">Reynolds-averaged Navier-Stokes solver</a> </td> </tr> <tr> <td>Related Software:</td> <td> <a href="/software/503">LAPACK</a>; <a href="/software/3258">CUDA</a>; <a href="/software/4012">PETSc</a>; <a href="/software/830">ScaLAPACK</a>; <a href="/software/3216">BLAS</a>; <a href="/software/4273">PVM</a>; <a href="/software/4089">METIS</a>; <a href="/software/6126">MPI/MPICH</a>; <a href="/software/558">Matlab</a>; <a href="/software/7060">OpenCL</a>; <a href="/software/4697">ParMETIS</a>; <a href="/software/366">Gmsh</a>; <a href="/software/4028">Trilinos</a>; <a href="/software/4126">FFTW</a>; <a href="/software/4013">MUMPS</a>; <a href="/software/14460">Python</a>; <a href="/software/13111">OpenMPI</a>; <a href="/software/8853">NAS Parallel Benchmarks</a>; <a href="/software/8578">BLACS</a>; <a href="/software/4629">SparseMatrix</a> </td> </tr> <tr class="indexed"> <td>Cited in:</td> <td> <a href="/?q=si%3A6496">498&nbsp;Documents</a> </td> </tr> </table> </div> <div class="profile"> <div class="standard_articles publications"> <h3 style="margin-bottom: 0"> Standard Articles </h3> <table> <thead> <tr> <th> <strong> 1&nbsp;Publication describing the Software, including <a href="/?q=an%3A6086549">1&nbsp;Publication in zbMATH </a></strong> </th> <th> Year </th> </tr> </thead> <tbody> <tr> <td> <a class="black" href="/1251.65026">Automatic differentiation through the use of hyper-dual numbers for second derivatives.</a>&nbsp;<a class="label" href="/1251.65026">Zbl&nbsp;1251.65026</a><br><a href="/authors/fike.jeffrey-a" title="Author Profile">Fike, Jeffrey A.</a>; <a href="/authors/alonso.juan-j" title="Author Profile">Alonso, Juan J.</a> </td> <td> <div class="citation_year">2012</div> </td> </tr> </tbody> </table> </div> 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href="/classification/?q=cc%3A34" title="Mathematics Subject Classification"> Ordinary differential equations&nbsp;<span style="white-space: nowrap;">(34-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A49" title="Citing Publications in this Field">7</a> </td> <td class="text"> <a href="/classification/?q=cc%3A49" title="Mathematics Subject Classification"> Calculus of variations and optimal control; optimization&nbsp;<span style="white-space: nowrap;">(49-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A70" title="Citing Publications in this Field">7</a> </td> <td class="text"> <a href="/classification/?q=cc%3A70" title="Mathematics Subject Classification"> Mechanics of particles and systems&nbsp;<span style="white-space: nowrap;">(70-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A05" title="Citing Publications in this Field">6</a> </td> <td class="text"> <a href="/classification/?q=cc%3A05" title="Mathematics Subject Classification"> Combinatorics&nbsp;<span style="white-space: nowrap;">(05-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A60" title="Citing Publications in this Field">6</a> </td> <td class="text"> <a href="/classification/?q=cc%3A60" title="Mathematics Subject Classification"> Probability theory and stochastic processes&nbsp;<span style="white-space: nowrap;">(60-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A37" title="Citing Publications in this Field">5</a> </td> <td class="text"> <a href="/classification/?q=cc%3A37" title="Mathematics Subject Classification"> Dynamical systems and ergodic theory&nbsp;<span style="white-space: nowrap;">(37-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A94" title="Citing Publications in this Field">5</a> </td> <td class="text"> <a href="/classification/?q=cc%3A94" title="Mathematics Subject Classification"> Information and communication theory, circuits&nbsp;<span style="white-space: nowrap;">(94-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A11" title="Citing Publications in this Field">4</a> </td> <td class="text"> <a href="/classification/?q=cc%3A11" title="Mathematics Subject Classification"> Number theory&nbsp;<span style="white-space: nowrap;">(11-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A91" title="Citing Publications in this Field">4</a> </td> <td class="text"> <a href="/classification/?q=cc%3A91" title="Mathematics Subject Classification"> Game theory, economics, finance, and other social and behavioral sciences&nbsp;<span style="white-space: nowrap;">(91-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A85" title="Citing Publications in this Field">3</a> </td> <td class="text"> <a href="/classification/?q=cc%3A85" title="Mathematics Subject Classification"> Astronomy and astrophysics&nbsp;<span style="white-space: nowrap;">(85-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A93" title="Citing Publications in this Field">3</a> </td> <td class="text"> <a href="/classification/?q=cc%3A93" title="Mathematics Subject Classification"> Systems theory; control&nbsp;<span style="white-space: nowrap;">(93-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A00" title="Citing Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A00" title="Mathematics Subject Classification"> General and overarching topics; collections&nbsp;<span style="white-space: nowrap;">(00-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A45" title="Citing Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A45" title="Mathematics Subject Classification"> Integral equations&nbsp;<span style="white-space: nowrap;">(45-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A53" title="Citing Publications in this Field">2</a> </td> <td class="text"> <a href="/classification/?q=cc%3A53" title="Mathematics Subject Classification"> Differential geometry&nbsp;<span style="white-space: nowrap;">(53-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A14" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A14" title="Mathematics Subject Classification"> Algebraic geometry&nbsp;<span style="white-space: nowrap;">(14-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A17" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A17" title="Mathematics Subject Classification"> Nonassociative rings and algebras&nbsp;<span style="white-space: nowrap;">(17-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A20" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A20" title="Mathematics Subject Classification"> Group theory and generalizations&nbsp;<span style="white-space: nowrap;">(20-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A33" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A33" title="Mathematics Subject Classification"> Special functions&nbsp;<span style="white-space: nowrap;">(33-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A39" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A39" title="Mathematics Subject Classification"> Difference and functional equations&nbsp;<span style="white-space: nowrap;">(39-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A41" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A41" title="Mathematics Subject Classification"> Approximations and expansions&nbsp;<span style="white-space: nowrap;">(41-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A52" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A52" title="Mathematics Subject Classification"> Convex and discrete geometry&nbsp;<span style="white-space: nowrap;">(52-XX)</span> </a> </td></tr><tr class="more"> <td class="number"> <a href="/?q=si%3A6496+cc%3A83" title="Citing Publications in this Field">1</a> </td> <td class="text"> <a href="/classification/?q=cc%3A83" title="Mathematics Subject Classification"> Relativity and gravitational theory&nbsp;<span style="white-space: nowrap;">(83-XX)</span> </a> </td></tr> </table> </div> <div class="diagram svg-diagram"> <h3>Citations by Year</h3> <div class="diagram si-diagram" aria-label="citing publications by year"></div> <style> rect:hover { fill: steelblue; } .axis path, .axis line { fill: none; stroke: #000; shape-rendering: crispEdges; } .bar { fill: steelblue; } a:hover .bar, a:focus .bar { stroke: black; fill-opacity: 60%; } </style> <script src="/static/js/d3.v3.min.js"></script> <script> var margin = { top: 20, right: 0, bottom: 30, left: 50 }; var width = 930 - margin.left - margin.right; var height = 150 - margin.top - margin.bottom; var svg = d3.selectAll(".si-diagram").append("svg") .attr("width", width + margin.left + margin.right) .attr("height", height + margin.top + margin.bottom) .append("g") .attr("transform", "translate(" + margin.left + "," + margin.top + ")"); var data = [{ year:1990, frequency:1 },{ year:1996, frequency:2 },{ year:1997, frequency:5 },{ year:1998, frequency:7 },{ year:1999, frequency:10 },{ year:2000, frequency:17 },{ year:2001, frequency:19 },{ year:2002, frequency:25 },{ year:2003, frequency:13 },{ year:2004, frequency:16 },{ year:2005, frequency:23 },{ year:2006, frequency:19 },{ year:2007, frequency:21 },{ year:2008, frequency:25 },{ year:2009, frequency:24 },{ year:2010, frequency:22 },{ year:2011, frequency:17 },{ year:2012, frequency:22 },{ year:2013, frequency:30 },{ year:2014, frequency:18 },{ year:2015, frequency:37 },{ year:2016, frequency:16 },{ year:2017, frequency:15 },{ year:2018, frequency:30 },{ year:2019, frequency:16 },{ year:2020, frequency:12 },{ year:2021, frequency:13 },{ year:2022, frequency:12 },{ year:2023, frequency:5 },{ year:2024, frequency:6 }]; data.forEach(function(d) { d.year = +d.year; d.frequency = +d.frequency; }); var xScale = d3.scale.ordinal() .rangeRoundBands([0, width], .1); var yScale = d3.scale.linear() .range([height, 0]); // fill if less than 20 years span var zero = d3.max( [ 20 - ( d3.max( data, d => d.year ) + 1 - d3.min( data, d => d.year ) ), 0 ] ); // generate range from min to max xScale.domain( d3.range( d3.min( data, d => d.year ), d3.max( data, d => d.year ) + 1 + zero ) ); yScale.domain( [ 0, d3.max( data, d => d.frequency ) ] ); var xAxis = d3.svg.axis() .scale(xScale) .tickValues( // show ticks every 5 years for range up to 50 years, every 10 // years up to 100 years, and every 20 years above that xScale.domain().filter( function(d, i) { let ticks; if (xScale.domain().length <= 50) { ticks = 5; } else if (xScale.domain().length <= 100) { ticks = 10; } else { ticks = 20; } return !(d % ticks); } ) ) .tickSize(6,3,0) // removes end tick .orient("bottom"); var yAxis = d3.svg.axis() .scale(yScale) .ticks(3) // number of ticks .tickFormat(d3.format("d")) // only integers .tickSize(6,3,0) // removes end tick .orient("left"); svg.selectAll(".bar") .data(data) .enter() .append("a") .attr( "xlink:href", d => "/?q=si%3A6496+py%3A" + d.year ) .attr( "title", d => d.frequency + " Publication" + (d.frequency > 1 ? "s" : "") + " in " + d.year ) .append("rect") .attr("class", "bar") .attr("x", d => xScale(d.year)) .attr("width", xScale.rangeBand()) .attr("y", d => yScale(d.frequency)) .attr("height", d => height - yScale(d.frequency)); svg.append("g") .attr("class", "x axis") .attr("transform", "translate(0," + height + ")") .call(xAxis); svg.append("g") .attr("class", "y axis") .call(yAxis) .append("text") .attr("transform", "rotate(-90)") .attr("y", 6) .attr("dy", ".75em") .style("text-anchor", "end") .text(""); </script> </div> </div> </article> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> &copy; 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms &amp; Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none">&nbsp;<span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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