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<!DOCTYPE html> <html lang="en"> <head> <title>Msolve -- Macaulay2 interface for msolve; computes real solutions and Groebner basis, etc.</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="Macaulay2 interface for msolve; computes real solutions and Groebner basis, etc." href="index.html">Msolve</a> :: <a title="Macaulay2 interface for msolve; computes real solutions and Groebner basis, etc." href="index.html">Msolve</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> <a href="_msolve__Eliminate.html">next</a> | previous | <a href="_msolve__Eliminate.html">forward</a> | backward | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>Msolve -- Macaulay2 interface for msolve; computes real solutions and Groebner basis, etc.</h1> <div> <h2>Description</h2> <div> <p>This package provides a Macaulay2 interface for the msolve library [1] developed by Jérémy Berthomieu, Christian Eder, and Mohab Safey El Din.</p> <p>The package has functions to compute Groebner basis, in <a title="graded reverse lexicographical monomial ordering" href="../../Macaulay2Doc/html/___G__Rev__Lex.html">GRevLex</a> order only, for ideals with rational or finite field coefficients. Finite field characteristics must be less than $2^{31}$. There are also functions to compute elimination ideals, for ideals with rational or finite field coefficients.</p> <p>The <a title="saturation of ideal or submodule" href="../../Saturation/html/_saturate.html">saturation</a> of an ideal by a single polynomial may be computed for ideals with finite field coefficients, again with characteristic less than $2^{31}$.</p> <p>For zero dimensional polynomial ideals, with integer or rational coefficients, there are functions to compute all real solutions, and to compute a rational univariate representation of all (complex) solutions.</p> <p>The M2 interface assumes that the binary executable is named "msolve" is on the executable path.</p> <p>For all functions the option <span class="tt">Verbosity</span> can be used. It has levels 0, 1, 2. The default is 0.</p> <p>Msolve supports parallel computations. The option <span class="tt">Threads</span> is used to set this. The default value is allowableThreads, but this can be set manually by the user when calling a function. E.g. for an ideal I:</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : R = QQ[x,y,z] o1 = R o1 : PolynomialRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : I = ideal(x, y, z) o2 = ideal (x, y, z) o2 : Ideal of R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : msolveGB(I, Verbosity => 2, Threads => 6) -- running: /usr/libexec/Macaulay2/bin/msolve -g 2 -t 6 -v 2 -f /tmp/M2-331862-0/0-in.ms -o /tmp/M2-331862-0/0-out.ms --------------- INPUT DATA --------------- #variables 3 #equations 3 #invalid equations 0 field characteristic 0 homogeneous input? 1 signature-based computation 0 monomial order DRL basis hash table resetting OFF linear algebra option 2 initial hash table size 131072 (2^17) max pair selection ALL reduce gb 1 #threads 6 info level 2 generate pbm files 0 ------------------------------------------ Legend for f4 information -------------------------------------------------------- deg current degree of pairs selected in this round sel number of pairs selected in this round pairs total number of pairs in pair list mat matrix dimensions (# rows x # columns) density density of the matrix new data # new elements for basis in this round # zero reductions during linear algebra time(rd) time of the current f4 round in seconds given for real and cpu time -------------------------------------------------------- deg sel pairs mat density new data time(rd) in sec (real|cpu) ------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------ reduce final basis 3 x 3 33.33% 3 new 0 zero 0.00 | 0.00 ------------------------------------------------------------------------------------------------------ ---------------- TIMINGS ---------------- overall(elapsed) 0.00 sec overall(cpu) 0.00 sec select 0.00 sec 0.0% symbolic prep. 0.00 sec 0.2% update 0.00 sec 58.5% convert 0.00 sec 31.8% linear algebra 0.00 sec 1.2% reduce gb 0.00 sec 0.0% ----------------------------------------- ---------- COMPUTATIONAL DATA ----------- size of basis 3 #terms in basis 3 #pairs reduced 0 #GM criterion 3 #redundant elements 0 #rows reduced 3 #zero reductions 0 max. matrix data 3 x 3 (33.333%) max. symbolic hash table size 2^11 max. basis hash table size 2^16 ----------------------------------------- ---------- COMPUTATIONAL DATA ----------- [3] #polynomials to lift 3 ----------------------------------------- ---------------- TIMINGS ---------------- multi-mod overall(elapsed) 0.00 sec learning phase 0.00 Gops/sec application phase 0.00 Gops/sec ----------------------------------------- multi-modular steps ------------------------------------------------------------------------------------------------------ {1}{2}<100.00%> ------------------------------------------------------------------------------------ msolve overall time 0.02 sec (elapsed) / 0.02 sec (cpu) ------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------ ---------- COMPUTATIONAL DATA ----------- Max coeff. bitsize 1 #primes 3 #bad primes 0 ----------------------------------------- ---------------- TIMINGS ---------------- CRT (elapsed) 0.00 sec ratrecon(elapsed) 0.00 sec ----------------------------------------- o3 = | z y x | 1 3 o3 : Matrix R <-- R</code></pre> </td> </tr> </table> </div> <div> <h2>References</h2> <div> <p>[1] The msolve library: <a href="https://msolve.lip6.fr">https://msolve.lip6.fr</a>;</p> <p></p> </div> </div> <div> <div> <div> <h2>Authors</h2> <ul> <li><a href="http://martin-helmer.com/">Martin Helmer</a><span> <<a href="mailto:mhelmer%40ncsu.edu">mhelmer@ncsu.edu</a>></span></li> <li><a href="https://math.cornell.edu/michael-e-stillman">Mike Stillman</a><span> <<a href="mailto:mike%40math.cornell.edu">mike@math.cornell.edu</a>></span></li> <li><a href="https://antonleykin.math.gatech.edu/">Anton Leykin</a><span> <<a href="mailto:leykin%40math.gatech.edu">leykin@math.gatech.edu</a>></span></li> </ul> </div> <div> <h2>Version</h2> <p>This documentation describes version <b>1.24.05</b> of Msolve, released <b>July 2024</b>.</p> </div> <div> <h2>Citation</h2> <p>If you have used this package in your research, please cite it as follows:</p> <table class="examples"> <tr> <td> <pre><code class="language-bib">@misc{MsolveSource, title = {{Msolve: A \emph{Macaulay2} package. Version~1.24.05}}, author = {Martin Helmer and Mike Stillman and Anton Leykin}, howpublished = {A \emph{Macaulay2} package available at \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}} } </code></pre> </td> </tr> </table> </div> <div> <h2>Exports</h2> <div class="exports"> <ul> <li>Types <ul> <li><span><a title="the class of all rational intervals" href="___Q__Qi.html">QQi</a> -- the class of all rational intervals</span></li> </ul> </li> <li>Functions and commands <ul> <li><span><a title="compute the elimination ideal of a given ideal" href="_msolve__Eliminate.html">msolveEliminate</a> -- compute the elimination ideal of a given ideal</span></li> <li><span><a title="compute generators of a Groebner basis in GRevLex order" href="_msolve__G__B.html">msolveGB</a> -- compute generators of a Groebner basis in GRevLex order</span></li> <li><span><a title="compute the leading monomials of a Groebner basis in GRevLex order" href="_msolve__Lead__Monomials.html">msolveLeadMonomials</a> -- compute the leading monomials of a Groebner basis in GRevLex order</span></li> <li><span><a title="compute all real solutions to a zero dimensional system using symbolic methods" href="_msolve__Real__Solutions.html">msolveRealSolutions</a> -- compute all real solutions to a zero dimensional system using symbolic methods</span></li> <li><span><a title="compute the rational univariate representation using symbolic methods" href="_msolve__R__U__R.html">msolveRUR</a> -- compute the rational univariate representation using symbolic methods</span></li> <li><span><a title="compute a Groebner basis for the saturation of an ideal by a single polynomial in GRevLex order" href="_msolve__Saturate.html">msolveSaturate</a> -- compute a Groebner basis for the saturation of an ideal by a single polynomial in GRevLex order</span></li> </ul> </li> <li>Methods <ul> <li><span><span class="tt">diameter(QQi)</span> (missing documentation)<!--tag: (diameter,QQi)--> </span></li> <li><span><span class="tt">interval(QQi)</span> (missing documentation)<!--tag: (interval,QQi)--> </span></li> <li><span><span class="tt">lift(QQi,type of Number)</span> (missing documentation)<!--tag: (lift,QQi,Number)--> </span></li> <li><span><kbd>msolveEliminate(Ideal,List)</kbd> -- see <span><a title="compute the elimination ideal of a given ideal" href="_msolve__Eliminate.html">msolveEliminate</a> -- compute the elimination ideal of a given ideal</span></span></li> <li><span><kbd>msolveEliminate(Ideal,RingElement)</kbd> -- see <span><a title="compute the elimination ideal of a given ideal" href="_msolve__Eliminate.html">msolveEliminate</a> -- compute the elimination ideal of a given ideal</span></span></li> <li><span><kbd>msolveEliminate(List,Ideal)</kbd> -- see <span><a title="compute the elimination ideal of a given ideal" href="_msolve__Eliminate.html">msolveEliminate</a> -- compute the elimination ideal of a given ideal</span></span></li> <li><span><kbd>msolveEliminate(RingElement,Ideal)</kbd> -- see <span><a title="compute the elimination ideal of a given ideal" href="_msolve__Eliminate.html">msolveEliminate</a> -- compute the elimination ideal of a given ideal</span></span></li> <li><span><kbd>msolveGB(Ideal)</kbd> -- see <span><a title="compute generators of a Groebner basis in GRevLex order" href="_msolve__G__B.html">msolveGB</a> -- compute generators of a Groebner basis in GRevLex order</span></span></li> <li><span><kbd>msolveLeadMonomials(Ideal)</kbd> -- see <span><a title="compute the leading monomials of a Groebner basis in GRevLex order" href="_msolve__Lead__Monomials.html">msolveLeadMonomials</a> -- compute the leading monomials of a Groebner basis in GRevLex order</span></span></li> <li><span><kbd>msolveRealSolutions(Ideal)</kbd> -- see <span><a title="compute all real solutions to a zero dimensional system using symbolic methods" href="_msolve__Real__Solutions.html">msolveRealSolutions</a> -- compute all real solutions to a zero dimensional system using symbolic methods</span></span></li> <li><span><kbd>msolveRealSolutions(Ideal,Ring)</kbd> -- see <span><a title="compute all real solutions to a zero dimensional system using symbolic methods" href="_msolve__Real__Solutions.html">msolveRealSolutions</a> -- compute all real solutions to a zero dimensional system using symbolic methods</span></span></li> <li><span><kbd>msolveRealSolutions(Ideal,RingFamily)</kbd> -- see <span><a title="compute all real solutions to a zero dimensional system using symbolic methods" href="_msolve__Real__Solutions.html">msolveRealSolutions</a> -- compute all real solutions to a zero dimensional system using symbolic methods</span></span></li> <li><span><kbd>msolveRUR(Ideal)</kbd> -- see <span><a title="compute the rational univariate representation using symbolic methods" href="_msolve__R__U__R.html">msolveRUR</a> -- compute the rational univariate representation using symbolic methods</span></span></li> <li><span><kbd>msolveSaturate(Ideal,RingElement)</kbd> -- see <span><a title="compute a Groebner basis for the saturation of an ideal by a single polynomial in GRevLex order" href="_msolve__Saturate.html">msolveSaturate</a> -- compute a Groebner basis for the saturation of an ideal by a single polynomial in GRevLex order</span></span></li> <li><span><span class="tt">Number == QQi</span> (missing documentation)<!--tag: (==,Number,QQi)--> </span></li> <li><span><span class="tt">precision(QQi)</span> (missing documentation)<!--tag: (precision,QQi)--> </span></li> <li><span><span class="tt">promote(Number,type of QQi)</span> (missing documentation)<!--tag: (promote,Number,QQi)--> </span></li> <li><span><span class="tt">QQi == Number</span> (missing documentation)<!--tag: (==,QQi,Number)--> </span></li> <li><span><span class="tt">ring(QQi)</span> (missing documentation)<!--tag: (ring,QQi)--> </span></li> </ul> </li> </ul> </div> </div> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="Macaulay2 interface for msolve; computes real solutions and Groebner basis, etc." href="index.html">Msolve</a> is <span>a <a title="the class of all packages" href="../../Macaulay2Doc/html/___Package.html">package</a></span>, defined in <span class="tt">Msolve.m2</span>, with auxiliary files in <span class="tt">Msolve/</span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Msolve.m2:636:0</span>.</p> </div> </div> </div> </body> </html>