{"id":213,"date":"2009-05-26T09:11:28","date_gmt":"2009-05-26T07:11:28","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/le-paquet-pro-mat\/"},"modified":"2023-10-14T20:12:25","modified_gmt":"2023-10-14T18:12:25","slug":"le-paquet-pro-mat","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/edition-mathematique\/professor\/les-paquets-de-professor-sty-2\/paquets-obsoletes\/le-paquet-pro-mat\/","title":{"rendered":"Le paquet pro-mat"},"content":{"rendered":"<p><strong>pro-mat.sty<\/strong> facilite l&rsquo;\u00e9criture de documents contenant du calcul matriciel : produit, inverse, d\u00e9terminant, etc.<\/p>\n<h2>Dans le pr\u00e9ambule<\/h2>\n<hr \/>\n<p>On rajoute ceci :<\/p>\n<p><code>\\usepackage[xcas]{pro-mat}<\/code><\/p>\n<hr \/>\n<h2>matmat<\/h2>\n<hr \/>\n<p>Permet d&rsquo;afficher une matrice avec la syntaxe XCAS :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"latex\">\\begin{matmat}\nmatmat([[112,2,cos(alpha)],[sqrt(2),0,1],[1\/2,2,3]])\n\\end{matmat}<\/pre>\n<p>On obtient :<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-850\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat9.jpg\" alt=\"promat9.jpg\" width=\"295\" height=\"190\" align=\"center\" \/><\/p>\n<h2>promat<\/h2>\n<hr \/>\n<p>Permet d&rsquo;effectuer des produits de matrices de tailles quelconques. On entre les deux matrices puis des options dans une troisi\u00e8me liste. La premi\u00e8re contient la liste des noms des matrices \u00e0 afficher. Elle peut \u00eatre vide. On peut mettre en deuxi\u00e8me option trigo si on veut r\u00e9\u00e9crire plus joliment certaines expressions trigonom\u00e9triques :<\/p>\n<p><strong>Un produit de matrices de tailles diff\u00e9rentes :<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"latex\">\\begin{promat}\npromat([[112,2,0],[0,0,1],[1,2,3]],[[1],[5],[0]],[[\"R\",\"Z\"]])\n\\end{promat}<\/pre>\n<p>On obtient :<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-851\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat1.jpg\" alt=\"promat1.jpg\" width=\"540\" height=\"464\" align=\"center\" srcset=\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat1.jpg 540w, https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat1-300x258.jpg 300w\" sizes=\"auto, (max-width: 540px) 100vw, 540px\" \/><\/p>\n<hr \/>\n<p><strong>Un carr\u00e9 de matrice carr\u00e9 avec l&rsquo;option trigo&#8230;<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"latex\">\\begin{promat}\npromat([[cos(theta),-sin(theta),0],[sin(theta),cos(theta),0],[0,0,1]],\n[[cos(theta),-sin(theta),0],[sin(theta),cos(theta),0],[0,0,1]],\n[[\"R\",\"R\",\"R^2\"],trigo])\n\\end{promat}<\/pre>\n<p>On obtient :<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-852\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat2.jpg\" alt=\"promat2.jpg\" width=\"735\" height=\"406\" align=\"center\" srcset=\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat2.jpg 735w, https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat2-300x166.jpg 300w\" sizes=\"auto, (max-width: 735px) 100vw, 735px\" \/><\/p>\n<hr \/>\n<p><strong>Un produit de matrices de m\u00eame taille sans option :<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"latex\">\\begin{promat}\npromat([[1,2,0],[0,0,1],[1,2,3]],[[1,4,0],[5,6,0],[0,0,1]],[[]])\n\\end{promat}<\/pre>\n<p>On obtient :<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-853\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat3.jpg\" alt=\"promat3.jpg\" width=\"402\" height=\"282\" align=\"center\" srcset=\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat3.jpg 402w, https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat3-300x210.jpg 300w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/p>\n<h2>detmat<\/h2>\n<hr \/>\n<p>Permet de calculer des d\u00e9terminants. On entre la matrice et en option on peut rajouter factor si on veut le r\u00e9sultat factoris\u00e9.<\/p>\n<p><strong>Un calcul de d\u00e9terminant sans factorisation~:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"latex\">\\begin{detmat}\ndetmat([[cos(theta),-sin(theta),0],[sin(theta),cos(theta),0],[0,0,1]],[])\n\\end{detmat}<\/pre>\n<p>On obtient :<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-854\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat4.jpg\" alt=\"promat4.jpg\" width=\"380\" height=\"143\" align=\"center\" srcset=\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat4.jpg 380w, https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat4-300x113.jpg 300w\" sizes=\"auto, (max-width: 380px) 100vw, 380px\" \/><\/p>\n<hr \/>\n<p><strong>Un calcul de d\u00e9terminant factoris\u00e9~:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"latex\">\\begin{detmat}\ndetmat([[1-t,2,0],[1,2-t,0],[0,0,1-t]],[factor])\n\\end{detmat}<\/pre>\n<p>On obtient :<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-855\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat5.jpg\" alt=\"promat5.jpg\" width=\"529\" height=\"156\" align=\"center\" srcset=\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat5.jpg 529w, https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat5-300x88.jpg 300w\" sizes=\"auto, (max-width: 529px) 100vw, 529px\" \/><\/p>\n<h2>invmat<\/h2>\n<hr \/>\n<p>Permet de calculer l&rsquo;inverse d&rsquo;une matrice&#8230;inversible. On entre la matrice.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"latex\">\\begin{invmat}\n invmat([[a,-b,3],[1,0,0],[0,0,1]])\n\\end{invmat}<\/pre>\n<p>On obtient :<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-856\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat6.jpg\" alt=\"promat6.jpg\" width=\"423\" height=\"158\" align=\"center\" srcset=\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat6.jpg 423w, https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat6-300x112.jpg 300w\" sizes=\"auto, (max-width: 423px) 100vw, 423px\" \/><\/p>\n<h2>puimat<\/h2>\n<hr \/>\n<p>Permet de calculer les puissances d&rsquo;une matrice. On entre la matrice, la puissance et la liste des options : trigo ou rien.<\/p>\n<p><strong>Sans trigo<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"latex\">\\begin{puimat}\npuimat([[1,1,1],[1,1,1],[1,1,1]],5,[])\n\\end{puimat}<\/pre>\n<p>On obtient :<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-857\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat7.jpg\" alt=\"promat7.jpg\" width=\"375\" height=\"128\" align=\"center\" srcset=\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat7.jpg 375w, https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat7-300x102.jpg 300w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><\/p>\n<hr \/>\n<p><strong>Avec trigo<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"latex\">\\begin{puimat}\npuimat([[cos(theta),-sin(theta),0],[sin(theta),cos(theta),0],[0,0,1]],\n3,[trigo])\n\\end{puimat}<\/pre>\n<p>On obtient :<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-858\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat8.jpg\" alt=\"promat8.jpg\" width=\"706\" height=\"143\" align=\"center\" srcset=\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat8.jpg 706w, https:\/\/wordpress.callac.online\/wp-content\/uploads\/2009\/05\/jpg_promat8-300x61.jpg 300w\" sizes=\"auto, (max-width: 706px) 100vw, 706px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>pro-mat.sty facilite l&rsquo;\u00e9criture de documents contenant du calcul matriciel : produit, inverse, d\u00e9terminant, etc. Dans le pr\u00e9ambule On rajoute ceci : \\usepackage[xcas]{pro-mat} matmat Permet d&rsquo;afficher une matrice avec la syntaxe&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2249,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-213","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Le paquet pro-mat - Maths &amp; Num\u00e9rique<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/wordpress.callac.online\/index.php\/edition-mathematique\/professor\/les-paquets-de-professor-sty-2\/paquets-obsoletes\/le-paquet-pro-mat\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Le paquet pro-mat - Maths &amp; Num\u00e9rique\" \/>\n<meta property=\"og:description\" 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