Jacobian matrix of two functions - Online Technical Discussion Groups

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width: 780px; border:none;"> <a id="_19_message_3330242"></a> <table class="thread-message-view portlet-section-body results-row" id="_19_message_3330242"> <tr> <td class="lfr-top"> <div class="thread-body"> <p>Greetings -- </p> <p>Apologies if this is posted to the wrong forum. Have been using Maple and Maxima for 20+ years, and have only recently started using Mathematica (v. 14). Having a heck of a time getting Mathematica to do what is trivial in either Maple or Maxima (not a slam on Mathematica - just an honest statement of where I am on the learning curve). Simple example: 2 equations in 2 unknowns (say, x1 and x2). Want to derive the Jacobian of these equations wrt x1 and x2, and print said Jacobian in matrix form. This is basically 3-4 lines in Maple or Maxima. But in Mathematica? Here is what I've tried. </p> <pre class="prettyprint lang-mma"> (*Define the functions*) f1[x1_, x2_] := x1^2 + x2^2 f2[x1_, x2_] := x1 x2 (*Compute the Jacobian matrix with respect to x1 and x2*) jacobian = JacobianMatrix[{f1[x1, x2], f2[x1, x2]}, {x1, x2}] (*Display the Jacobian matrix*) MatrixForm[jacobian] </pre> <p>But, the final command to display the Jacobian returns nada of any use. It simply returns the following:</p> <pre class="prettyprint lang-mma"> JacobianMatrix[{x1^2+x2^2,x1x2},{x1,x2}] </pre> <p>So, how the heck do I get Mathematica to output what Maple (for example - same code more or less in Maxima) outputs in one command, looking like what I expect (i.e., the formatted Jacobian matrix, below):</p> <p><img src="https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-11-28135520.jpg&userId=3330227" alt="enter image description here" /></p> <p>Many thanks in advance. I was warned the learning curve for Mathematica was appreciably steeper than (say) Maple, but I wasn't expected even something this simple to stump me quite so soon.</p> <div class="custom-attributes"> <div class="taglib-custom-attributes-list"> </div> </div> </div> </td> </tr> <tr> <td class="thread-bottom"> <div class="entry-links"> </div> <ul class="edit-controls lfr-component"> </ul> </td> </tr> </table> <div class="root-bottom-view"> <div class="author"> POSTED BY: <span class="author-red"><a href="/web/evancooch">Evan Cooch</a></span> </div> <div class="subject"> </div> <div class="thread-bottom-controls" style="align:left;"> <ul class="edit-controls lfr-component"> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Reply</a> </li> <li style="color: #999;"> | </li> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Flag</a> </li> </ul> </div> </div> </div> </div> <div class="root-message-info"> <span class="reply-count"> 8 Replies </span> <div class="sorting"> <span style="display:inline-block;font-size:15px;font-family:'Source Sans Pro'; 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return false;"> </div> <div class="like-counter like-counter-margin" id="twwx_counter_child">0</div> </div> <div class="user-image"> <div class="taglib-user-display display-style-2"> <a href="https://community.wolfram.com/c/my_sites/view?groupId=3330362&privateLayout=0" > <span class="user-profile-image"> <div class="avatar-border"> <div class="avatar-spacer"> <img alt="kaylene ginny" class="avatar" src="/image/user_male_portrait?img_id=0&t=1733767396490" width="65" /> </div> </div> </span> <span class="user-name"> kaylene ginny </span> </a> <div class="user-details"> </div> </div> </div> <div class="post-details"> <div class="author-info"> <a href="/web/doris">kaylene ginny, Data Recovery Software</a> </div> <div class="time-posted"> Posted <span class="author-red">11 days ago</span> </div> </div> </div> <div class="message-container" style="margin-left: 0px; width: 780px; border:none;"> <a id="_19_message_3330857"></a> <table class="thread-message-view portlet-section-alternate results-row alt" id="_19_message_3330857"> <tr> <td class="lfr-top"> <div class="thread-body"> <pre class='prettyprint lang-mma'>(* Define the functions *) f1[x1_, x2_] := x1^2 + x2^2 f2[x1_, x2_] := x1 x2 (* Compute the Jacobian matrix with respect to x1 and x2 *) jacobian = D[{f1[x1, x2], f2[x1, x2]}, {{x1, x2}}] (* Display the Jacobian matrix *) MatrixForm[jacobian] </pre> <div class="custom-attributes"> <div class="taglib-custom-attributes-list"> </div> </div> </div> </td> </tr> <tr> <td class="thread-bottom"> <div class="entry-links"> </div> <ul class="edit-controls lfr-component"> </ul> </td> </tr> </table> <div class="thread-bottom-view"> <div class="author"> POSTED BY: <span class="author-red"><a href="/web/doris">kaylene ginny</a></span> </div> <div class="subject"> </div> <div class="thread-bottom-controls" style="align:left;"> <ul class="edit-controls lfr-component"> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Reply</a> </li> <li style="color: #999;"> | </li> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Flag</a> </li> </ul> </div> </div> </div> <script> var gkow_curCounter_child = 3; 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width: 780px;"> <div class="like-component"> <div class="like-button"> <input id="does-not-like" type="image" src="/community-hook/images/like-default.png" onclick="signInFunc(); return false;"> </div> <div class="like-counter like-counter-margin" id="gkow_counter_child">3</div> </div> <div class="user-image"> <div class="taglib-user-display display-style-2"> <a href="https://community.wolfram.com/c/my_sites/view?groupId=70296&privateLayout=0" > <span class="user-profile-image"> <div class="avatar-border"> <div class="avatar-spacer"> <img alt="Gianluca Gorni" class="avatar" src="/image/user_male_portrait?img_id=0&t=1733767396490" width="65" /> </div> </div> </span> <span class="user-name"> Gianluca Gorni </span> </a> <div class="user-details"> </div> </div> </div> <div class="post-details"> <div class="author-info"> <a href="/web/gianlucagorni">Gianluca Gorni, University of Udine</a> </div> <div class="time-posted"> Posted <span class="author-red">12 days ago</span> </div> </div> </div> <div class="message-container" style="margin-left: 0px; width: 780px; border:none;"> <a id="_19_message_3330481"></a> <table class="thread-message-view portlet-section-body results-row" id="_19_message_3330481"> <tr> <td class="lfr-top"> <div class="thread-body"> <p>You can simulate the <code>Maple</code> syntax quite easily:</p> <pre class='prettyprint lang-mma'>f1 = x1^2 + x2^2; f2 = x1*x2; jac = D[{f1, f2}, {{x1, x2}}]; MatrixForm[jac] </pre><p>The only notable difference is the display of the matrix.</p> <div class="custom-attributes"> <div class="taglib-custom-attributes-list"> </div> </div> </div> </td> </tr> <tr> <td class="thread-bottom"> <div class="entry-links"> </div> <ul class="edit-controls lfr-component"> </ul> </td> </tr> </table> <div class="thread-bottom-view"> <div class="author"> POSTED BY: <span class="author-red"><a href="/web/gianlucagorni">Gianluca Gorni</a></span> </div> <div class="subject"> </div> <div class="thread-bottom-controls" style="align:left;"> <ul class="edit-controls lfr-component"> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Reply</a> </li> <li style="color: #999;"> | </li> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Flag</a> </li> </ul> </div> </div> </div> <script> var wfcu_curCounter_child = 0; 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width: 780px;"> <div class="like-component"> <div class="like-button"> <input id="does-not-like" type="image" src="/community-hook/images/like-default.png" onclick="signInFunc(); return false;"> </div> <div class="like-counter like-counter-margin" id="wfcu_counter_child">0</div> </div> <div class="user-image"> <div class="taglib-user-display display-style-2"> <a href="https://community.wolfram.com/c/my_sites/view?groupId=3330229&privateLayout=0" > <span class="user-profile-image"> <div class="avatar-border"> <div class="avatar-spacer"> <img alt="Evan Cooch" class="avatar" src="/image/user_male_portrait?img_id=0&t=1733767396490" width="65" /> </div> </div> </span> <span class="user-name"> Evan Cooch </span> </a> <div class="user-details"> </div> </div> </div> <div class="post-details"> <div class="author-info"> <a href="/web/evancooch">Evan Cooch </a> </div> <div class="time-posted"> Posted <span class="author-red">12 days ago</span> </div> </div> </div> <div class="message-container" style="margin-left: 0px; width: 780px; border:none;"> <a id="_19_message_3330312"></a> <table class="thread-message-view portlet-section-alternate results-row alt" id="_19_message_3330312"> <tr> <td class="lfr-top"> <div class="thread-body"> <p>Following works - but having to figure out/remember "ResourceFunction" is clunky...and I'm still nt entirely sure I know what a 'resource function' is. </p> <pre class='prettyprint lang-mma'>f1 = (x1)^2+(x2)^2 f2 = (x1)*(x2) jac = ResourceFunction["JacobianMatrix"][{f1,f2},{x1,x2}] MatrixForm[jac] </pre><p>Compare this to (say) Maxima (lest someone think I'm only trolling a comparison of Maple and Mathematica) -- note that Maxima by default outputs each step, properly formatted so that it actually looks like math (still have no idea how to get Mathematica to do that). </p><p><img src="https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-11-28162535.jpg&userId=3330227" alt="enter image description here"/></p> <div class="custom-attributes"> <div class="taglib-custom-attributes-list"> </div> </div> </div> </td> </tr> <tr> <td class="thread-bottom"> <div class="entry-links"> </div> <ul class="edit-controls lfr-component"> </ul> </td> </tr> </table> <div class="thread-bottom-view"> <div class="author"> POSTED BY: <span class="author-red"><a href="/web/evancooch">Evan Cooch</a></span> </div> <div class="subject"> </div> <div class="thread-bottom-controls" style="align:left;"> <ul class="edit-controls lfr-component"> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Reply</a> </li> <li style="color: #999;"> | </li> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Flag</a> </li> </ul> </div> </div> </div> <script> var ksaq_curCounter_child = 1; 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width: 760px;"> <div class="like-component"> <div class="like-button"> <input id="does-not-like" type="image" src="/community-hook/images/like-default.png" onclick="signInFunc(); return false;"> </div> <div class="like-counter like-counter-margin" id="ksaq_counter_child">1</div> </div> <div class="user-image"> <div class="taglib-user-display display-style-2"> <a href="https://community.wolfram.com/c/my_sites/view?groupId=587989&privateLayout=0" > <span class="user-profile-image"> <div class="avatar-border"> <div class="avatar-spacer"> <img alt="Eric Rimbey" class="avatar" src="/image/user_male_portrait?img_id=2751015&t=1733945020570" width="65" /> </div> </div> </span> <span class="user-name"> Eric Rimbey </span> </a> <div class="user-details"> </div> </div> </div> <div class="post-details"> <div class="author-info"> <a href="/web/eric3">Eric Rimbey </a> </div> <div class="time-posted"> Posted <span class="author-red">12 days ago</span> </div> </div> </div> <div class="message-container" style="margin-left: 20px; width: 760px; border:none;"> <a id="_19_message_3330315"></a> <table class="thread-message-view portlet-section-body results-row" id="_19_message_3330315"> <tr> <td class="lfr-top"> <div class="thread-body"> <p>Resource functions are just useful functions that have been submitted to the resource function repository by users. There is a whole system for submitting them and getting them accepted. They aren't part of the core language, so to access them, you need to go through the resource function repository. But again, there's <code>D</code>, which is core to the language, so I'm not sure what the problem is. The Jacobian is even mentioned in the documentation for <code>D</code>.</p><p>Side note: comparing Mathematica to Maxima or Maple is not really appropriate for this forum. This forum is just here to help folks with Mathematica. If you're suggesting feature requests or criticisms, that's something you should send to Wolfram directly, not this forum.</p> <div class="custom-attributes"> <div class="taglib-custom-attributes-list"> </div> </div> </div> </td> </tr> <tr> <td class="thread-bottom"> <div class="entry-links"> </div> <ul class="edit-controls lfr-component"> </ul> </td> </tr> </table> <div class="thread-bottom-view"> <div class="author"> POSTED BY: <span class="author-red"><a href="/web/eric3">Eric Rimbey</a></span> </div> <div class="subject"> </div> <div class="thread-bottom-controls" style="align:left;"> <ul class="edit-controls lfr-component"> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Reply</a> </li> <li style="color: #999;"> | </li> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Flag</a> </li> </ul> </div> </div> </div> <script> var rzea_curCounter_child = 2; var rzea_myCounter_child = 0.0; var rzea_voteOrNot_child = false; if(rzea_myCounter_child > 0) { rzea_voteOrNot_child = true; } var rzea_currId = "rzea_counter_child"; function rzea_update_counter() { document.getElementById(rzea_currId).innerHTML = (function() { if(!rzea_voteOrNot_child) { rzea_voteOrNot_child = true; $("#rzea_reply .aui-rating-element").removeClass("wolfram-like-off"); $("#rzea_reply .aui-rating-element").addClass("wolfram-like-on"); return rzea_curCounter_child += 1; } else { rzea_voteOrNot_child = false; $("#rzea_reply .aui-rating-element").removeClass("wolfram-like-on"); $("#rzea_reply .aui-rating-element").addClass("wolfram-like-off"); return rzea_curCounter_child -= 1; } })(); } $(document).ready(function() { $("#rzea_reply .thumbs .aui-rating-element").click( function() { rzea_update_counter(); }); }); </script> <style> .root-post .like-component { align-items: center; } .root-post .like-button { margin-left: 0; } </style> <div class="reply_posts" id="rzea_reply" style="margin-left: 0px; width: 780px;"> <div class="like-component"> <div class="like-button"> <input id="does-not-like" type="image" src="/community-hook/images/like-default.png" onclick="signInFunc(); return false;"> </div> <div class="like-counter like-counter-margin" id="rzea_counter_child">2</div> </div> <div class="user-image"> <div class="taglib-user-display display-style-2"> <a href="https://community.wolfram.com/c/my_sites/view?groupId=587989&privateLayout=0" > <span class="user-profile-image"> <div class="avatar-border"> <div class="avatar-spacer"> <img alt="Eric Rimbey" class="avatar" src="/image/user_male_portrait?img_id=2751015&t=1733945020570" width="65" /> </div> </div> </span> <span class="user-name"> Eric Rimbey </span> </a> <div class="user-details"> </div> </div> </div> <div class="post-details"> <div class="author-info"> <a href="/web/eric3">Eric Rimbey </a> </div> <div class="time-posted"> Posted <span class="author-red">12 days ago</span> </div> </div> </div> <div class="message-container" style="margin-left: 0px; width: 780px; border:none;"> <a id="_19_message_3330309"></a> <table class="thread-message-view portlet-section-alternate results-row alt" id="_19_message_3330309"> <tr> <td class="lfr-top"> <div class="thread-body"> <p>Oh, if it's a resource function, then just "fetch" it from the resource repository.</p> <pre class='prettyprint lang-mma'>f1[x1_, x2_] := x1^2 + x2^2; f2[x1_, x2_] := x1 x2; ResourceFunction["JacobianMatrix"][{f1[x1, x2], f2[x1, x2]}, {x1, x2}] (* {{2 x1, 2 x2}, {x2, x1}} *) </pre><p>If you don't like typing all of that each time, you can define a symbol for it:</p> <pre class='prettyprint lang-mma'>myJacobian = ResourceFunction["JacobianMatrix"]; myJacobian[{f1[x1, x2], f2[x1, x2]}, {x1, x2}] </pre><p>But I don't really see what's so cumbersome about just using the built in <code>D</code> symbol.</p> <pre class='prettyprint lang-mma'>D[{f1[x1, x2], f2[x1, x2]}, {{x1, x2}}] </pre> <div class="custom-attributes"> <div class="taglib-custom-attributes-list"> </div> </div> </div> </td> </tr> <tr> <td class="thread-bottom"> <div class="entry-links"> </div> <ul class="edit-controls lfr-component"> </ul> </td> </tr> </table> <div class="thread-bottom-view"> <div class="author"> POSTED BY: <span class="author-red"><a href="/web/eric3">Eric Rimbey</a></span> </div> <div class="subject"> </div> <div class="thread-bottom-controls" style="align:left;"> <ul class="edit-controls lfr-component"> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Reply</a> </li> <li style="color: #999;"> | </li> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Flag</a> </li> </ul> </div> </div> </div> <script> var kxdi_curCounter_child = 3; 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width: 780px;"> <div class="like-component"> <div class="like-button"> <input id="does-not-like" type="image" src="/community-hook/images/like-default.png" onclick="signInFunc(); return false;"> </div> <div class="like-counter like-counter-margin" id="kxdi_counter_child">3</div> </div> <div class="user-image"> <div class="taglib-user-display display-style-2"> <a href="https://community.wolfram.com/c/my_sites/view?groupId=587989&privateLayout=0" > <span class="user-profile-image"> <div class="avatar-border"> <div class="avatar-spacer"> <img alt="Eric Rimbey" class="avatar" src="/image/user_male_portrait?img_id=2751015&t=1733945020570" width="65" /> </div> </div> </span> <span class="user-name"> Eric Rimbey </span> </a> <div class="user-details"> </div> </div> </div> <div class="post-details"> <div class="author-info"> <a href="/web/eric3">Eric Rimbey </a> </div> <div class="time-posted"> Posted <span class="author-red">13 days ago</span> </div> </div> </div> <div class="message-container" style="margin-left: 0px; width: 780px; border:none;"> <a id="_19_message_3329958"></a> <table class="thread-message-view portlet-section-body results-row" id="_19_message_3329958"> <tr> <td class="lfr-top"> <div class="thread-body"> <p>I don't know where you came across the symbol <code>JacobianMatrix</code>, but I don't think that's a built in symbol. You can just use the normal derivative.</p> <pre class='prettyprint lang-mma'>D[{x1^2 + x2^2, x1 x2}, {{x1, x2}}] (* {{2 x1, 2 x2}, {x2, x1}} *) </pre><p>And just let me say proactively, that <code>MatrixForm</code> is only for display (which is fine for what you have so far), so don't try to compute further with that specific form.</p> <div class="custom-attributes"> <div class="taglib-custom-attributes-list"> </div> </div> </div> </td> </tr> <tr> <td class="thread-bottom"> <div class="entry-links"> </div> <ul class="edit-controls lfr-component"> </ul> </td> </tr> </table> <div class="thread-bottom-view"> <div class="author"> POSTED BY: <span class="author-red"><a href="/web/eric3">Eric Rimbey</a></span> </div> <div class="subject"> </div> <div class="thread-bottom-controls" style="align:left;"> <ul class="edit-controls lfr-component"> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Reply</a> </li> <li style="color: #999;"> | </li> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Flag</a> </li> </ul> </div> </div> </div> <script> var osef_curCounter_child = 0; var osef_myCounter_child = 0.0; var osef_voteOrNot_child = false; if(osef_myCounter_child > 0) { osef_voteOrNot_child = true; } var osef_currId = "osef_counter_child"; function osef_update_counter() { document.getElementById(osef_currId).innerHTML = (function() { if(!osef_voteOrNot_child) { osef_voteOrNot_child = true; $("#osef_reply .aui-rating-element").removeClass("wolfram-like-off"); $("#osef_reply .aui-rating-element").addClass("wolfram-like-on"); return osef_curCounter_child += 1; } else { osef_voteOrNot_child = false; $("#osef_reply .aui-rating-element").removeClass("wolfram-like-on"); $("#osef_reply .aui-rating-element").addClass("wolfram-like-off"); return osef_curCounter_child -= 1; } })(); } $(document).ready(function() { $("#osef_reply .thumbs .aui-rating-element").click( function() { osef_update_counter(); }); }); </script> <style> .root-post .like-component { align-items: center; } .root-post .like-button { margin-left: 0; } </style> <div class="reply_posts" id="osef_reply" style="margin-left: 20px; width: 760px;"> <div class="like-component"> <div class="like-button"> <input id="does-not-like" type="image" src="/community-hook/images/like-default.png" onclick="signInFunc(); return false;"> </div> <div class="like-counter like-counter-margin" id="osef_counter_child">0</div> </div> <div class="user-image"> <div class="taglib-user-display display-style-2"> <a href="https://community.wolfram.com/c/my_sites/view?groupId=3330229&privateLayout=0" > <span class="user-profile-image"> <div class="avatar-border"> <div class="avatar-spacer"> <img alt="Evan Cooch" class="avatar" src="/image/user_male_portrait?img_id=0&t=1733767396490" width="65" /> </div> </div> </span> <span class="user-name"> Evan Cooch </span> </a> <div class="user-details"> </div> </div> </div> <div class="post-details"> <div class="author-info"> <a href="/web/evancooch">Evan Cooch </a> </div> <div class="time-posted"> Posted <span class="author-red">12 days ago</span> </div> </div> </div> <div class="message-container" style="margin-left: 20px; width: 760px; border:none;"> <a id="_19_message_3330306"></a> <table class="thread-message-view portlet-section-alternate results-row alt" id="_19_message_3330306"> <tr> <td class="lfr-top"> <div class="thread-body"> <p>Simple - JacobianMatrix (or equivalent) is baked in to Maple, Maxima, MATLAB, and every other CAS or CAS-like environment I've used. And, it is in Mathematica, but apparently it is something called a 'Resource Function' (no idea what that is). See below:</p><p><img src="https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-11-28161336.jpg&userId=3330227" alt="enter image description here"/></p><p>What you suggested works, but it is cumbersome for large sets of equations. </p> <div class="custom-attributes"> <div class="taglib-custom-attributes-list"> </div> </div> </div> </td> </tr> <tr> <td class="thread-bottom"> <div class="entry-links"> </div> <ul class="edit-controls lfr-component"> </ul> </td> </tr> </table> <div class="thread-bottom-view"> <div class="author"> POSTED BY: <span class="author-red"><a href="/web/evancooch">Evan Cooch</a></span> </div> <div class="subject"> </div> <div class="thread-bottom-controls" style="align:left;"> <ul class="edit-controls lfr-component"> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Reply</a> </li> <li style="color: #999;"> | </li> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Flag</a> </li> </ul> </div> </div> </div> <script> var lukr_curCounter_child = 0; var lukr_myCounter_child = 0.0; var lukr_voteOrNot_child = false; if(lukr_myCounter_child > 0) { lukr_voteOrNot_child = true; } var lukr_currId = "lukr_counter_child"; function lukr_update_counter() { document.getElementById(lukr_currId).innerHTML = (function() { if(!lukr_voteOrNot_child) { lukr_voteOrNot_child = true; $("#lukr_reply .aui-rating-element").removeClass("wolfram-like-off"); $("#lukr_reply .aui-rating-element").addClass("wolfram-like-on"); return lukr_curCounter_child += 1; } else { lukr_voteOrNot_child = false; $("#lukr_reply .aui-rating-element").removeClass("wolfram-like-on"); $("#lukr_reply .aui-rating-element").addClass("wolfram-like-off"); return lukr_curCounter_child -= 1; } })(); } $(document).ready(function() { $("#lukr_reply .thumbs .aui-rating-element").click( function() { lukr_update_counter(); }); }); </script> <style> .root-post .like-component { align-items: center; } .root-post .like-button { margin-left: 0; } </style> <div class="reply_posts" id="lukr_reply" style="margin-left: 40px; width: 740px;"> <div class="like-component"> <div class="like-button"> <input id="does-not-like" type="image" src="/community-hook/images/like-default.png" onclick="signInFunc(); return false;"> </div> <div class="like-counter like-counter-margin" id="lukr_counter_child">0</div> </div> <div class="user-image"> <div class="taglib-user-display display-style-2"> <a href="https://community.wolfram.com/c/my_sites/view?groupId=53589&privateLayout=0" > <span class="user-profile-image"> <div class="avatar-border"> <div class="avatar-spacer"> <img alt="Michael Rogers" class="avatar" src="/image/user_male_portrait?img_id=1219018&t=1733944941563" width="65" /> </div> </div> </span> <span class="user-name"> Michael Rogers </span> </a> <div class="user-details"> </div> </div> </div> <div class="post-details"> <div class="author-info"> <a href="/web/mroge02">Michael Rogers, Emory University</a> </div> <div class="time-posted"> Posted <span class="author-red">11 days ago</span> </div> </div> </div> <div class="message-container" style="margin-left: 40px; width: 740px; border:none;"> <a id="_19_message_3330711"></a> <table class="thread-message-view portlet-section-body results-row" id="_19_message_3330711"> <tr> <td class="lfr-top"> <div class="thread-body"> <p>Why do you keep ignoring <code>D[{f1, f2}, {{x1, x2}}]</code>, which a couple of others have mentioned? (Assumes <code>f1 = x1^2 + x2^2; f2 = x1 x2</code>.)</p><p>Is it just because it's not named "Jacobian"? It's one of the problems when we adopt a person's name as the basis for calling a common object, such as the derivative, something else. (Of course, I believe the "Jacobian matrix" came into use before a vector-matrix-tensor view of multivariate functions and their derivatives became dominant. So there's a historical reason why "Jacobian" is used.)</p><p>Anyway, <code>D[{f1, f2}, {{x1, x2}}]</code> is shorter than <code>Jacobian[{f1, f2}, {x1, x2}]</code>. And so is <code>Grad[{f1, f2}, {x1, x2}]</code>, which also works.</p><p><code>D[{f1, f2}, {{x1, x2}}]</code> is the currently documented way to calculate the Jacobian (in the docs for <code>D[]</code>). The method from the version 2 <em>Mathematica</em> book is <code>Outer[D, {f1, f2}, {x1, x2}]</code>, which also appears in the docs for <code>D[]</code>. When I search the help center for "jacobian" (lower case), <code>D[]</code> is the fourth hit in the desktop documentation; it's a disappointing eighth in the online docs, after the despis猫d <code>"JacobianMatrix"</code> resource function.</p><p>You mentioned large sets of equations. It's not exactly clear what you mean, but here's what I do when I have equations and variables that I don't want retype. You need a list of the variables, and their order matters usually. If you can name them such that <code>Sort[]</code> puts them in the desired order, then great, you can just extract the variables from the formulas and <code>Union[]</code> them. Otherwise, you'll probably have to type them by hand.</p> <pre class='prettyprint lang-mma'>vars = {x1, x2, x3, x4}; funcs ={f1, f2, f3, f4}; (* pretend they've been defined in terms of vars *) jac = D[funcs, {vars}] </pre> <div class="custom-attributes"> <div class="taglib-custom-attributes-list"> </div> </div> </div> </td> </tr> <tr> <td class="thread-bottom"> <div class="entry-links"> </div> <ul class="edit-controls lfr-component"> </ul> </td> </tr> </table> <div class="thread-bottom-view"> <div class="author"> POSTED BY: <span class="author-red"><a href="/web/mroge02">Michael Rogers</a></span> </div> <div class="subject"> </div> <div class="thread-bottom-controls" style="align:left;"> <ul class="edit-controls lfr-component"> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Reply</a> </li> <li style="color: #999;"> | </li> <li> <a class="taglib-icon" href="#" onclick="signInFunc();return false;">Flag</a> </li> </ul> </div> </div> </div> </div> </form> 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