http://www.mapleprimes.com/questions/129549-Fundiff-With-Anticommuting-Functions en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Thu, 11 Jun 2026 14:30:11 GMT Thu, 11 Jun 2026 14:30:11 GMT The latest answers and comments added to the Question, Fundiff with anticommuting functions http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/questions/129549-Fundiff-With-Anticommuting-Functions http://www.mapleprimes.com/questions/129549-Fundiff-With-Anticommuting-Functions?ref=Feed:MaplePrimes:Fundiff with anticommuting functions:Comments#answer149632 <p><br> </p> <form name="worksheet_form"> <table style="width: 576px;" align="center"> <tbody> <tr> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">Yes you can perform functional differentiation with anticommutative functions, or with tensor quantum operators for instance, anticommutative or not.</span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">&nbsp; </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">Now your example had some invalid input as pointed in another reply. So assuming you meant product,</span></p> <table style="margin-left: 0px; margin-right: 0px;"> <tbody> <tr valign="baseline"> <td><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"> &gt;&nbsp;</span></td> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;">with(Physics):</span></p> </td> </tr> </tbody> </table> <table style="margin-left: 0px; margin-right: 0px;"> <tbody> <tr valign="baseline"> <td><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"> &gt;&nbsp;</span></td> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;">Setup(anticommutativeprefix = {Q});</span></p> </td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">Fix your input say taking the product of two anticommutative functions</span></p> <table style="margin-left: 0px; margin-right: 0px;"> <tbody> <tr valign="baseline"> <td><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"> &gt;&nbsp;</span></td> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;">G := Intc(Q2(x) * Q1(y),x,y);</span></p> </td> </tr> </tbody> </table> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -20;" src="/view.aspx?sf=149632/465591/02a7f2273b0625f8c0e9fea1914e5252.gif" alt="Int(Int(-Physics:-`*`(Q1(y), Q2(x)), x = -infinity .. infinity), y = -infinity .. infinity)" width="215" height="50"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(1)</td> </tr> </tbody> </table> <table style="margin-left: 0px; margin-right: 0px;"> <tbody> <tr valign="baseline"> <td><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"> &gt;&nbsp;</span></td> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;">Fundiff(G, Q1(u));</span></p> </td> </tr> </tbody> </table> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -20;" src="/view.aspx?sf=149632/465591/1278c19e39e48998d1ba5188cbd7879f.gif" alt="-(Int(Q2(x), x = -infinity .. infinity))" width="96" height="50"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(2)</td> </tr> </tbody> </table> <table style="margin-left: 0px; margin-right: 0px;"> <tbody> <tr valign="baseline"> <td><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"> &gt;&nbsp;</span></td> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;">&nbsp; </span></p> </td> </tr> </tbody> </table> </td> </tr> </tbody> </table> <input type="hidden" name="sequence" value="1"> <input type="hidden" name="cmd" value="none"></form> <p>Edgardo S. Cheb-Terrab<br>Physics, Maplesoft<br> </p> <p><a href="/view.aspx?sf=149632/465591/FundiffAnticommutati.mw">Download FundiffAnticommutati.mw</a></p> <p><br> </p> <form name="worksheet_form"> <table style="width: 576px;" align="center"> <tbody> <tr> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">Yes you can perform functional differentiation with anticommutative functions, or with tensor quantum operators for instance, anticommutative or not.</span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">&nbsp; </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">Now your example had some invalid input as pointed in another reply. So assuming you meant product,</span></p> <table style="margin-left: 0px; margin-right: 0px;"> <tbody> <tr valign="baseline"> <td><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"> &gt;&nbsp;</span></td> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;">with(Physics):</span></p> </td> </tr> </tbody> </table> <table style="margin-left: 0px; margin-right: 0px;"> <tbody> <tr valign="baseline"> <td><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"> &gt;&nbsp;</span></td> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;">Setup(anticommutativeprefix = {Q});</span></p> </td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">Fix your input say taking the product of two anticommutative functions</span></p> <table style="margin-left: 0px; margin-right: 0px;"> <tbody> <tr valign="baseline"> <td><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"> &gt;&nbsp;</span></td> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;">G := Intc(Q2(x) * Q1(y),x,y);</span></p> </td> </tr> </tbody> </table> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -20;" src="/view.aspx?sf=149632/465591/02a7f2273b0625f8c0e9fea1914e5252.gif" alt="Int(Int(-Physics:-`*`(Q1(y), Q2(x)), x = -infinity .. infinity), y = -infinity .. infinity)" width="215" height="50"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(1)</td> </tr> </tbody> </table> <table style="margin-left: 0px; margin-right: 0px;"> <tbody> <tr valign="baseline"> <td><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"> &gt;&nbsp;</span></td> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;">Fundiff(G, Q1(u));</span></p> </td> </tr> </tbody> </table> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -20;" src="/view.aspx?sf=149632/465591/1278c19e39e48998d1ba5188cbd7879f.gif" alt="-(Int(Q2(x), x = -infinity .. infinity))" width="96" height="50"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(2)</td> </tr> </tbody> </table> <table style="margin-left: 0px; margin-right: 0px;"> <tbody> <tr valign="baseline"> <td><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;"> &gt;&nbsp;</span></td> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #ff0000; font-size: 100%; font-family: Courier New,monospace; font-weight: bold; font-style: normal;">&nbsp; </span></p> </td> </tr> </tbody> </table> </td> </tr> </tbody> </table> <input type="hidden" name="sequence" value="1"> <input type="hidden" name="cmd" value="none"></form> <p>Edgardo S. Cheb-Terrab<br>Physics, Maplesoft<br> </p> <p><a href="/view.aspx?sf=149632/465591/FundiffAnticommutati.mw">Download FundiffAnticommutati.mw</a></p> 149632 Sat, 20 Jul 2013 06:22:52 Z ecterrab ecterrab http://www.mapleprimes.com/questions/129549-Fundiff-With-Anticommuting-Functions?ref=Feed:MaplePrimes:Fundiff with anticommuting functions:Comments#answer150056 <p>Hi<br>Note also tthere is now access to the version of Physics under development, available for download at http://www.maplesoft.com/products/maple/features/physicsresearch.aspx, including adjustments and fixes as they are ready.</p> <p>Edgardo S. Cheb-Terrab<br>Physics, Maplesoft</p> <p>Hi<br>Note also tthere is now access to the version of Physics under development, available for download at http://www.maplesoft.com/products/maple/features/physicsresearch.aspx, including adjustments and fixes as they are ready.</p> <p>Edgardo S. Cheb-Terrab<br>Physics, Maplesoft</p> 150056 Fri, 02 Aug 2013 22:28:38 Z ecterrab ecterrab