MaplePrimes - Questions and Posts tagged with equations
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en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSat, 28 May 2016 07:59:06 GMTSat, 28 May 2016 07:59:06 GMTThe most recent questions and posts on MaplePrimes tagged with equationshttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Questions and Posts tagged with equations
http://www.mapleprimes.com/tags/equations
Parametric linear system
http://www.mapleprimes.com/questions/212805-Parametric-Linear-System-?ref=Feed:MaplePrimes:Tagged With equations
<p>Hi,</p>
<p> </p>
<p>I am trying to solve a simple system of the form AX=0, where A is a N*N matrix, X is an N*1 vector (and the right-hand side of the equation is an N*1 vector of zeros, I apologize for the inexact notation). The difficulty comes from the fact that the values of A are parameterized by 2*N parameters (that I will write as the 2*N vector P), and I would like to get a solution in the form X=f(P).</p>
<p> </p>
<p>One solution is to try to use LinearAlgebra[LinearSolve], but it only returns the trivial solution X=0, which I am not interested in.</p>
<p>Another solution is to compute analytically the Moore-Penrose pseudoinverse A<sup>g</sup> of A, as the general solution is of the form</p>
<p>(I - A<sup>g </sup>A)f ;</p>
<p>where f is a vector of free parameters. However, even for a small matrix size (N=4), Maple is still computing after 3 hours on my (fairly powerful) machine, and it is taking more and more memory over time. As the results are polynomial/rational equations in the parameters P, I was actually expecting Maple to be more powerful than other softwares, but for this particular problem, Matlab's symbolic toolbox (muPAD) gives quick solutions until N=6. I need, in the end, to solve additional polynomial/rational equations that are derived from the solutions X=f(P), where Matlab fails. This is why I would really like to be able to solve the above-mentioned problem AX=0 with Maple in order to try to solve the subsequent step of the problem (polynomial system) with Maple.</p>
<p> </p>
<p>Any suggestions on how to do this would be highly appreciated! Thank you very much for your time and help.</p>
<p> </p>
<p>Laureline</p><p>Hi,</p>
<p> </p>
<p>I am trying to solve a simple system of the form AX=0, where A is a N*N matrix, X is an N*1 vector (and the right-hand side of the equation is an N*1 vector of zeros, I apologize for the inexact notation). The difficulty comes from the fact that the values of A are parameterized by 2*N parameters (that I will write as the 2*N vector P), and I would like to get a solution in the form X=f(P).</p>
<p> </p>
<p>One solution is to try to use LinearAlgebra[LinearSolve], but it only returns the trivial solution X=0, which I am not interested in.</p>
<p>Another solution is to compute analytically the Moore-Penrose pseudoinverse A<sup>g</sup> of A, as the general solution is of the form</p>
<p>(I - A<sup>g </sup>A)f ;</p>
<p>where f is a vector of free parameters. However, even for a small matrix size (N=4), Maple is still computing after 3 hours on my (fairly powerful) machine, and it is taking more and more memory over time. As the results are polynomial/rational equations in the parameters P, I was actually expecting Maple to be more powerful than other softwares, but for this particular problem, Matlab's symbolic toolbox (muPAD) gives quick solutions until N=6. I need, in the end, to solve additional polynomial/rational equations that are derived from the solutions X=f(P), where Matlab fails. This is why I would really like to be able to solve the above-mentioned problem AX=0 with Maple in order to try to solve the subsequent step of the problem (polynomial system) with Maple.</p>
<p> </p>
<p>Any suggestions on how to do this would be highly appreciated! Thank you very much for your time and help.</p>
<p> </p>
<p>Laureline</p>212805Fri, 27 May 2016 18:48:17 ZlogiacologiacoInteger solution of system
http://www.mapleprimes.com/questions/212705-Integer-Solution-Of-System?ref=Feed:MaplePrimes:Tagged With equations
<p><br>Dear all,</p>
<p>I wold like to find the solution of the next system of two equations with three unknowns but we assume that the unknows are positive integers. How the following code can work. Many thanks</p>
<p> </p>
<p> </p>
<p> </p>
<p>> restart;<br>> assume(J, integer, J >= 0);<br>> assume(A, integer, A >= 0);<br>> assume(T, integer, T >= 0);<br>> eq1 := J+10*A+50*T=500;<br> eq2 := J+A+T = 100;<br> solve( {eq1,eq2},{J,A,T});<br><br></p><p><br>Dear all,</p>
<p>I wold like to find the solution of the next system of two equations with three unknowns but we assume that the unknows are positive integers. How the following code can work. Many thanks</p>
<p> </p>
<p> </p>
<p> </p>
<p>> restart;<br>> assume(J, integer, J >= 0);<br>> assume(A, integer, A >= 0);<br>> assume(T, integer, T >= 0);<br>> eq1 := J+10*A+50*T=500;<br> eq2 := J+A+T = 100;<br> solve( {eq1,eq2},{J,A,T});<br><br></p>212705Tue, 24 May 2016 22:02:16 ZZeinebZeinebEquidistant surface
http://www.mapleprimes.com/posts/203796-Equidistant-Surface-?ref=Feed:MaplePrimes:Tagged With equations
<p style="margin: 0cm 0cm 10pt;"><span style="color: windowtext; line-height: 115%; font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-size: 10.0pt; mso-ansi-language: EN;"> Example of <span><span style="color: windowtext;">the equidistant</span></span> surface at a distance of 0.25 to the surface<br> <strong>x3</strong></span><strong><span style="color: windowtext; line-height: 115%; font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-size: 10.0pt; mso-ansi-language: EN;">-</span></strong><span style="color: windowtext; line-height: 115%; font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-size: 10.0pt; mso-ansi-language: EN;"><strong>0.1 * (sin (4 * x1) + sin (3 * x2 + x3) + sin (2 * x2)) = 0</strong><br> Constructed on the basis of universal parameterization of surfaces.<br><br><a href="/view.aspx?sf=203796_post/equidistant_surface.mw">equidistant_surface.mw</a> <br><br><img src="/view.aspx?sf=203796_post/equidistant_SURFACE.gif" alt=""><br></span></p><p style="margin: 0cm 0cm 10pt;"><span style="color: windowtext; line-height: 115%; font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-size: 10.0pt; mso-ansi-language: EN;"> Example of <span><span style="color: windowtext;">the equidistant</span></span> surface at a distance of 0.25 to the surface<br> <strong>x3</strong></span><strong><span style="color: windowtext; line-height: 115%; font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-size: 10.0pt; mso-ansi-language: EN;">-</span></strong><span style="color: windowtext; line-height: 115%; font-family: 'Arial','sans-serif'; font-size: 9pt; mso-bidi-font-size: 10.0pt; mso-ansi-language: EN;"><strong>0.1 * (sin (4 * x1) + sin (3 * x2 + x3) + sin (2 * x2)) = 0</strong><br> Constructed on the basis of universal parameterization of surfaces.<br><br><a href="/view.aspx?sf=203796_post/equidistant_surface.mw">equidistant_surface.mw</a> <br><br><img src="/view.aspx?sf=203796_post/equidistant_SURFACE.gif" alt=""><br></span></p>203796Sun, 15 May 2016 18:42:53 Zone manone manGenerate matrix form
http://www.mapleprimes.com/questions/212213-Generate-Matrix-Form-?ref=Feed:MaplePrimes:Tagged With equations
<p>Hello,</p>
<p>I cant find solution how to create matrix form from equations of motion. Equations looks like this:</p>
<p><img src="http://www.efunda.com/formulae/vibrations/mdof_images/MDOF_eg_EMO1.gif" alt=""></p>
<p>My equations ar much more complicated and one of them looks something like this:</p>
<p> http://i63.tinypic.com/21c5ctk.png</p>
<p>and I want form like this:</p>
<p><img src="http://www.efunda.com/formulae/vibrations/mdof_images/MDOF_eom_matrix.gif" alt=""></p>
<p>I tried to do it using the Generate Matrix but it does not work as I expected. How can you get this form?</p><p>Hello,</p>
<p>I cant find solution how to create matrix form from equations of motion. Equations looks like this:</p>
<p><img src="http://www.efunda.com/formulae/vibrations/mdof_images/MDOF_eg_EMO1.gif" alt=""></p>
<p>My equations ar much more complicated and one of them looks something like this:</p>
<p> http://i63.tinypic.com/21c5ctk.png</p>
<p>and I want form like this:</p>
<p><img src="http://www.efunda.com/formulae/vibrations/mdof_images/MDOF_eom_matrix.gif" alt=""></p>
<p>I tried to do it using the Generate Matrix but it does not work as I expected. How can you get this form?</p>212213Wed, 11 May 2016 11:21:46 ZspalinowyspalinowyRootFinding[Isolate] vs solve
http://www.mapleprimes.com/questions/211910-RootFindingIsolate-Vs-Solve?ref=Feed:MaplePrimes:Tagged With equations
<p> For solving polynomial systems I used RootFinding[Isolate]. But after discussing the question http://www.mapleprimes.com/questions/211774-Roots-Of--Expz--1<br>I decided to compare Isolate and evalf(solve ([...], [...])). It seemed to me that solve some convenient. The only if in the equation there are integers as a real, they should be recorded with a decimal point. (For real solutions of this procedure should be used with (RealDomain).) Examples:</p>
<p><a href="/view.aspx?sf=211910_question/SOLVE_ISOLATE.mw">SOLVE_ISOLATE.mw</a> <br><br> I wonder why then the need Root Finding [Isolate]?</p><p> For solving polynomial systems I used RootFinding[Isolate]. But after discussing the question http://www.mapleprimes.com/questions/211774-Roots-Of--Expz--1<br>I decided to compare Isolate and evalf(solve ([...], [...])). It seemed to me that solve some convenient. The only if in the equation there are integers as a real, they should be recorded with a decimal point. (For real solutions of this procedure should be used with (RealDomain).) Examples:</p>
<p><a href="/view.aspx?sf=211910_question/SOLVE_ISOLATE.mw">SOLVE_ISOLATE.mw</a> <br><br> I wonder why then the need Root Finding [Isolate]?</p>211910Tue, 03 May 2016 16:13:07 Zone manone manHow to rearrange equations
http://www.mapleprimes.com/questions/211788-How-To-Rearrange-Equations?ref=Feed:MaplePrimes:Tagged With equations
<p>Hello,</p>
<p> </p>
<p>I have a complex set of non linear diff eqns in the form :</p>
<p>y1'' = f(y1',y1,y2'',y2',y2,y3'',y3',y3,y4'',....,y6'',y6',y6,u1,u2,u3,u4) ;</p>
<p>y2'' = f(y1'',y1',y1,y2',y2,y3'',y3',y3,y4'',....,y6'',y6',y6,u1,u2,u3,u4)</p>
<p>and so on ... y6''=(...)</p>
<p>As I want to resolve this coupled systeme in matlab using @ODE45... I wanted the equations in the form : y1''=f(y1',y1,y2',y2,....) and so on ... => X'[] = f(X[],U[])</p>
<p> </p>
<p>How can I force maple to rearrange a system of coupled eqns with only the variables i want ?</p>
<p> </p>
<p>I know this is possible beacause it is a nonlinear state space model but maple do not work with nonlinear state space model... It give me error when I tried to create statespace model with my non linear diff eqns.</p>
<p> </p>
<p>Thanks a lot !</p><p>Hello,</p>
<p> </p>
<p>I have a complex set of non linear diff eqns in the form :</p>
<p>y1'' = f(y1',y1,y2'',y2',y2,y3'',y3',y3,y4'',....,y6'',y6',y6,u1,u2,u3,u4) ;</p>
<p>y2'' = f(y1'',y1',y1,y2',y2,y3'',y3',y3,y4'',....,y6'',y6',y6,u1,u2,u3,u4)</p>
<p>and so on ... y6''=(...)</p>
<p>As I want to resolve this coupled systeme in matlab using @ODE45... I wanted the equations in the form : y1''=f(y1',y1,y2',y2,....) and so on ... => X'[] = f(X[],U[])</p>
<p> </p>
<p>How can I force maple to rearrange a system of coupled eqns with only the variables i want ?</p>
<p> </p>
<p>I know this is possible beacause it is a nonlinear state space model but maple do not work with nonlinear state space model... It give me error when I tried to create statespace model with my non linear diff eqns.</p>
<p> </p>
<p>Thanks a lot !</p>211788Fri, 29 Apr 2016 10:42:40 Zrdpdordpdo