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en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSat, 07 May 2016 00:26:24 GMTSat, 07 May 2016 00:26:24 GMTThe most recent questions and posts on MaplePrimes tagged with symbolichttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Questions and Posts tagged with symbolic
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Problem with symbolical solution
http://www.mapleprimes.com/questions/211684-Problem-With-Symbolical-Solution?ref=Feed:MaplePrimes:Tagged With symbolic
<p>Hi,</p>
<p>I have been trying to solve the following equation with respect to <strong>y</strong>, but I have not been successful. In fact, I always get answer<strong> RootOf(...</strong><strong>). </strong>I should mention that all variables and parameters are real non-negative. I have also tested with "assume", but it did not help. Any suggestion would be appreciated. </p>
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<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -23px;" src="/view.aspx?sf=211684_question/84eaca27a1dac8886baabd2af76ecfd8.gif" alt="with(RealDomain):" width="768" height="40" align="middle"></p>
<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -7px;" src="/view.aspx?sf=211684_question/6b9f57e8106f27b77c8be7bed6ee29a4.gif" alt="eq := -((y-b)*mu-y)*x^beta*alpha+y^beta*varepsilon*(x-a) = 0" width="295" height="31"></p>
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<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -7px;" src="/view.aspx?sf=211684_question/855cbf564b3c9f3d1de1314f4bb24cd1.gif" alt="-((y-b)*mu-y)*x^beta*alpha+y^beta*varepsilon*(x-a) = 0" width="259" height="31"></p>
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<td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(1)</td>
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<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6px;" src="/view.aspx?sf=211684_question/712a2ba955c4f2a0e1921e7b8c0541fc.gif" alt="solve(eq, y)" width="77" height="23"></p>
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<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -7px;" src="/view.aspx?sf=211684_question/03804b2af0514f78e50c63b832c685d9.gif" alt="RootOf(-x^beta*alpha*b*mu+x^beta*alpha*mu*_Z-x^beta*alpha*_Z+_Z^beta*varepsilon*a-_Z^beta*varepsilon*x)" width="376" height="31"></p>
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<td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(2)</td>
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<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6px;" src="/view.aspx?sf=211684_question/0a53d1f02bbaaa442b4305a86b00c2ef.gif" alt="remove_RootOf(%)" width="128" height="23"></p>
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<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -7px;" src="/view.aspx?sf=211684_question/4c9612726c3ffc1dcf9626d6a5d43791.gif" alt="-x^beta*alpha*b*mu = 0" width="84" height="31"></p>
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<td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(3)</td>
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<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6px;" src="/view.aspx?sf=211684_question/6411add5b6380fd109ab98bc6cf45859.gif" alt="``" width="11" height="23"></p>
<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6px;" src="/view.aspx?sf=211684_question/9deac4064200799e8ec74f19fb4cba41.gif" alt="``" width="11" height="23"></p>
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<p><a href="/view.aspx?sf=211684_question/Equation.mw">Download Equation.mw</a></p>
<p> </p>
<p>Thanks.</p><p>Hi,</p>
<p>I have been trying to solve the following equation with respect to <strong>y</strong>, but I have not been successful. In fact, I always get answer<strong> RootOf(...</strong><strong>). </strong>I should mention that all variables and parameters are real non-negative. I have also tested with "assume", but it did not help. Any suggestion would be appreciated. </p>
<form name="worksheet_form"><input type="hidden" name="md.ref" value="98C5A6C236530C8C8618778DDD0FE6FA">
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<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -23px;" src="/view.aspx?sf=211684_question/84eaca27a1dac8886baabd2af76ecfd8.gif" alt="with(RealDomain):" width="768" height="40" align="middle"></p>
<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -7px;" src="/view.aspx?sf=211684_question/6b9f57e8106f27b77c8be7bed6ee29a4.gif" alt="eq := -((y-b)*mu-y)*x^beta*alpha+y^beta*varepsilon*(x-a) = 0" width="295" height="31"></p>
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<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -7px;" src="/view.aspx?sf=211684_question/855cbf564b3c9f3d1de1314f4bb24cd1.gif" alt="-((y-b)*mu-y)*x^beta*alpha+y^beta*varepsilon*(x-a) = 0" width="259" height="31"></p>
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<td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(1)</td>
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<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6px;" src="/view.aspx?sf=211684_question/712a2ba955c4f2a0e1921e7b8c0541fc.gif" alt="solve(eq, y)" width="77" height="23"></p>
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<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -7px;" src="/view.aspx?sf=211684_question/03804b2af0514f78e50c63b832c685d9.gif" alt="RootOf(-x^beta*alpha*b*mu+x^beta*alpha*mu*_Z-x^beta*alpha*_Z+_Z^beta*varepsilon*a-_Z^beta*varepsilon*x)" width="376" height="31"></p>
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<td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(2)</td>
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<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6px;" src="/view.aspx?sf=211684_question/0a53d1f02bbaaa442b4305a86b00c2ef.gif" alt="remove_RootOf(%)" width="128" height="23"></p>
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<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -7px;" src="/view.aspx?sf=211684_question/4c9612726c3ffc1dcf9626d6a5d43791.gif" alt="-x^beta*alpha*b*mu = 0" width="84" height="31"></p>
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<td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(3)</td>
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<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6px;" src="/view.aspx?sf=211684_question/6411add5b6380fd109ab98bc6cf45859.gif" alt="``" width="11" height="23"></p>
<p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6px;" src="/view.aspx?sf=211684_question/9deac4064200799e8ec74f19fb4cba41.gif" alt="``" width="11" height="23"></p>
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<p> </p>
<p>Thanks.</p>211684Wed, 27 Apr 2016 09:08:17 ZMohsenReisiMohsenReisiSymbolic calculation of matrix rank
http://www.mapleprimes.com/questions/210704-Symbolic-Calculation-Of-Matrix-Rank?ref=Feed:MaplePrimes:Tagged With symbolic
<p>Hello,</p>
<p>I would like to symbolically determine the rank of a jacobian matrix. In the help, I have seen that the Rank function of the LinearAlgebra can be used for this purpose. However, when I use this function, the function doesn't allow to find the different singularities that can occur on my jacobian matrix.</p>
<p>Here a exemple of a jacobian matrix that I obtain on a slidercrank mechanism:<br><br><img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=c72de696a96bb9c2417ee400bd893dae.gif" alt="Phi := Matrix(2, 3, {(1, 1) = -l1*sin(theta(t)), (1, 2) = -1, (1, 3) = l2*cos(beta(t)), (2, 1) = l1*cos(theta(t)), (2, 2) = 0, (2, 3) = l2*sin(beta(t))})"></p>
<p>The rank of this jaobian (Phi) gives 2 whatever the values of theta(t) and beta(t). However, if the values of theta(t) and beta(t) are :theta(t)=Pi/2,beta(t)=0. The rank shouldn't be 2 but 1.</p>
<p>Is a way to obtain the symbolic calculation of the rank of a jacobian matrix which can distinguish different cases following the values of the parameters ? In others words, my dream will be to have a Rank function (or another algorithm) which can gives :<br>the rank is 2 if theta(t) different of Pi/2 [Pi] and beta(t)=0 [Pi] <br>and otherwise 1 if ...<br>and perhaps 0 if ...</p>
<p>Thanks a lot for your help.</p>
<p>I let a piece of code with an example of calculation of the rank</p>
<p><a href="/view.aspx?sf=210704_question/RankMatrix.mw">RankMatrix.mw</a></p><p>Hello,</p>
<p>I would like to symbolically determine the rank of a jacobian matrix. In the help, I have seen that the Rank function of the LinearAlgebra can be used for this purpose. However, when I use this function, the function doesn't allow to find the different singularities that can occur on my jacobian matrix.</p>
<p>Here a exemple of a jacobian matrix that I obtain on a slidercrank mechanism:<br><br><img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=c72de696a96bb9c2417ee400bd893dae.gif" alt="Phi := Matrix(2, 3, {(1, 1) = -l1*sin(theta(t)), (1, 2) = -1, (1, 3) = l2*cos(beta(t)), (2, 1) = l1*cos(theta(t)), (2, 2) = 0, (2, 3) = l2*sin(beta(t))})"></p>
<p>The rank of this jaobian (Phi) gives 2 whatever the values of theta(t) and beta(t). However, if the values of theta(t) and beta(t) are :theta(t)=Pi/2,beta(t)=0. The rank shouldn't be 2 but 1.</p>
<p>Is a way to obtain the symbolic calculation of the rank of a jacobian matrix which can distinguish different cases following the values of the parameters ? In others words, my dream will be to have a Rank function (or another algorithm) which can gives :<br>the rank is 2 if theta(t) different of Pi/2 [Pi] and beta(t)=0 [Pi] <br>and otherwise 1 if ...<br>and perhaps 0 if ...</p>
<p>Thanks a lot for your help.</p>
<p>I let a piece of code with an example of calculation of the rank</p>
<p><a href="/view.aspx?sf=210704_question/RankMatrix.mw">RankMatrix.mw</a></p>210704Sat, 26 Mar 2016 13:18:23 ZBendesartsBendesartsHow to import matrix from MATLAB?
http://www.mapleprimes.com/questions/209991-How-To-Import-Matrix-From-MATLAB-?ref=Feed:MaplePrimes:Tagged With symbolic
<p>Hi guys,<br>I want to import symbolic matrix from matlab to Maple, How I can do that ? <br><br><br></p><p>Hi guys,<br>I want to import symbolic matrix from matlab to Maple, How I can do that ? <br><br><br></p>209991Thu, 03 Mar 2016 15:18:05 Zangel222angel222How is basis chosen?
http://www.mapleprimes.com/questions/208981-How-Is-Basis-Chosen?ref=Feed:MaplePrimes:Tagged With symbolic
<p>I solve a linear system of equations which is <em>rank deficient. </em>Naturally, when Maple solves it symbolically, it chooses some of its variables to use them as a basis to express the solution. </p>
<p>In a specific problem I'm solving, the basis chosen by Maple is -very- smart, showing a good <em>exploitation</em> of the problem structure. </p>
<p>I'm curious as to what kind of factorization is used by default, or if there's a lot of by hand "black magic" involved, what are its general characteristics. </p>
<p> </p>
<p>Best regards</p>
<p>Claudio</p><p>I solve a linear system of equations which is <em>rank deficient. </em>Naturally, when Maple solves it symbolically, it chooses some of its variables to use them as a basis to express the solution. </p>
<p>In a specific problem I'm solving, the basis chosen by Maple is -very- smart, showing a good <em>exploitation</em> of the problem structure. </p>
<p>I'm curious as to what kind of factorization is used by default, or if there's a lot of by hand "black magic" involved, what are its general characteristics. </p>
<p> </p>
<p>Best regards</p>
<p>Claudio</p>208981Mon, 01 Feb 2016 15:00:11 ZcladelpinocladelpinoSymbolic matrix calculus in Maple
http://www.mapleprimes.com/questions/208653-Symbolic-Matrix-Calculus-In-Maple?ref=Feed:MaplePrimes:Tagged With symbolic
<p>Sorry for the uninformative title. I've never used Maple, but I'm willing to buy a student license and learn it. But before spending too much effort and money I need to know if it suits my needs.</p>
<p>Basically what I need to do is:</p>
<p>1) I have a positive definite symmetric matrix of size nxn, where n can range from 2 to inf. I don't know the elements, except the fact that the diagonal has ones everywhere. All I know is that the elements out of the diagonal are in the range [0,1)</p>
<p>2) I have to compute the lower triangular cholesky decomposition of this matrix, lets call it L.</p>
<p>3) I need to subtract from each element of L the mean of the elements in the respective column. Lets call this matrix L*</p>
<p>4) Then I need to evaluate another nxn matrix computed from the elements of L* following a simple pattern.</p>
<p>5) Finally I need to find the eigenvalues of this last matrix.</p>
<p>What I would ideally want is to get a symbolic representation of the n eigenvalues as symbolic functions of the (unknown) elements of the matrix at point 1.</p>
<p>I can drop the assumption of n being unknown, i.e. fix n=3 and get the 3 functions that, after replacing the right values, give me the eigenvalues, then fix n=4 and get 4 functions, etc.</p>
<p>Is this possible to do in maple?</p>
<p>Thank you</p><p>Sorry for the uninformative title. I've never used Maple, but I'm willing to buy a student license and learn it. But before spending too much effort and money I need to know if it suits my needs.</p>
<p>Basically what I need to do is:</p>
<p>1) I have a positive definite symmetric matrix of size nxn, where n can range from 2 to inf. I don't know the elements, except the fact that the diagonal has ones everywhere. All I know is that the elements out of the diagonal are in the range [0,1)</p>
<p>2) I have to compute the lower triangular cholesky decomposition of this matrix, lets call it L.</p>
<p>3) I need to subtract from each element of L the mean of the elements in the respective column. Lets call this matrix L*</p>
<p>4) Then I need to evaluate another nxn matrix computed from the elements of L* following a simple pattern.</p>
<p>5) Finally I need to find the eigenvalues of this last matrix.</p>
<p>What I would ideally want is to get a symbolic representation of the n eigenvalues as symbolic functions of the (unknown) elements of the matrix at point 1.</p>
<p>I can drop the assumption of n being unknown, i.e. fix n=3 and get the 3 functions that, after replacing the right values, give me the eigenvalues, then fix n=4 and get 4 functions, etc.</p>
<p>Is this possible to do in maple?</p>
<p>Thank you</p>208653Wed, 20 Jan 2016 13:25:08 ZxarzxarzHow to optimize solving process?
http://www.mapleprimes.com/questions/208268-How-To-Optimize-Solving-Process?ref=Feed:MaplePrimes:Tagged With symbolic
<p>I am able to get unlimeted numbers of equations describing my system. These equations are generally relate quotients of multivariate polynomials. Each additional equation I get is generally less than twice the length of the last, and it is not always the case that an equation is independant of the previous equations. Although I can get unlimited numbers of equations describing the system, it is not overdetermined.</p>
<p>I am interested in solving these equations for their variables. There are about 30 cases I am working on, the smallest number of evariables is six, the largest would be twenty.<br><br>I want to be able to solve these equations in the minimal time possible. But I don't understand the function solve well enough to do so.<br><br>How do I choose the equations to minimise the time taken for the command solve to proccess them?<br>How does the command solve work?</p>
<p>particularly:</p>
<ol>
<li>if I process the command <em>solve([Eq1,Eq2,Eq3...Eqn],variables)</em> would the command <em>solve([Eq[1],Eq[2],Eq[3]...Eq[n],Eq[n+1]],variables)</em> take longer if <em>Eq[n+1]</em> is not indipendant of the previous equations? </li>
<li>Is there a way of checking whether <em>Eq[n+1]</em> is independant of the previous vequations, fast enough for it to be useful to check the equations before they are processed?</li>
<li>Does the ordering of the equations affect the speed of solve?</li>
<li>Is there a way of pre processing the equations before they are put into solve that will save it time? (for example factorising them, simplifying them etc...)</li>
</ol>
<p> </p>
<p> </p><p>I am able to get unlimeted numbers of equations describing my system. These equations are generally relate quotients of multivariate polynomials. Each additional equation I get is generally less than twice the length of the last, and it is not always the case that an equation is independant of the previous equations. Although I can get unlimited numbers of equations describing the system, it is not overdetermined.</p>
<p>I am interested in solving these equations for their variables. There are about 30 cases I am working on, the smallest number of evariables is six, the largest would be twenty.<br><br>I want to be able to solve these equations in the minimal time possible. But I don't understand the function solve well enough to do so.<br><br>How do I choose the equations to minimise the time taken for the command solve to proccess them?<br>How does the command solve work?</p>
<p>particularly:</p>
<ol>
<li>if I process the command <em>solve([Eq1,Eq2,Eq3...Eqn],variables)</em> would the command <em>solve([Eq[1],Eq[2],Eq[3]...Eq[n],Eq[n+1]],variables)</em> take longer if <em>Eq[n+1]</em> is not indipendant of the previous equations? </li>
<li>Is there a way of checking whether <em>Eq[n+1]</em> is independant of the previous vequations, fast enough for it to be useful to check the equations before they are processed?</li>
<li>Does the ordering of the equations affect the speed of solve?</li>
<li>Is there a way of pre processing the equations before they are put into solve that will save it time? (for example factorising them, simplifying them etc...)</li>
</ol>
<p> </p>
<p> </p>208268Thu, 07 Jan 2016 20:29:03 ZAnnonymouseAnnonymouse