MaplePrimes - Questions and Posts tagged with symbolic
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en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 11 Feb 2016 12:59:52 GMTThu, 11 Feb 2016 12:59:52 GMTThe most recent questions and posts on MaplePrimes tagged with symbolichttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Questions and Posts tagged with symbolic
http://www.mapleprimes.com/tags/symbolic
How 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 ZAnnonymouseAnnonymouseHow to find exact value of it?
http://www.mapleprimes.com/questions/207779-How-To-Find--Exact-Value-Of-It?ref=Feed:MaplePrimes:Tagged With symbolic
<p>I try to find the exact (symbolic) value of</p>
<p>(-2*sqrt(7)-4)*EllipticK((1/8)*sqrt(2)*(-3+sqrt(7)))^2+4*EllipticE(-(1/8)*sqrt(2)*(-3+sqrt(7)))*sqrt(7)*EllipticK((1/8)*sqrt(2)*(-3+sqrt(7)))</p>
<p>I tried 'simplify' with different options and 'convert'. It would be pi=3.141... as numerical approximation suggests.</p>
<p>Many thanks.</p><p>I try to find the exact (symbolic) value of</p>
<p>(-2*sqrt(7)-4)*EllipticK((1/8)*sqrt(2)*(-3+sqrt(7)))^2+4*EllipticE(-(1/8)*sqrt(2)*(-3+sqrt(7)))*sqrt(7)*EllipticK((1/8)*sqrt(2)*(-3+sqrt(7)))</p>
<p>I tried 'simplify' with different options and 'convert'. It would be pi=3.141... as numerical approximation suggests.</p>
<p>Many thanks.</p>207779Wed, 16 Dec 2015 11:08:53 ZSandorSzaboSandorSzaboHow to plot parametric integral
http://www.mapleprimes.com/questions/206846-How-To-Plot-Parametric-Integral-?ref=Feed:MaplePrimes:Tagged With symbolic
<p>when the variable is in limits of integration?</p>
<p><a href="/view.aspx?sf=206846_question/hw2_example.mw">hw2_example.mw</a></p>
<p>there exist an error : </p>
<p>Error, (in int) unable to compute a numeric answer for symbolic limits, q = -3.141592654+arccos(11./(1.+.1000000000*t)) .. 3.141592654-1.*arccos(11./(1.+.1000000000*t))</p>
<p>How to make this code work?</p><p>when the variable is in limits of integration?</p>
<p><a href="/view.aspx?sf=206846_question/hw2_example.mw">hw2_example.mw</a></p>
<p>there exist an error : </p>
<p>Error, (in int) unable to compute a numeric answer for symbolic limits, q = -3.141592654+arccos(11./(1.+.1000000000*t)) .. 3.141592654-1.*arccos(11./(1.+.1000000000*t))</p>
<p>How to make this code work?</p>206846Wed, 11 Nov 2015 07:49:42 Zwant to be a permanent veganwant to be a permanent veganHow to check input in Maple TA?
http://www.mapleprimes.com/questions/206295-How-To-Check-Input-In-Maple-TA?ref=Feed:MaplePrimes:Tagged With symbolic
<p>Assume the inequality x<sub>A,2</sub>+x<sub>B,2</sub>+x<sub>C,2</sub> ≤ 110 has to be entered as "symbolic entry only".</p>
<p>How can I check that in Maple T.A.?</p>
<p>It seems that there are type conversions necessary. I attempted to use the MathML package without any luck.</p>
<ol>
<li>Tried to transform $ANSWER within the <em>answer field</em> using MathML[ExportPresentation]( x[A,2]+x[B,2]+x[C,2] <= 110) and compare it with evalb(($ANSWER)=($RESPONSE)) in the <em>grading code field</em></li>
<li>Tried to transform $RESPONSE in the <em>grading code</em>: evalb(($ANSWER)=( MathML[ImportContent] ($RESPONSE)))</li>
</ol>
<p>What’s the format of a symbolic entry? Is it really MathML!?</p>
<p>What is the correct way to do it?</p>
<ol>
<li>answer: ?</li>
<li>grading code: ?</li>
<li>expression type: Maple syntax?!</li>
<li>Text/Symbolic entry: Symbolic entry only</li>
</ol><p>Assume the inequality x<sub>A,2</sub>+x<sub>B,2</sub>+x<sub>C,2</sub> ≤ 110 has to be entered as "symbolic entry only".</p>
<p>How can I check that in Maple T.A.?</p>
<p>It seems that there are type conversions necessary. I attempted to use the MathML package without any luck.</p>
<ol>
<li>Tried to transform $ANSWER within the <em>answer field</em> using MathML[ExportPresentation]( x[A,2]+x[B,2]+x[C,2] <= 110) and compare it with evalb(($ANSWER)=($RESPONSE)) in the <em>grading code field</em></li>
<li>Tried to transform $RESPONSE in the <em>grading code</em>: evalb(($ANSWER)=( MathML[ImportContent] ($RESPONSE)))</li>
</ol>
<p>What’s the format of a symbolic entry? Is it really MathML!?</p>
<p>What is the correct way to do it?</p>
<ol>
<li>answer: ?</li>
<li>grading code: ?</li>
<li>expression type: Maple syntax?!</li>
<li>Text/Symbolic entry: Symbolic entry only</li>
</ol>206295Tue, 20 Oct 2015 10:36:46 Zwgarnwgarn