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en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemWed, 23 Aug 2017 11:40:43 GMTWed, 23 Aug 2017 11:40:43 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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Exact symbolic solution of a system of partial differential equations with boundary conditions
https://www.mapleprimes.com/questions/222164-Exact-Symbolic-Solution-Of-A-System?ref=Feed:MaplePrimes:Tagged With symbolic
<p>Hi Everybody,</p>
<p>I have a simple question: Does Maple solve systems of partial differential equations with boundary conditions?</p>
<p>Can somebody give me an example? </p>
<p>I have only found numerical solutions to this kind of systems but no symbolic example.</p>
<p>Thanks a lot for yor help.</p>
<p> </p>
<p>Hi Everybody,</p>
<p>I have a simple question: Does Maple solve systems of partial differential equations with boundary conditions?</p>
<p>Can somebody give me an example? </p>
<p>I have only found numerical solutions to this kind of systems but no symbolic example.</p>
<p>Thanks a lot for yor help.</p>
<p> </p>
222164Mon, 19 Jun 2017 17:40:22 Zjamunozjamunozdifferences between numeric and symbolic eigendecompostion of symmetric matrix?
https://www.mapleprimes.com/questions/221363-Differences-Between--Numeric-And-Symbolic?ref=Feed:MaplePrimes:Tagged With symbolic
<p>Dear Maple experts,</p>
<p>I am struggling with a difference between the symbolic and numerical solution of an eigendecomposition of a symmetric positive definite matrix. Numerically the solution seems correct, but the symbolic solution puzzles me. In the symbolic solution the reconstructed matrix is different from the original matrix (although the difference between the original and the reconstructed matrix seems to be related to an unknown scalar multiplier.</p>
<p>restart;<br>
with(LinearAlgebra);<br>
Lambda := Matrix(5, 1, symbol = lambda);<br>
Theta := Matrix(5, 5, shape = diagonal, symbol = theta);<br>
#Ω is the matrix that will be diagonalized.<br>
Omega := MatrixPower(Theta, -1/2) . Lambda . Lambda^%T . MatrixPower(Theta, -1/2);<br>
#Ω is symmetric and in practice always positive definite, but I do not know how to specify the assumption of positivess definiteness in Maple<br>
IsMatrixShape(Omega, symmetric);</p>
<p># the matrix Omega is very simple and Maple finds a symbolic solution<br>
E, V := Eigenvectors(Omega);</p>
<p># this will not return the original matrix</p>
<p>simplify(V . DiagonalMatrix(E) . V^%T)</p>
<p># check this numerically with the following values.</p>
<p>lambda[1, 1] := .9;lambda[2, 1] := .8;lambda[3, 1] := .7;lambda[4, 1] := .85;lambda[5, 1] := .7;<br>
theta[1, 1] := .25;theta[2, 2] := .21;theta[3, 3] := .20;theta[4, 4] := .15;theta[5, 5] := .35;</p>
<p>The dotproduct is not always zero, although I thought that the eigenvectors should be orthogonal.</p>
<p>I know eigenvector solutions may be different because of scalar multiples, but here I am not able to understand the differences between the numerical and symbolic solution.</p>
<p>I probably missed something, but I spend the whole saturday trying to solve this problem, but I can not find it.</p>
<p>I attached both files.</p>
<p>Anyone? Thank in advance,</p>
<p>Harry</p>
<p><a href="/view.aspx?sf=221363_question/eigendecomposition_numeric.mw">eigendecomposition_numeric.mw</a></p>
<p><a href="/view.aspx?sf=221363_question/eigendecomposition_symbolic.mw">eigendecomposition_symbolic.mw</a></p>
<p>Dear Maple experts,</p>
<p>I am struggling with a difference between the symbolic and numerical solution of an eigendecomposition of a symmetric positive definite matrix. Numerically the solution seems correct, but the symbolic solution puzzles me. In the symbolic solution the reconstructed matrix is different from the original matrix (although the difference between the original and the reconstructed matrix seems to be related to an unknown scalar multiplier.</p>
<p>restart;<br>
with(LinearAlgebra);<br>
Lambda := Matrix(5, 1, symbol = lambda);<br>
Theta := Matrix(5, 5, shape = diagonal, symbol = theta);<br>
#Ω is the matrix that will be diagonalized.<br>
Omega := MatrixPower(Theta, -1/2) . Lambda . Lambda^%T . MatrixPower(Theta, -1/2);<br>
#Ω is symmetric and in practice always positive definite, but I do not know how to specify the assumption of positivess definiteness in Maple<br>
IsMatrixShape(Omega, symmetric);</p>
<p># the matrix Omega is very simple and Maple finds a symbolic solution<br>
E, V := Eigenvectors(Omega);</p>
<p># this will not return the original matrix</p>
<p>simplify(V . DiagonalMatrix(E) . V^%T)</p>
<p># check this numerically with the following values.</p>
<p>lambda[1, 1] := .9;lambda[2, 1] := .8;lambda[3, 1] := .7;lambda[4, 1] := .85;lambda[5, 1] := .7;<br>
theta[1, 1] := .25;theta[2, 2] := .21;theta[3, 3] := .20;theta[4, 4] := .15;theta[5, 5] := .35;</p>
<p>The dotproduct is not always zero, although I thought that the eigenvectors should be orthogonal.</p>
<p>I know eigenvector solutions may be different because of scalar multiples, but here I am not able to understand the differences between the numerical and symbolic solution.</p>
<p>I probably missed something, but I spend the whole saturday trying to solve this problem, but I can not find it.</p>
<p>I attached both files.</p>
<p>Anyone? Thank in advance,</p>
<p>Harry</p>
<p><a href="/view.aspx?sf=221363_question/eigendecomposition_numeric.mw">eigendecomposition_numeric.mw</a></p>
<p><a href="/view.aspx?sf=221363_question/eigendecomposition_symbolic.mw">eigendecomposition_symbolic.mw</a></p>
221363Sat, 04 Mar 2017 21:46:19 ZHarry GarstHarry GarstMaple Formula Input
https://www.mapleprimes.com/questions/220308-Maple-Formula-Input?ref=Feed:MaplePrimes:Tagged With symbolic
<p>Hallo,</p>
<p>im currently using Mathcad 15 and i want to change to a newer and better software with more possibilities.</p>
<p>But up to now i have not found a better software for calculating. One big advantage with mathcad is the possibilitie of symbolic formula input and calculation with units.</p>
<p>Now my question: Is it possible with Maple to write symbolic formulas (2D Structure of big formulas)</p>
<p>I dont write a formula in one row. Its nearly impossible ...</p>
<p>And can i calculate with units?</p>
<p>Thx Stefan</p>
<p> </p>
<p>Hallo,</p>
<p>im currently using Mathcad 15 and i want to change to a newer and better software with more possibilities.</p>
<p>But up to now i have not found a better software for calculating. One big advantage with mathcad is the possibilitie of symbolic formula input and calculation with units.</p>
<p>Now my question: Is it possible with Maple to write symbolic formulas (2D Structure of big formulas)</p>
<p>I dont write a formula in one row. Its nearly impossible ...</p>
<p>And can i calculate with units?</p>
<p>Thx Stefan</p>
<p> </p>
220308Sun, 04 Dec 2016 07:18:57 ZsolettosolettoHow can I solve this symbolic nonlinear system?
https://www.mapleprimes.com/questions/220112-How-Can-I-Solve-This-Symbolic-Nonlinear-System?ref=Feed:MaplePrimes:Tagged With symbolic
<p>I meet a interesting nonlinear system in the analysis of an mechanics problem. This system can be shown as following:</p>
<p><img src="/view.aspx?sf=220112_question/QQ截图20161123191735.jpg"></p>
<p>wherein, the X and Y is the solutions. A, B, S, and T is the symbolic parameters.</p>
<p>I want to express X and Y with A, B, S, T. Who can give me a help, thanks a lot!</p>
<p>PS:the mw file is given here.</p>
<p><a href="/view.aspx?sf=220112_question/A_symbolic_nonlinear_system.mw">A_symbolic_nonlinear_system.mw</a></p>
<p>I meet a interesting nonlinear system in the analysis of an mechanics problem. This system can be shown as following:</p>
<p><img src="/view.aspx?sf=220112_question/QQ截图20161123191735.jpg"></p>
<p>wherein, the X and Y is the solutions. A, B, S, and T is the symbolic parameters.</p>
<p>I want to express X and Y with A, B, S, T. Who can give me a help, thanks a lot!</p>
<p>PS:the mw file is given here.</p>
<p><a href="/view.aspx?sf=220112_question/A_symbolic_nonlinear_system.mw">A_symbolic_nonlinear_system.mw</a></p>
220112Wed, 23 Nov 2016 11:26:42 ZarousecoolarousecoolSolve symbolic integral function with various parameters
https://www.mapleprimes.com/questions/218622-Solve-Symbolic-Integral-Function-With?ref=Feed:MaplePrimes:Tagged With symbolic
<p>I can not find a solution to the integral of the function below the maple, can anyone help me?</p>
<p> </p>
<p>restart;<br>with(Student[MultivariateCalculus]);<br>with(Student[Calculus1]);</p>
<p>assume(-1 < rho and rho < 1, alpha1 > 0, beta1 > 0, alpha2 > 0, beta2 > 0, t1 > 0, t2 > 0)</p>
<p>f := proc (t1, t2, alpha1, beta1, alpha2, beta2, rho) options operator, arrow; (1/4)*(sqrt(beta1/t1)+(beta1/t1)^(3/2))*(sqrt(beta2/t2)+(beta2/t2)^(3/2))*exp(-((sqrt(t1/beta1)-sqrt(beta1/t1))^2/alpha1^2+(sqrt(t2/beta2)-sqrt(beta2/t2))^2/alpha2^2-2*rho*(sqrt(t1/beta1)-sqrt(beta1/t1))*(sqrt(t2/beta2)-sqrt(beta2/t2))/(alpha1*alpha2))/(2-2*rho^2))/(alpha1*beta1*alpha2*beta2*Pi*sqrt(1-rho^2)) end proc</p>
<p>int(int(f(t1, t2, alpha1, beta1, alpha2, beta2, rho), t2 = 1 .. infinity), t1 = 0.1e-2 .. y)</p>
<p> </p><p>I can not find a solution to the integral of the function below the maple, can anyone help me?</p>
<p> </p>
<p>restart;<br>with(Student[MultivariateCalculus]);<br>with(Student[Calculus1]);</p>
<p>assume(-1 < rho and rho < 1, alpha1 > 0, beta1 > 0, alpha2 > 0, beta2 > 0, t1 > 0, t2 > 0)</p>
<p>f := proc (t1, t2, alpha1, beta1, alpha2, beta2, rho) options operator, arrow; (1/4)*(sqrt(beta1/t1)+(beta1/t1)^(3/2))*(sqrt(beta2/t2)+(beta2/t2)^(3/2))*exp(-((sqrt(t1/beta1)-sqrt(beta1/t1))^2/alpha1^2+(sqrt(t2/beta2)-sqrt(beta2/t2))^2/alpha2^2-2*rho*(sqrt(t1/beta1)-sqrt(beta1/t1))*(sqrt(t2/beta2)-sqrt(beta2/t2))/(alpha1*alpha2))/(2-2*rho^2))/(alpha1*beta1*alpha2*beta2*Pi*sqrt(1-rho^2)) end proc</p>
<p>int(int(f(t1, t2, alpha1, beta1, alpha2, beta2, rho), t2 = 1 .. infinity), t1 = 0.1e-2 .. y)</p>
<p> </p>218622Tue, 04 Oct 2016 19:51:35 ZfsbmatfsbmatSymbolic summation gives wrong result?
https://www.mapleprimes.com/questions/215193-Symbolic-Summation-Gives-Wrong-Result?ref=Feed:MaplePrimes:Tagged With symbolic
<p>Hi,</p>
<p>I have encountered some strange issue with symbolic summation. Would be grateful for any help.</p>
<p>Here is the code (inserted as image):</p>
<p><img src="http://www.advanpix.com/downloads/SymSum2.png" alt="Symbolic summation of powers of sines & cosines" width="701" height="197"></p>
<p> </p>
<p>Code in text:</p>
<pre>restart;<br>F:=(n,a,b)->sum(r^(a+b)*cos(2*Pi/n*j+t)^a*sin(2*Pi/n*j+t)^b,j=0..n-1);<br><br>F(n,2,2);<br>F(4,2,2); <br><br></pre>
<p>The issue is that symbolic summation produces the formula (for general n) which contradicts the particular case (n=4).<br><br>Could somebody explain why this is happening? Is it a bug or am I missing something here?</p>
<p>I have tried all versions of Maple downto 14 - same situation.<br>Also Mathematica givers the same answer.<br><br></p>
<p>Thank you in advance,<br>Pavel Holoborodko.<br><br>--<br>Multiprecision Computing Toolbox<br>http://www.advanpix.com/</p><p>Hi,</p>
<p>I have encountered some strange issue with symbolic summation. Would be grateful for any help.</p>
<p>Here is the code (inserted as image):</p>
<p><img src="http://www.advanpix.com/downloads/SymSum2.png" alt="Symbolic summation of powers of sines & cosines" width="701" height="197"></p>
<p> </p>
<p>Code in text:</p>
<pre>restart;<br>F:=(n,a,b)->sum(r^(a+b)*cos(2*Pi/n*j+t)^a*sin(2*Pi/n*j+t)^b,j=0..n-1);<br><br>F(n,2,2);<br>F(4,2,2); <br><br></pre>
<p>The issue is that symbolic summation produces the formula (for general n) which contradicts the particular case (n=4).<br><br>Could somebody explain why this is happening? Is it a bug or am I missing something here?</p>
<p>I have tried all versions of Maple downto 14 - same situation.<br>Also Mathematica givers the same answer.<br><br></p>
<p>Thank you in advance,<br>Pavel Holoborodko.<br><br>--<br>Multiprecision Computing Toolbox<br>http://www.advanpix.com/</p>215193Thu, 28 Jul 2016 02:35:27 ZPavel HoloborodkoPavel Holoborodko