For questions about symbolic computation, as opposed to numerical computations.

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3answers
362 views

Sqrt — how to get negative branch?

One of the many attractions of Mathematica is that integers are generally treated as exact symbolic entities, and not just as numbers. I was just playing with Sqrt, and was puzzled by what appeared to ...
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3answers
173 views

How to code the following product?

I am trying to examine the properties of the following product for a given tuple $\vec \lambda = (\lambda_1, \lambda_2, \dots, \lambda_n)$, then the product is as follows: $$ \dim \Gamma_\lambda = ...
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2answers
100 views

Symbolic integral with distributions

Why is Integrate[ HeavisideTheta[1 - x^2] DiracDelta[1 - x^2] , {x, 0, 1} ] (*0*) It should be HeavisideTheta[0]?
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1answer
140 views

Improve performance for finding Fibonacci number which have divisibility property

In this post, the OP requires finding a Fibonacci number having some divisibility property with Mathematica and Maxima. I tired tried that Mathematica code on Mathematica 9.0 and it's still slow ...
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1answer
157 views

Why is a non-convergent series simplified to zero?

Sum[Sin[n*x]*Sin[n] /. x -> 1, {n, 1, Infinity}] == Sum[Sin[n*x]*Sin[n], {n, 1, Infinity}] /. x -> 1 Sum::div: Sum does not converge. >> ...
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1answer
332 views

How to define a derivative/Variation operation in Mathematica from scratch

I am looking for a method in Mathematica 8 to define my own derivative/variation (independent of built-in operations). I do not want to re-define built-in objects since I fear that this could cause ...
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2answers
216 views

Symbolically associate vectors and their norms

I am wondering how to handle the following situation: I do have vectors of known dimension that I would like to handle symbolically. I suppose I can do something like ...
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1answer
75 views

How can I check if one expression implies another?

Say I have one expression, for example $x^3-3 + c = y$, and I want to check if it implies another with some set of explicitly stated assumptions. With the previous example, assuming all variables are ...
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1answer
86 views

Linearity of a function in Mathematica

I have a function which has something like myFunc[q,a state[c,d]] a could be anything, and I want to tell Mathematica that ...
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3answers
246 views

RowReduce for symbolic matrices

I'd like to invoke RowReduce on some matrices with a time parameter. For example consider A = {{1, 0}, {0, t}} If ...
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1answer
158 views

Generating a list of symbolic coefficients [duplicate]

I am trying to do something which I assume should be very simple: I want to generate a list with symbolic coefficients that looks like this: ...
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1answer
102 views

Only perform a symbolic differentiation once

I want to define a function that involves a differentiation step that Mathematica can do easily, which might be of the form ...
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1answer
183 views

Symbolic calculation

Is there any software where this kind of symbolic calculation is possible? s = 0 for i = 1 to m j = 2 i + a - t if (j > 0) s = s + a I want s as a ...
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2answers
74 views

Symbolic solution of system

everyone! I am sorry, but I am an abcolute novice of Mathematica (to be more precise this is my first day of using it) and even after surfing the web and all documents I am not able to solve the ...
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1answer
60 views

Why TensorReduce not working here?

I would like to use TensorReduce to work on the tensor contraction $y_{ib}y_{ia}$ (where index $i$ is summed). However, ...
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1answer
107 views

Finding exact local extrema of simple functions

I want to exactly find all the local maxima of f[x_] := x^4/4 - x^2/2 over the interval [-Sqrt[2], 1 + Pi/10]. The correct ...
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2answers
115 views

Expansion with binomial coefficients

How can I get binomial coefficients in expansion of $(n x+i) (1+i x)^n+(n x-i) (1-i x)^n$, where $i=\sqrt{-1}$ and $n$ is an integer. I have no idea how to coax Mathematica to do something remotely ...
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1answer
173 views

Comparative Statics on Mathematica

Let me first explain what I am doing then I will mention my little problem that I could not figure out. I am using Mathematica version 7. I have an equation named "fd" and I took the derivative of ...
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1answer
110 views

How to perform a symbolic minimization?

Can Mathematica determine the symbolic expression in terms of τ that minimizes f[τ] ? ...
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0answers
57 views

ExpToTrig transforms solution to 4th order ODE into unwanted form

Mathematica gives the solution of the second order differential equation DSolve[a y''[x] + b*y[x] == 0, y[x], x] in trigonometric form ...
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0answers
66 views

(Symbolic) LinearSolve is slower/different after upgrading to Mathematica 9

Yesterday I upgraded from mathematica 8.0.4.0 to 9.0.1.0. Trying to run the same notebook I used many times before, it takes ages to evaluate a symbolic (linearsolve) expression which before was ...
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0answers
32 views

Matching Root[…] objects with patterns, unexpected hidden argument

I needed to write patterns that could distinguish between arbitrary-function and polynomial forms of Root objects, for example, ...
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0answers
603 views

Solve huge symbolic system of linear equations

I have a system of 76 symbolic linear equations (i.e. some coefficients are symbolic) with a sparse coefficient matrix. However, neither Solve[] nor ...
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1answer
179 views

Functions that operate on symbolic matrices?

I'd like to write functions that operate on symbolic matrices, and do nothing when fed anything else. ...
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1answer
208 views

Is the formula $\sum _{m=1}^{n-1} \prod _{k=m+1}^n x_k x_m$ wrong in the wiki's page

SymmetricPolynomial[2, {Subscript[x, 1], Subscript[x, 2], Subscript[x, 3], Subscript[x, 4]}] $$\begin{align*}x_1 x_2+x_3 x_2+x_4 x_2+x_1 x_3+x_1 x_4+x_3 ...
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2answers
60 views

How to do symbolic definite integral without copy and paste the intermediate results?

I am do a symbolic definite integral, I am doing it like this: Integrate[1/Sqrt[(ϵ + u)^2 + Δ^2], ϵ] // FullSimplify It gives an output: ...
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2answers
110 views

How to display output as symbols?

I have this piece of code which populates a matrix following different rules depending on row and column number: ...
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1answer
64 views

Decompose Expression into Segments

Say I have an expression test = 3 x1^2 - 2 x3^-3 and I would like to decompose the expression into {3 x1^2, -(2/x3^3)}, I can do ...
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2answers
246 views

Dropping Higher Order Terms in symbolic evaluation

I have a series of symbolic manipulations (along with some coefficients). As a sample, here is one of the intermediate forms ...
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1answer
147 views

Alleviating a bottleneck involving a function call with symbolic derivatives

I have a bottleneck problem involving a function call with symbolic derivatives. I don't have much experience with Mathematica (or any dynamic language) and I'm certain that the way I've set this up ...
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1answer
137 views

Industrial Level Applications. Recipe for mixed notation of equations set

I am working with large (linear) equations set within Mathematica in numerical notation. For example, set from 4056 eq. is solved for a second, no more. There is no doubt, result is great. But even ...
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2answers
54 views

Are solid spherical harmonics implemented in Mathematica?

In certain applications, solid spherical harmonics can be very useful. They are essentially the usual, 'surface' spherical harmonics, with the appropriate power of the radius inserted: ...
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1answer
107 views

Symbolic matrix simplification and solving

I am trying to expand or solve an equation that contains matrices for a certain matrix, but it is not working: ...
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1answer
83 views

Symbolically implementing the following product

I have two products I hope to compare symbolically and I am hoping to use Mathematica for this. They are as follows: $$ \prod_{1 \leq i < j \leq n} {(a_i + ...
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1answer
123 views

Pattern match with Table for matrix dimension check

In Mathematica, often an expression involving matrices will encounter dimension mismatch errors, like we are multiplying a 3x2 matrix to a 3x4 matrix. Below we define a new symbol Dim, which can be ...
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1answer
82 views

Replacement rules in combination with pure functions to make a change of variables

I have defined my function in this way w = f[r,Θ] ; After some calculations i obtained my results with respect to the previous function. For instance: ...
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1answer
166 views

How to find the inverse a symbolic matrix that Mathematica thinks might be singular

I have a square matrix depending on a parameter "a". When "a" has a numeric value (eg 2.1 * 10 ^ 8) through the inverse function Inverse[] I can invert the matrix. If I write the matrix as a function ...
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1answer
93 views

Symbolic vs. numeric evaluation is incorrect [closed]

In Mathematica 9: I have two functions f[v] and g[v]. When I do f[g[0]], I get the correct ...
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2answers
88 views

setting real parameters in Hamiltonian matrix

The following Matrix represents my Hamiltonian. m = {{ B/2 - d - j/2 + a, (Sqrt[2]*j)/2, M}, {(Sqrt[2]*j)/2, B/2 + a, 0}, {M, 0, (-3*B)/2 - d + j/2 + a} How can ...
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1answer
101 views

Symbolic Constrained Optimization

I have a question regarding evaluating constrained optimization problems in symbolic terms. I would like to perform How can I implement the method of Lagrange multipliers to find constrained extrema? ...
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1answer
86 views

Is there any automatic method for rating function arguments importance?

If I have a function: y = 2a + 5b + c It can be easily seen that b is the most important parameter, next ...
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1answer
148 views

Import symbolic variables from Matlab with MATLink

I'm trying to manipulate with Mathematica symbolic expression created in Matlab. I'm using the MATLink package, and I've succedeed in importing numerical variables, but not symbolic ones : ...
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1answer
111 views

Trouble carrying out symbolic operations on matrixes

I have some problems. First of all, I declare matrices like below ...
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0answers
32 views

Derive a PDE from other PDEs

I'm trying to do some symbolic calculation like this: Substitute (11.2) into the last two of equations (11.1) and, in turn, substitute these into the first of equations(11.1), I want to ...
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0answers
36 views

Computing residues of matrix valued functions symbolically

I have a somewhat specific application in mind, but I've run into this kind of problem a few times and never found an elegant solution. Is there an efficient way to get Mathematica to recognize that ...
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0answers
64 views

Eigenvectors for a large symbolic matrix

I'm trying to compute the eigenvectors for a 42x42 symbolic matrix (with one variable) in Mathematica. I get the following error: Eigenvectors::eivec0: Unable to find all eigenvectors. >> and the ...
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0answers
13 views

Use of N@ with Table [duplicate]

I have read a code at Wolfran Demonstration where I could see "N@Table[..... ]". Is this similar to use the code "Table[....]//N" ? I would like to know where I could see the use of this kind of ...
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0answers
48 views

Speeding up inversion of symbolic matrices by invoking caching

Is it possible to reduce the computation time taken to find inverse of symbolic matrices USING CACHING TECHNIQUES accessible (if any)? I am trying to compute inverse of symbolic matrices of size ...
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0answers
47 views

eigenvalues and eigenvectors without Root answers

I'd like to find eigen values and vectors of parametric 21*21 Matrix and i cant solve the root problem.please help me to find the answers without Root. My Matrix is: ...
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0answers
68 views

Patterns and replacements

I basically need to read off informations from an expression in order to apply some recursion relations. The terms I encounter have a form like $f(k) = (1+ k_{\alpha}^{n1} k_\beta^{m1} ...