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

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2
votes
2answers
204 views

Rewriting one expression using a variable representing another expression [duplicate]

I have two expressions: w1 = (a+b)/c^2; w2 = (a^3 + 3 a^2 b + 3 a b^2 + b^3)/c^6; How can I ask Mathematica to try to find an alternative expression for ...
0
votes
1answer
76 views

Numerical vs Symbolic Integration: Loss of precision

I am trying to integrate the following expression over the time interval $0\leq t \leq \text{period}$. ...
18
votes
2answers
273 views

Negative probability?

I am trying to get the sum of the squares of seven random variables, all uniformly distributed. This is what I tried. ...
1
vote
1answer
85 views

Symbolic multiplicative partitions

Let $p_n\#\equiv\prod_{k=1}^{n}p_k$ (primorial): p[n_] := Times @@ Prime[Range[n]] then the multiplicative partitions of $p_{1,2,3,4}\#$ are $$ \{\{2\}\},$$$$ ...
0
votes
3answers
83 views

Place symbols from small to big

I am wondering how to compare the different values of ω I derived in this code, and place them in order as follows. (use Print ...
3
votes
1answer
173 views

Strange behavior of Reduce with a cubic equation

This equation: $(\frac{-a}{x})^2=\sqrt{\frac{1}{x}}$ at $a > 0$ and $x > 0$ has a clear solution $x=a^{4/3}$, doesn't it? However, ...
1
vote
1answer
79 views

Calculate the algebraic multiplicity of known eigenvalues of a large, sparse matrix

I have a large (and sparse) matrix with size 1000x1000 -- 10000x10000. I believe i know all eigenvalues for the matrices. All entries are integers and so are the eigenvalues. I want to check this by ...
0
votes
0answers
65 views

Can Mathematica do this summation?

I was very pleased to discover that Mathematica could do this summation and produce a symbolic result. ...
1
vote
0answers
75 views

What summations can Mathematica do? [closed]

I was very pleased to discover that Mathematica could do this summation and produce a symbolic result. ...
0
votes
0answers
108 views

Symbolic tensor product calculation

I am trying to calculate the symbolic tensor product $\langle \nabla f\otimes f,\nabla g\otimes g\rangle ^2+(\langle \nabla f\otimes g,\nabla f\otimes g\rangle +\langle \nabla g\otimes f,\nabla ...
2
votes
1answer
104 views

Prove (or check) an expression is positive given constraints on variables?

I'm trying to figure out whether an expression is always positive given positive parameters. When the expression is complicated, I can't do this by eye. Is there any way to make Mathematica prove ...
1
vote
1answer
94 views

Simplifying fractions

What ComplexityFunction (or other technique) can I use to have Mathematica pull things out of fractions? I have a rational function of several variables and I'd ...
5
votes
1answer
103 views

MarginalDistribution with Symbolic range in ProbabilityDistribution

Given the following joint density: for 10 < x < 20, x/2 < y < x. To find the marginal density for X we do: ...
0
votes
1answer
248 views

Solving a large system of non-linear equations

I am new to Mathematica, and I am currently trying to use it to solve a large symbolic system of non-linear equations. I began the code below about 30 hrs ago, and the Mathematica Kernal has been ...
0
votes
0answers
46 views

Find the values of parameters so that the matrix is symmetric positive definite

Good evening , I have a matrix 20x20 in symbolic form. The matrix depends on 5 parameters (a,b,c,d,e). I would like to get the interval of each parameters that ensures that the matrix S is symmetric ...
4
votes
1answer
88 views

When to use GenerateConditions -> True

Many functions, usuallly those involving integration, take a GenerateConditions option which often defaults to False, or at ...
2
votes
1answer
164 views

Integrate does not accept my integrand expression

I want to calculate the symbolic integral, but I could not obtain the final results from Mathematica. ...
0
votes
0answers
57 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 ...
0
votes
0answers
61 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 ...
0
votes
2answers
110 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: ...
7
votes
1answer
194 views

Symbolic scalar-by-matrix derivative

Let's say I want to calculate the following scalar-by-matrix derivative $$\frac{\partial}{\partial A} \text{tr} \left[(\vec X^T A)^T (\vec X^T A)\right],$$ with $\vec X$ and $A$ being a $n \times 1$ ...
3
votes
1answer
149 views

Covariant derivative for symbolic tensors

I want to define a "prefix" (D_i) covariant derivative operator CD[] for symbolic tensors in form of a function, i.e. for ...
0
votes
3answers
102 views

Symbolic derivatives of special functions yield incorrect results

When I evaluate with Mathematica this expression D[ Abs[ Zeta[x + I y]], {x, 2}] + D[ Abs[ Zeta[x + I y]], {y, 2}] 0 the ...
0
votes
1answer
103 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: ...
0
votes
0answers
106 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 ...
3
votes
1answer
201 views
1
vote
0answers
80 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 ...
0
votes
2answers
92 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: ...
0
votes
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 ...
0
votes
1answer
438 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 ...
0
votes
1answer
77 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 ...
0
votes
0answers
140 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 ...
3
votes
1answer
124 views

How to do this complex integration on the real line?

$m, r$ are parameters in the following integral: Integrate[z Exp[I z r]/Sqrt[z^2 + m^2], {z, -∞, ∞}] How to do this integration directly? The result should be ...
3
votes
0answers
114 views

Fourier transformation of HeavisideTheta functions

I want to find 2D-Fourier transformation of the function given below f = HeavisideTheta[y1]*HeavisideTheta[y2 - y1] For the purpose, I use built-in function in ...
2
votes
4answers
226 views

Working with symmetric polynomials

I have a question related to working with symmetric polynomials in some variables. Let us say, I have an expression ...
2
votes
1answer
377 views

Solve[Tan[theta] == (b*Sin[t])/(a*Cos[t]), theta] breaks when “Reals” is added?

Mathematica solves this equation fine: Solve[ Tan[theta] == (b*Sin[t])/(a*Cos[t]), theta] // InputForm ...
0
votes
1answer
99 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 ...
1
vote
0answers
81 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 ...
1
vote
1answer
90 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 ...
1
vote
2answers
97 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 ...
0
votes
0answers
55 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: ...
3
votes
2answers
132 views

How to define the irrational domain or any other arbitrary domain?

I have found no way to define the domain of Irrational numbers. I can easily define a test to see if a number is irrational by defining: ...
0
votes
2answers
131 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 ...
5
votes
0answers
63 views

When and why are Assuming and Assumptions not equivalent? [duplicate]

In this question there's an example of an integral where using Assuming and Assumptions give different results: ...
3
votes
1answer
80 views

Problem with limit that requires L'Hôpital's rule to compute

Consider the following limit. Limit[(a - Sqrt[a^2 + x])/(a^2 - a*Sqrt[a^2 - x]), x -> 0, Assumptions -> {a > 0}] Mathematica 9.0.1.0 gives ...
3
votes
0answers
104 views

What is so special about variable s$?

I found a nice bug in Mathematica 9.0.1.0. Could anyone check to reproduce it? Create a file temp.txt with one line: ...
0
votes
1answer
139 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? ...
4
votes
3answers
236 views

Running out of variables

I am running symbolic calculations with Mathematica. Simplification of algebraic expressions is an important part of them as very often final results can be simplified considerably. Typically my ...
0
votes
2answers
120 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: ...
1
vote
1answer
77 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, ...