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

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7 views

Solving PDEs with complicated boundary conditions

The system I'm trying to solve is $$\nabla^2 C_{(r,\theta)} =0$$ $$C_{(\infty,\theta)}=C_0$$ $$ [ \frac{\partial C_{(r,\theta)}}{\partial r} cos(\theta)+\frac{1}{r}\frac{\partial ...
15
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2answers
286 views

Symbolic solution(s) to Heat equation/ Green functions to standard PDEs

Symbolic solution(s) to Heat equation? or more generally, Green functions to known PDEs I am interested in variations of the heat equation: I understand that Mathematica cannot provide a symbolic ...
3
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1answer
53 views

Factoring a differential equation into an operator product

Following the fundamental theorem of algebra, I can (as stated here in Sec. 1.1.4) factor an $n$th-order linear ordinary differential equation $$ a_n \frac{d^n x}{dt^n} + a_{n-1} \frac{d^{n-1} ...
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1answer
51 views

Compute integral symbolically

I want to compute the following integral: ...
2
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2answers
92 views

Finding Expectation of function of a Log-normal distribution

Say $Y=g(X)$ and $p_X = \frac{e^{-\frac{(\mu -\log (x))^2}{2 \sigma ^2}}}{\sqrt{2 \pi } x \sigma }$ is Log-normal density function: [Wiki] Find E[Y]? Since $E[Y] = \int_0^\infty y f_Y \ dy = ...
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0answers
138 views

Calculating probabilities symbolically

Is there a way to solve for statistical quantities analytically/symbolically in Mathematica? example 1: Lets say that I want to do a calculation that requires Bayes theorem. I know p(a), p(b) and ...
1
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1answer
84 views

Generate conditions seems to not work [closed]

I am trying to compute the following integral Integrate[E^(I*k*Omega*t), {t,0,T}, GenerateConditions->True] for which Mathematica returns ...
2
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1answer
111 views

What's the differences between the shift-enter and MakeBoxes running?

I know the example usages of MakeBoxes in the Tutorial like this. but I want to know a subtle distinction between (1) and (3) ...
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0answers
51 views

Define an operator with commutative, associative and distributive properties

I need to define a symbolic operator with commutative, associative and distributive properties, in the same way as the sum and product operator for real numbers. I have started with: ...
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1answer
91 views

Factoring terms out of a polynomial

I don't do much algebra in Mathematica and was surprised to discover, while attempting to answer this question, that I had no idea how to factor out an expression from a polynomial. The question was, ...
3
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1answer
72 views

Symbolic Output after numerical computation

I have a small question about the symbolic output. I started to write a program that generates the coordinates of n-dimensional polytopes by Wythoff construction. For crystallographic groups, all is ...
0
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0answers
54 views

A derivative encountered in matrix factorization using gradient descent

I want to factorize a matrix $a_{ij}$ as $$ a_{ij} = \sum_k u_{ik} v_{jk} $$ using variational method for some reason. That is, I want to minimize the cost function $$ F = \sum_{ij} b_{ij}^2 $$ with ...
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1answer
76 views

Symbolic evaluation of the sum of KroneckerDelta

I want to evaluate this simple expression $$ \sum_n f(n)\delta_{mn} = f(m) $$ using this: Sum[KroneckerDelta[m, n] f[n], {n, Infinity}] However Mathematica ...
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0answers
29 views

How to calculate this derivative? [duplicate]

Can Mathematica do the following simple calculation? $$F(x_0, x_1, x_2, ...) \equiv \sum_n x_n^2$$ I want to do the symbolic calculation: $$ \frac{\partial F}{\partial x_m} = \sum_n 2 x_n ...
2
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1answer
64 views

Defining a function (but not explicitly)

I have a question that must have a simple answer, but googling and searching this website did not produce an answer, so I'm asking it here. I'm working with three variables $x, y, \theta$, and I want ...
0
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1answer
122 views

Is this function convex?

How can I determine convexity of the function f = Log[ x, 1 + (x^a - 1) (x^b - 1)/(x - 1)] with the parameters $a,\,b$ belonging to the interval $(0,1)$ in ...
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2answers
213 views

How to make Mathematica use the chain rule?

Lets say I have the following PDE: $$x^2 u_{xx} - u_{yy} + u_y = 0$$ And I have the following change of variables: $$ s(x,y) = x e^y \, \, \, , \, \, t(x,y) = x e^{-y}$$ How can I use Mathematica ...
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0answers
46 views

Expectation taking unusually long to evaluate

I am trying to evaluate an expectation, but it is taking an extremely long time although the expression itself should not be too complicated. My code is ...
1
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1answer
102 views

Compute symbolic Expectation of a summation

I am required to computed following Expectations : $E[\displaystyle\sum\limits_{i=1}^N \frac{X_{i}}{N}] = \bar{x}_{0}$ & $E[\displaystyle(\sum\limits_{i=1}^N \frac{X_{i}}{N})^2] = ...
3
votes
2answers
138 views

A suspicious result of an integral

I integrated this term in Mathematica: $$\int_{-\infty}^{\infty} d\omega*\sin(s*\omega)*\frac{1}{e^{\beta*\hbar*\omega}-1}*\frac{\omega}{\omega^{2}+\gamma^{2}}$$ The code in Mathematica: ...
1
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2answers
92 views

Assign a Distribution to a group of symbolic variable [closed]

I'm looking to compute this Expectation : "i" represent a individual and h(i) is value. I would like the compute the Expected value of his value times the mean of the groups. Everything is unknown ...
2
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2answers
170 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
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1answer
73 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
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2answers
268 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
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1answer
82 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 $$ \{\{2\}\},$$$$ ...
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1answer
48 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
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1answer
170 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
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1answer
68 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
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0answers
58 views

Can Mathematica do this summation?

I was very pleased to discover that Mathematica could do this summation and produce a symbolic result. ...
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0answers
66 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
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0answers
81 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
82 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
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1answer
77 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
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1answer
91 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: ...
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1answer
174 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
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0answers
41 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
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1answer
84 views

When to use GenerateConditions -> True

Many functions, usuallly those involving integration, take a GenerateConditions option which often defaults to False, or at ...
2
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1answer
160 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. ...
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0answers
56 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
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0answers
58 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
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2answers
85 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: ...
6
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1answer
167 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 $n \times 1$ ...
2
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1answer
96 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 ...
-1
votes
3answers
98 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
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1answer
92 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
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0answers
81 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
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1answer
191 views
1
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0answers
74 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
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2answers
88 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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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 ...