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Questions tagged [symbolic]

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

146 questions with no upvoted or accepted answers
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134 views

Summing the probability distribution to 1 to convince myself

I have worked out a probability distribution and want to check its sum which is necessarily 1. First we write $$ r \triangleq \frac{(2 \lambda + \mu)^2}{2(\mu + \lambda)^2}, \quad s \triangleq \...
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58 views

Why does integration of a radical times HeavisideTheta give a conditional expression?

If I want to compute an integral over x^p HeavisideTheta[y-x] where p is some fraction, I do not get the desired result, but ...
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130 views

Giving hints to Integrate

I working with the integral ...
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373 views

Calculate the power spectral density of a Markov chain

I would like to calculate the symbolic power spectral density of a two state Markov process with a symbolic transition matrix characterised by two parameters. I have tried the code below, but it ...
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320 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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387 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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154 views

Recognizing a generalized function as zero

Consider the following expression: HeavisideTheta[x]HeavisideTheta[-x] Mathematica will not simplify it further. But $\Theta(x)\Theta(-x)$ is zero if considered ...
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58 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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28 views

PlanarAngle symbolic equalities return contradictory results

PlanarAngle[OO->{A,B}]==PlanarAngle[OO->{B,A}]/.{OO->{0,0},A->{1,0},B->{1,1}} False ...
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66 views

How to calculate integration with undefined functions?

There are two functions inside the integral symbol, one is related to the independent variable and the other is independent of the independent variable. Both are the derivative and Tload is a ...
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27 views

How to display partial derivatives correctly after making a change of variables

I am currently looking into a way of being able to easily non-dimensionalise differential equations (such as the Navier-Stokes equation) in Mathematica, so that I can then seek an asymptotic expansion ...
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35 views

Symbolic Subset Sum Problem

I am interested in solving the following problem with Mathematica, but I do not know if it can be done or how it could be done. Given a finite set of terms $M=\{a_i(p_1, \ldots,p_m) \}_{i=1}^n$, ...
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28 views

Relating `DSolve` solution to initial data for a PDE

The Liouville equation for a free particle is the PDE $$\frac{p P^{(1,0,0)}(x,p,t)}{m}+P^{(0,0,1)}(x,p,t)=0$$ For which Mathematica gives the solution in terms of the arbitrary function $$P(x,p,t)\...
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35 views

Is there a feasible computation?

I have to find the values of $p_1$ and $p_2$ which minimizes the expression $G$. However, when I took the partial differentiation of $G$ with respect to $p_1$ and $p_2$, the equations I obtained were ...
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32 views

Why can Mathematica detect a linear term in a series expansion only in special cases?

The series expansion Series[Sqrt[2 - 2 Cos[d k]], {k, 0, 5}] Is in odd powers of Abs[k], or more precisely ...
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30 views

Exact Solution to Maximum with constraint, no output

I am new to Mathematica. I am trying to solve a maximum problem with several constraints. Here is my input. ...
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38 views

How to convert a symbolic recursive formula to a non-recursive one

I am new to Mathematica. I want to convert a recursive formula to a non-recursive one using symbolic math. Specifically, I have a recursive formula similar to this: $a_n = f_a(c_{n-1}, x_{n-1})$ $...
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59 views

Simplifying a differential equation acting on a product of functions

I have a function $f(x_1, \ldots , x_n)$ in $n$-variables that satisfies a fourth order linear differential equation (say $Df=0$). The function $f(x_1, \ldots, x_n)$ is of the form $f(x_1, \ldots, x_n)...
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52 views

How to multiply the elements of each site of tensor products to each other while using symbolic representation?

If I have, say three sites in a symbolic operator which is of the form A = a⊗1⊗c and I want it to act on another operator B = a1⊗b⊗1 in order to find the commutator A.B - B....
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107 views

Need help with symbolic integration

I have f[x_] := g[x]/g'[x] FullSimplify[Integrate[f[x], x]] I'm trying to get F[x] in terms of ...
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41 views

Algebraic manipulation on removing common factor outside

d[i,j] and M[i,j] are elements of size arrays of size 2x2 After some manipulations I get this as Output ...
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39 views

Analytically integrating bivariate Gaussian PDF

I have this somewhat complicated expression in terms of the following 8 variables (note: actually, $X$ and $Y$ are variables, and $a,b,c,d,e,f$ are longer expressions as a funtion two other variables, ...
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39 views

Why does Refine not use transformation rules for a user-defined function?

I defined a transformation rule for a symbol L that takes a sequence of numbers ...
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73 views

Limiting solution space for symbolic algebra problems

I have a system of 12 quadratic equations with 12 variables (x11, x12, x21, x22, x23, x33, p1, p2, p3, ϕ, μ, τ) and several positive constants,w, q1, q2. ... > 0<...
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40 views

Evaluating Fourier coefficients when Exponential terms are present

I am trying an analytical solution for a 3D Laplace equaition, and just wanted to know if I could use the symbolic calculation capabilities of Mathematica to calculate the Fourier coefficients ...
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29 views

Linear dependency of vectors of functions

I would like to find a symbolic way to obtain a Q-function (Boolean output) for the following problem. I have the following inputs: ...
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75 views

symbolic solution pde

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56 views

Define some variables to be real within the whole notebook

I want to define some variables to be real within the whole notbook? How can I do this? In the following you can find my code. I think the last step will be computed in seconds when I tell mathematica ...
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44 views

How can I simplify expressions correctly?

the final output of my code gives this expression which i call ttt: ...
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71 views

Parametric minimization running forever

I am trying to solve for the minimum distance between a line and a cone, for all possible lines in 3D space. I've formulated this as a call to Minimize, but it ...
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106 views

How do I tell Mathematica to assume a symbol is bound to a matrix?

Is it possible to tell Mathematica to treat symbols as matrices instead of scalars? For example, instead of getting Solve[r == c*n*r + d, r] ...
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75 views

Linear programming with parameters

I am trying to run LinearProgramming with a vector and a matrix that depend on some parameters, but it's not working. The message I get is that my code "contains ...
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71 views

Multivariate hypergeometric functions

Anybody knows of any Mathematica implementation of multivariate hypergeometric functions? It requires Jack polynomials, or at least Schur polynomials for the real case. In addition it requires ...
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56 views

Using Refine function and take real part of a symbolic expression

I am trying to take the real part of the a complex expression using Refine function. However, the result doesn't come out as expected. The final result still ...
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154 views

How to get Mathematica to evaluate trig function derivatives in a expression

I am working on a problem that results in expressions with trig functions and their derivatives along with several other functions and derivatives. At one point, the subtraction of two expressions ...
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50 views

Why does Mathematica take an aeon to solve an inequality?

I gave Mathematica this inequality to solve: ...
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114 views

Question arising from research into relation between Pi and its convergents

I am researching my conjecture (-1)^n*(Pi−A002485(n)/A002486(n))=(Abs(m)*2^j)^(-1)*Integrate[(x^l*(1-x)^(2*(j+2))*(k+(m+k)*x^2))/(1+x^2),{x,0,1}] (1) where ...
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114 views

Troubleshooting Notation Package

I would like to switch some mathematica functions (and variables) to forms that are more readable. I am hoping simply to change some notation for derivatives and make it so that I can symbolize ...
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186 views

Mathematical symbol and name for Symbolic Replacement

(Originally from math.SE, but might be better here) I'm searching for a mathematical symbol, that describes the symbolic replacement done for instance in Mathematica: ...
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167 views

Alternative to Series

Here is a sample of my code: ...
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633 views

Simplifying terms in a Sum expression

I have a sum in the form of pure function s = Sum[f[k], {k, 0, # - 1}] & of perhaps complicated terms f[k]. The terms <...
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195 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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570 views

Symbolic tensor product calculation

I am trying to calculate the a 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 g\...
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470 views

Eigensystem without Root objects

I'd like to find eigenvalues and eigenvectors of the parametric, 21x21, matrix below without Root objects. My matrix is: ...
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577 views

How to correctly calculate symbolic eigenvectors

I give a minimalistic example of my problem: I have a matrix: m[a_,b_]:={{0,-a+b},{b,0}}; I define the eigenvectors as: ...
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99 views

How to solve differential equation of this type?

So, I tried so solve the first equation, where I am looking for $p_2$, in Mathematica with next command: ...