# Questions tagged [symbolic-computation]

Numeric computation usually uses floating point numbers. Symbolic computations use symbols, and can give exact answers, such as $\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$. Mathematica, Maple, and Geometry Expressions all use symbolic computation, when desired. An online source is WolframAlpha.

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21 views

### Identifying Hamiltonian dynamics in 2D

While studying a physical system I've encountered an two dimensional autonomous ODE defined on a torus. The vector field describing it is a messy expression involving rational functions of ...
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### Partial derivative of a heat kernel

I happen to have the heat kernel on the two-dimensional hyperbolic space and I need to take partial derivatives in order to check that it satisfies the heat equation as expected. The problem is I can ...
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### Solving first-order linear recurrences with polynomial coefficients in terms of roots

Suppose $K$ is a characteristic zero field with decidable equality, and $a(n), b(n), c(n) \in K[n]$ are polynomials with all roots in $K$ (i.e., these polynomials split over $K$). I am trying to ...
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### How to use Octave with real numbers and syms at one time

I want to use GNU Octave to solve my equations. Equations contain syms variables and vectors with decimal numbers in them. How properly solve these equations without getting warnings that im doing ...
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### Integral of Squared Sum of Sine [closed]

Let's say we have the following function $$\int \left( \sum_{i = 1}^\infty a_i \sin(b_ix)\right)^2$$ Assuming that this series converges (it is actually a Fourier Series of the Lagrangian of the Wave ...
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### A very heavy computation

I'm doing calculations about elliptic curve, which involve the sum of two rational points and birational transformation. I need help regarding the symbolic substitution below, where $u,d,x,y$ are ...
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### Relation between symbolic computation and symbolic dynamics

From what I read about the fields symbolic computation and symbolic dynamics , I expect these two fields to be having vivid connections . I would like to know what are some of the prominent topics ...
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### What are $c$'s in antiderivative of double integral in Wolfram Alpha

I would like to solve the following double integral: $$\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} (x y)^{-\theta - 1} dx \hspace{1mm} dy$$ Using Wolfram Alpha for symbolic algebra, it gives a ...
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### What is parametric equation of a cylinder with an arbitrary norm in Cartesian system?

I just need to intersect a plane and a cylinder for an industry application and latter we would fit the intersection curve on to some sample data we have and that supposed to provide us with some ...
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### Pull t out of trig functions and solve it

I'm trying to come up with an analytical solution for inverse kinematics for my robot; but some of my trig has left my brain! The robot is very simple; with one rotary and one prismatic joint. I'm ...
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### Symbolic sum similar to Zeta function or harmonic number

(I have no idea why this was closed, nor did I receive any information/email regarding what details or clarity were missing. I have rendered the Mathematica into mathematics.) copied from mathematica....
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### How do I extend SymPy pretty printing for new structures in Jupyter notebook?

Note 1: I am asking this on Math Stack Exchange rather than Stack Overflow, where most SymPy questions are, because StackOverflow doesn't have MathJax, making it very difficult to pose the question. ...
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### Construction of the Steinhaus probability space

Q: Please let me know if the following sketch of the build-up of the Steinhaus probability space $(\Omega,{\cal A},P) = ((0,1), {\cal B}((0,1)), \lambda\vert_{[0,1]})$ is correct, as far as it goes: ...
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### Open source software for calculation of eigenvalues of symbolic matrix

I have following matrix \begin{bmatrix} -\alpha & 0 & \beta & \gamma\cdot\omega_m \\ 0 & -\alpha & -\gamma\cdot\omega_m & \beta \\ R_r\frac{L_h}{L_r} & 0 & -\frac{R_r}{...
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### Exact SVD algorithm of matrix with symbolic entries

I am making a library with symbolic computations which supports matrices. A matrix may have symbolic entries (eg be over the ring of polynomials of a variable $x$ ie $\mathbb{Q}[x]$). I have ...
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### Evaluating $\int_0^{\infty} x^r \exp(e^{-s x}) e^{-ax^b}dx$

Can you analytically evaluate the integral $$\int_0^{\infty} x^r \exp(e^{-s x}) e^{-ax^b}dx,$$ where $s,r,a,b>0$ are constants, $e$ is the exponential?
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### Simplifying $\frac{b^2+c^2-a^2}{(a-b)(a-c)}+\frac{c^2+a^2-b^2}{(b-c)(b-a)}+\frac{a^2+b^2-c^2}{(c-a)(c-b)}$

Simplify $$\frac{b^2+c^2-a^2}{(a-b)(a-c)}+\frac{c^2+a^2-b^2}{(b-c)(b-a)}+\frac{a^2+b^2-c^2}{(c-a)(c-b)}\,.$$ I tried very hard but I am not being able to solve it easily I opened up everything and ...
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### Simple upper bound for $t(2\Phi(\alpha/t) - 1)$, where $\alpha > 0$ and $t \in (0, 1)$

Let $\alpha > 0$ and $t \in (0, 1)$. For simplicity, take $\alpha=1$. Let $\Phi$ be the normal cumulative distribution function. Of course, the core of the problem is the term $t\Phi(\alpha/t)$. ...
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### How to solve for unknown symbols in a base-3 number system?

Imagine that someone has a base-3 number system which is represented by A, B, and C. A, B, and C correspond to our usual 0, 1, and 2, but you do not know which is 0, which is 1, and which is 2. ...
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### F5 algorithm for non-regular sequences

Faugère proves in his first Paper about the F5 algorithm the termination of the algorithm for regular sequences and mentions that some slight changes can be done to adapt this algorithm for non-...