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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18 views

When do blocks commute? Symbolic Dynamics and Coding Problem 1.1.6(b) [closed]

I solved part (a) which ask when do $u$,$v$ satisfy $uv=vu$ (Here multiplication is concatenation and the monoid is the free monoid on a finite number of letters) my answer was when there is a ...
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How do you express np.argmin(A, axis=1) with a formula?

I want to express np.argmin with axis with formula. How can I express np.argmin(A, axis=1) as mathematical formula?
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45 views

Symbolic solutions to system of Boolean equations

Is it possible to have a symbolic solution to a system of Boolean equations? E.g. (A and X) or (B and Y) = C (D and X) or (E and Y) = F Now produce solutions for X ...
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How to find solve for second order pde with initial conditions using Wolfram Mathematica?

I have next task: $$ \frac{\partial^2 u}{\partial x \partial y} = 0,~ u(x,x^2) = 0,~ \frac{\partial u}{\partial x}(x, x^2) = \sqrt{|x|},~|x| < 1 $$ I write this, but it don't work: ...
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53 views

How to use the Wolfram Language or another tool to find a second order pde solution with initial conditions?

I want to find a solution the Cauchy problem using the Wolfram Language or some other tool. I have next task: $$ 3\frac{\partial^2 u}{\partial x^2} + 8\frac{\partial^2 u}{\partial x \partial y} - 3\...
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pipe (vertical bar) symbol in function

could you please explain me what pipe symbols | means in bellow's function?! $$ force = -R_B * D(v_a^B|v_a^B|)*c_D $$ where we have introduced a notation $ D(b) = diag(b_x; b_y; b_z) $for a vector $...
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85 views

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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30 views

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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47 views

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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35 views

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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56 views

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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Sufficient conditions to ensure divergence of a sequence in Maxima

I am using Maxima to check whether a given sequence is diverging to $+\infty$. I know that this problem is undecidable and we note that Maxima is throwing an error: ...
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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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GAP - Is it possible to work with symbolic expressions?

Is GAP capable of symbolic calculations? For example, I would like to be able to expand and simplify long algebraic expressions such as $(ab+c)^4(a+3d)-bd+11$, define a matrix $\begin{pmatrix} a & ...
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How to simplify the polynomial $T=(a+t_1)+(a+t_1)(a+t_2)+\cdots\prod_{i=1}^n(a+t_i)-(a+a^2+\cdots a^n)$

Is it possible to simplify the following polynomial? $$T=(a+t_1)+(a+t_1)(a+t_2)+\cdots\prod_{i=1}^n(a+t_i)-(a+a^2+\cdots a^n)$$ What I think: We can first consider a special case when $t_1=t_2=\cdots=...
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27 views

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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Closed form solution of Integral with many “free variables”

I have a pretty complicated expression that I'm interested in integrating. There's a lot of parameters, so it looks pretty involved: $$ \int_{-\infty}^{\infty}d\Delta\frac{W \sqrt{\frac{\log (2)}{\pi ...
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How to assume positive sine in Maxima

I am new to using Maxima, and I am having some problems when developing some calculations in spherical coordinates. I used the following assumption: ...
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Symbolic computation software for macroeconomic model

I am looking for software that is capable of symbolically solving a typical macroeconomic model. The rest of my question gives an example of a small model. A country maximises: $$\mathbb{E}_0\sum_{t=...
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Inconsistent formulas when solving recurrent equations using sympy.rsolve_poly

I am getting inconsistent formulas when using sympy.rsolve_poly to solve recurrent equations. This first piece of code solves $a(n+1) = a(n) + 4n^3$ with $a(0) = 0$...
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Implement the Newton iteration method for multivalued vector functions

I need to implement the Newton Iteration method for multivalued vector functions. I have this differential equation that I have to solve $$\frac{dA}{dt} - \epsilon \frac{3i}{2} \lvert A \rvert^2 A - \...
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Are there hybrid (discrete-continuous) combinatorial structures? Semantic parsing of multimedia data.

Are there hybrid (discrete-continuous) combinatorial structures, which can grow (develop) according to the discrete and continuous rules at the same time: i.e. some part for some time can grow ...
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Expression simplification in sympy — symbolic integration

I am trying to integrate $$p_1=\int_0^1\int_z^1\int_y^1\frac{6x^2}{(x+y)(x+y+z)}\,\mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z$$ which arose in connection with an earlier question. When I plug it into sympy,...
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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-...
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Binary polynomial convolution-like or-ing

I have two binary polynomials. For example $a(t)$, $b(t)$. I would like an algorithm which calculates the binary polynomial $c(t)$ such that, $$c_n = \sum_{i=0}^{n} (a_i * b_{(n-i)} ) \, > 0. $$ ...
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How can I read the multinominal naive bayers in simple english?

I trying to studying about text classifier but I have some problems to understand the math representations of scikit.learn implementation: How can I describe this using simple english?
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Is there anything online like the old “calca”?

Calca was a tool for Windows/Mac where you could type formulas with markdown text interspersed, like: # My work a=7 b=2+a^2 b=> 51 Where it would dynamically ...
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Techniques for doing “handwritten” math with current 2020 technology?

A bit of a soft question here. But what techniques are people using to efficiently do analytical math that would have typically been handwritten in the past? For example, if you're working with a ...
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Prove that the vectors $\vec{v} = \langle a,b \rangle$ and $\vec{w}= \langle c,d \rangle$ are orthogonal if and only if $ac+bd=0$

I've been racking my brain over this question for awhile now but haven't been able to make any meaningful progress. I was told as a hint that the dot product formula... $$\vec{v}\bullet\vec{w} = \Vert ...
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Nonparametric (at leasat partial) Bayesian programming?

https://en.wikipedia.org/wiki/Bayesian_programming expects assumptions about the form of the probability distributions and hences - those distributions are parametric. But is there non-parametric ...
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1answer
66 views

An operator to check the relationship between two variables?

I want to know if there is an operator that can ask the following succinctly: 'What (if any)is the relationship between variable A and variable B?' I cannot find a symbol/operator and will be using ...
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Multisymmetric polynomials in SageMath or other CAS?

Is there a library to work with multisymmetric polynomials as studied by Dalbec, Vaccarino and others? Preferably in SageMath but any platform would be helpful.
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Reference request on the rank computation of symbolic matrices using numerical methods with arbitrary precision

I need to compute the rank of matrices with symbolic entries. At some complexity level this is unreliable, so I am looking for alternatives, e.g. substituting random numbers for each symbol and then ...
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Residue computation in maple

I was doing this computation in maple but was not successful so I ask if I can do it in Mathematica? I have competed successfully with this in past in maple. The following computation gives two ...
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Computing a symbolic sum

Here I asked the question below, of the Mathematica community. I would be just as happy to solve it other ways -- even analytically! :-) Here I asked about a symbolic sum, and received three very ...
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54 views

Why is a substitution like $(a+b)(c+d) = k(c+d) \;where\ k = a + b$ valid?

Why is a substitution like $$(a+b)(c+d) = k(c+d)\;where\ k = a + b$$ valid? I can tell that it just is, but I wouldn't be able to explain it to a child. My "best" explanation of when it's valid is ...
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49 views

Expediting Groebner basis computation

I am trying to solve a bunch of homogenous polynomial equations in several variables, using Groebner basis method. I expect to get a unique rational solution. The problem is that the coefficients of ...
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122 views

A property involving two commuting 3-by-3 matrices with non-negative entries

Consider real numbers $m,n,p,q\ge 0$ and the following two matrices $$M_1= \left(\begin{matrix} 0&0&1\\0&m&n\\1&n&q \end{matrix} \right), \ \ M_2= \left(\begin{matrix} 0&1&...
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Symbolic operations in MAPLE

I need assistance on how to achieve the following manipulation in Maple Software. The questions are how do I get eq. 3.1b from 3.1a, 3.3 from 3.2a and 3.9b from 3.9a? In 3.1b the integration was ...
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Changing form of ODE's system solution (strange results?) [maple]

I'm having trouble with solving this system of ODE's using Maple software: $\frac{2q(3q-1)}{\tau^2}f_{1,R}+2\frac{q}{\tau}\dot{f}_{1,R}+\ddot{f}_{1,R}+(\kappa^2+f_{2,T})(1+\omega)(\tau/\tau_0)^{(-3(3+...
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Using gröbner basis, express a differential equation in terms of generating functions

I have a generating set of differential equations: $$ I_1=u_t\\ I_2=-uu_{tt}\\ I_3=u^{-1}\\ I_4=uu_{xxx}-6u^2u_x $$ where $u=u(x,t)$. and the coordinate is $(x,t,u,u_x,u_t,u_{tt},u_{xxx})$. Infact we ...
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Symbolic approximation through integration by parts

This is a slightly soft question. Suppose I have an integral $f(x) =\int_a^x g(t) dt $ which cannot be expressed in terms of elementary functions. One might still be able to integrate by parts to get ...
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36 views

Program of symbolic algebra that allows to calculate derivatives.

I am looking for some symbolic algebra program that allows me to calculate (for example) the $k-$th derivative a function of type $ f (t) = (1 + a (t))^{- 1} $ with $ a $ infinitely differentiable . ...

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