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 ...

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61 views

Practical applications of computer algebra systems

(Sorry if this is not the correct place for the question) Are there practical applications of symbolic computation systems like Mathematica, Sage, Maxima and the like in software development? To ...
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32 views

Can the following system be solved symbolically/analytically?

I have the following system of equations with variables $a,m$, and I'm wondering—can this system be solved symbolically/analytically? \begin{align} m &= 100 + \frac{ \left( 200 ...
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2answers
68 views

Integrate gaussian times sqare root of x times polynomial of order 2

How does one evaluate integrals like: $$ \int_0^\infty{\sqrt{x}\,\dfrac{\left(x-a\right)^2}{2\sigma^2}\,\exp{\left(-\dfrac{\left(x-\mu\right)^2}{2\sigma^2}\right)}}\;dx $$ There is a real and finite ...
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41 views

How do you take divergence of this field?

I forgot how to do divergences 3 years ago, this one is very confusing. We used to take them with respect to $x,y,z$ but this one doesn't have them. Help me with this question Prove that $∇.E = 0$ ...
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1answer
51 views

How to collect coefficients of the same powers?

I am using the Symbolic Math Toolbox, and define polynomials as symbolic objects, e.g.: syms a x y; P = x^2*y + a*x*y^2 + x*y^2; I am looking for a function that ...
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44 views

How to solve 3D vector equations symbolically?

I'm trying to solve the following system of equations for $\vec{X}$: $$ \vec{A} \cdot \vec{X}=d_1 $$ $$ \vec{B} \cdot \vec{X}=d_2 $$ $$ (\vec{A} \times \vec{B}) \cdot \vec{X}=(\vec{A} \times \vec{B}) ...
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28 views

Symbolic expression of eigenvalues for this symmetry 3x3 matrix

Can anyone suggest if the analytical expressions of the eigenvalues for this symmetry real matrix $L$ exist or not? All variables are real. $$\begin{align} g_{11}&= ...
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1answer
41 views

What does $(y-c)^{*\beta}$ mean

I recently came across an equation which says: $$\alpha_0+\alpha_1y^{*\beta_1}+\alpha_2\left(y-c\right)^{*\beta_2}+\alpha_3\left(y-1\right)^{*\beta_3}$$ ...
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1answer
39 views

Maple, simplyfing ODEs questions

I'm a novice using Maple 16. I'm using it mostly to check my DE homework solutions. And it happens a lot that I get stuff like in the picture. I mean (if I'm not missing anything important) that ...
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3answers
72 views

Simplify ${\Gamma(\beta)\Gamma(u) \over \Gamma(\beta+u)}$ [closed]

Is it possible that the expression below be simplified to a simpler form: $${\Gamma(\beta)\Gamma(u) \over \Gamma(\beta+u)}$$ whereby $\beta$ is a variable
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683 views

Nspire cx CAS - Laplace inverse fails

I'm trying to calculate that easy integral but I get undef. When I replaced $\infty$ with $1000$, I got the right answer. ($e^{-1000}$ is zero roughly). Although this calculator knows that ...
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2answers
76 views

Maple: How do I type “solve” with an arrow under?

I am trying to learn using Maple 18 (Mac). I have defined a function with a list of X and Y values. f := x->LinReg(X, Y, x) Now I would like to output the unknown "x" value that correlates with ...
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1answer
276 views

Finding Maximum of Symbolic Function of Fourth Derivative Using MATLAB

I am trying to find the maximum $y$-value of the fourth derivative of the function $f(x) = \frac{1}{1.1+cos(x)}$. I am limited to real numbers. I know that the answer should be 6100 and occurs at ...
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1answer
31 views

Symbolic expansion of complex arithmetic expressions

I have a lengthy complex polynomial-type equation. There is a software that can solve this type of equations provided I pass it as a coupled system of two real-valued equations. Hence, I am wondering ...
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0answers
69 views

Software to solve basic set equations (in algebra of sets)?

What symbolic math software is able to solve basic set equations? E.g. $X \setminus A = C \setminus X $, for $X$
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0answers
62 views

Why does the eigenvector have to be positive here?

The following Pictures are taken from "Symbolic Dynamics and Coding" by Lind and Marcus.! Can you tell me why it is so important that the eigenvector $v$ is positive? Where exactly is this ...
2
votes
1answer
100 views

MuPAD - complicated solve() solutions

I am trying to solve an equation for one variable as shown in the picture: Judging from the output of the second command, I should be able to get an expression for $\ddot{\theta}$. I tried ...
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0answers
22 views

Evaluate function at specific value

I wonder whether the equation below has solution $$F(x)=-c x^{n+p} -b x^n + (a-c)x^p -b$$ where $c>0, \, \, a-c >0, \, \, 0<p<1, \, \, b>0 , n=2,3, \cdots$ In other wother word, ...
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1answer
155 views

Simplifying polynomials

Suppose I have a (multivariate) polynomial with coefficients in $\mathbb Z$ or $\mathbb Q$, given in fully expanded form. How can I simplify this to reduce the number of elementary operations ...
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1answer
53 views

Simplifying with wxMaxima

I have this expression in wxMaxima: ...
2
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0answers
42 views

Computer program to simplify formulas

What is the computer program that attempts to simplify sums of binomial coefficients, factorials, etc.? Possibly Zeilberger wrote it, but I'm unsure. If so, possibly it was talked about in his A=B ...
0
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1answer
41 views

symbolic solution to trig equation for a variable

Is it possible to solve the following singular transcendental equation in $a$ for the variable $a$? Any symbolic solution will do. $$\sqrt{s^2 - v^2} = 2a \, \sinh \left( \frac{h}{2a} \right)\,\,\,$$ ...
2
votes
1answer
62 views

Division by factorized polynomials in Macaulay2

I have this problem dividing by factorized polynomials, for example (x_1^4-x_2^4)//(factor(x_1^2-x_2^2)) does not work because the numerator is of "class R" (R is the ring kk[x_1..x_n]) and the ...
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0answers
122 views

Algorithms for solving overdetermined, homogeneous linear systems with multivariate polynomial coefficients

I would like to solve overdetermined, homogeneous linear systems of equations with multivariate polynomial coefficients, i.e., $Ap=0$ with $A$ an $m\times n$ matrix, $m\gg n$, and $a_{i,j} \in ...
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1answer
126 views

null space of a specific 4x4 symbolic matrix

I need to find the symbolic null space vector (let's call it X ) of a symbolic matrix: ...
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1answer
93 views

Symbolic solution to a nonlinear ordinary differential equation problem

Suppose $y=y(x)$ is infinite continuous in $\mathbb{R}$, and $y(-1)=0$, how can we obtain the analytic solution in closed form to the following nonlinear ordinary differential equation: $$ ...
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0answers
63 views

Can a Computer Algebra System 'experiment' with expressions?

I have recently been reading about software for symbolic manipulation, and I can see its use as a tool for performing large calculations that would be unfeasible otherwise. Given that these systems ...
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0answers
39 views

Symbolic math package for n-dimensional calculus

Is there a math package that can solve ODEs with $n$ derivatives with $n$ undefined and on $n$-dimensional vectors? I tried defining $n$-dimensional vectors in Matlab and Maple and had no luck.
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1answer
74 views

Simplification of expressions with radicals in Maple

Having for example the expression $$\frac{abc\sqrt2}{d\sqrt{ab}}$$ (which results from a sequence of manipulations), can I force Maple to write it in the form $$\frac{c\sqrt{2ab}}{d}.$$ Many might ...
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2answers
39 views

What does “symbolically tractable” mean?

What does "symbolically tractable" mean in the following quote? "Traditional treatments of mechanics concentrate most of their effort on the extremely small class of symbolically tractable dynamical ...
0
votes
1answer
25 views

symbolically solving nonlinear equations

I have two nonlinear function with variable $x,y,z$ and parameters $p_1,p_2,p_3$. $$2(x−p_1)+2(xy−p_3)y=0 ,\\ 2(y−p_2)+2(xy−p_3)x=0$$ what is the value of $x,y,z$ in terms of $p_1,p_2,p_3$?
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40 views

Comfirmation of third derivative of symbolic equation including summation

With previous help I was able to find the first derivative of an equation for a work project. Now I'm after the second and third derivative, for use in a program to find the maximum (Which I must do ...
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16 views

Symbolic math program capable of completing the square for linear gaussians

Consider the case of a linear gaussian: $P(X_2|X_1) = \mathcal{N}(x_2; ax_1+b,\sigma_2 ^2) $ and $ P(X_1) = \mathcal{N}(x_1; \mu_1, \sigma_1^2)$ If I want to calculate the joint distribution ...
2
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0answers
69 views

Are there high performance computing applications for symbolic integration?

Currently there are a number of applications for numerical integration in applied mathematics and physics. Many of these are integral transforms (often Fourier or Laplace), or solving definite ...
2
votes
1answer
59 views

Symbolic computations in finite fields of unspecified order

The general setting is that I want to multiply some matrices (to many to do it by hands) over a finite field. The problem is that these matrices depend on certain parameters taken from the field and ...
2
votes
0answers
88 views

Todd-Coxeter algorithm: coincidences

I'm trying to understand the Todd-Coxeter algorithm with the help of a multiplication and relator table, but there is one thing about coincidences that is not really clear. For some small groups (for ...
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0answers
118 views

Which symbolic programming language for manipulation of nonlinear equations?

I have a set of (multivariate, nonlinear) equations which I want wo modify according to my own rules, i.e. not in a standard ways such as matlab's simplify function. I am looking for a mathematical ...
1
vote
1answer
45 views

Online tool for symbolic calculation

I don't know the exact english terms needed to write a proper question or perform a proper search, so here it is a detailed explanation of what I need: I have these expressions: t = U * ...
2
votes
1answer
230 views

Can wolfram alpha compute symbolic vector derivatives

Can Wolfram alpha be used to find out say $$\nabla_x\left(\|y-Ax\|_2\right)$$ What command do I use? I tried some obvious ways, and googled a bit, but didn't find anything.
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0answers
67 views

Integral $\int_0^{\infty } \frac{1}{(\alpha x^2 + 1) \left(- 2 \sqrt{\frac{ x^2}{x^2+1}}+2 x+\pi \right)} \, dx$

Does the following integral admit a closed-form expression? $$\int_0^{\infty } \frac{1}{(\alpha x^2 + 1) \left(- 2 \sqrt{\frac{ x^2}{x^2+1}}+2 x+\pi \right)} \, dx \;\; , \;\; 0 \leq \alpha \leq ...
2
votes
0answers
77 views

Closed-form expression of a definite integral

Does this definite integral admit a closed-form in terms of elementary functions? $$\int_0^{\infty } \frac{x}{\left(x^4+1\right) \left(2 x^2-2 \arctan\left(x^2\right)+\pi \right)} \, dx.$$
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1answer
137 views

Computing univariate resultant via modified Euclidean algorithm

In an answer to the question Resultant of Two Univariate Polynomials, a PDF of course slides was linked which describes a modification of Euclid's algorithm for computing univariate polynomial ...
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2answers
127 views

Existing Algorithm / Code to calculate exact values of the Riemann Zeta function at even natural numbers?

I wanted to know if there's any existing algorithm to compute exact values of the Riemann Zeta function at even natural numbers? For example, it should compute $\zeta(4)$ as exactly $\frac{\pi^4}{90}$ ...
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vote
1answer
96 views

How to calculate resultant of two polynomials without knowing the roots.

So in Rothstein - Trager's Method of evaluating logarithmic part they need resultant of two polynomial as shown in the image. My question is that how do they calculate the resultant without knowing ...
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1answer
28 views

Multiplicative inverse (Sets of representatives)

The question is: "Decide which elements of $Z/12Z$ have inverses, and for each such element find its inverse, then solve $[11]_{12} X=[6]_{12}$" I belive that the only inverse of $Z/12Z$ are $[1]$ ...
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Symbolic math engines barf on this ostensibly tractable integral.

$$\frac14 \int_{-M\pi}^{N\pi - s} \cos(tu/M) \cos((t+s)u/M)(1-\cos(t/M))(1-\cos((t+s)/N))\space \mathrm d t$$ with integer $u$. Alpha runs out of time. Maxima gives a tremendous result that can ...
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1answer
48 views

Differentiating a product symbol

Can someone explain how to differentiate something like $$\prod\limits_{i<j}^N {(x_i-x_j)}$$ with respect to $x_i$ The product starts from 1 and goes to N. I started off by ignoring the $x_j$ as ...
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1answer
28 views

System of ODE's of rational form

I am faced with a system of differential equations of the form $$ \begin{align} f'(x) &= \frac{\sum_i{p_i(x,f(x),g(x))\mathrm{e}^{i f(x)}}}{\sum_j{q_j(x,f(x),g(x))\mathrm{e}^{j f(x)}}} \\\ g'(x) ...
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2answers
61 views

Polynomial Simplification

I've been working with Maxima and its thrown me an expression like this $$ \left( \left( \left( 6\,{w}_{1}-6\right) \,{p}_{2}-6\,{p}_{1}\,{w}_{1}+6\,{p}_{0}\right) \,{w}_{2}^{2}+\left( \left( ...
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vote
1answer
117 views

Resultant of Two Univariate Polynomials

I am trying to implement an algorithm for computing Res(f(x),g(x),x) where f(x) and g(x) uni variate polynomials with integer coefficients. Could any one list the various algorithms for computing ...