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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38 views

Solving a differential equation using symbolic computation

I have the initial value problem $$\ddot x (t) + k \sin(x(t)) = 0$$ with initial conditions $x(0) =: x_0 $ and $\dot x (0) =: v_0$. Using Maxima I should check that $$\frac{1}{2}(\dot x (t))^2 + k ...
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1answer
14 views

MuPAD: plot sum of list elements

I am receiving an unclear error when trying to plot partial sums of elements of a list in MuPAD. Any suggestions would be appreciated. ...
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1answer
28 views

double sum simplification

I'm looking for a simplification to the following expression $$ \sum_{j=0}^m\sum_{l=0}^m \binom{m}{j} \binom{m}{l} h(j+l) $$ where $h$ is a given function. I looked for a formula of the product of ...
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21 views

What does “symbolic computation” mean in this context?

From Wikipedia In computational mathematics, computer algebra, also called symbolic computation or algebraic computation is a scientific area that refers to the study and development of algorithms ...
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32 views

What would be a more compact way to write this equation

I have an equation $$E=\frac{1}{2}k(\varphi_1-\varphi_2)^2+\frac{1}{2}k(\varphi_2+\varphi_3)^2+\frac{1}{2}k(\varphi_4-\varphi_3)^2$$ that looks quite compact already but the problem is that the ...
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23 views

Looking for info on representation of a diophantine equation as system of equations over finite field/boolean algebra

Suppose that $x$ is a positive integer. Fix some prime $p$. Then there exists some non-negative integer, $L$, and $\{x_0, x_1, . . . , x_L\} \subseteq \{0,1,...,p-1\}$ such that, $$x = ...
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3answers
46 views

Is there a mathematical symbol that tells you at which index the sign in the sum should change

Let's say I want to write the following sum in a more compact way $$a=z_1+z_2+\dots +z_{n/2}-z_{n/2+1}-z_{n/2+2}-\dots -z_{n}$$ Is there some kind of syntax to write that in a more compact way... ...
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1answer
44 views

Is this correct math notation?

Is the following correct? $$ x_{ap} = x_{ij} \quad \forall a,i \in [1,4]\ \forall p,j \in [1,5] $$ I want to write that $x_{ap}$ is equal to $x_{ij}$. And $i$ and $a$ can only be values between $1$ ...
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1answer
28 views

How to express the following in mathematical symbols?

I have three types of measurements that will conditionally increment an X value given that the initial X value is zero. The three measurements are: E = e-value I = Percent Identity A = Alignment ...
2
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146 views

Summations and vectors in symbolic matlab

I've got a few ugly equations to take gradients of and I'd love to get matlab to validate my work, but I'm having trouble because the equations are mixed with variable length vectors and some gnarly ...
0
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1answer
94 views

Evaluating this surface integral

I want to evaluate the following surface integral $$\int_S d S \, \, \exp\left(\frac{\Gamma^2 (x^2 \sigma_x^2 + y^2 \sigma_y^2 + z^2 \sigma_z^2) - 2 c R \Gamma (x x_0 + y y_0 + z z_0)}{2 c^2 ...
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21 views

Does Magma let you specify primary invariants?

I am cross-posting this question from scicomp.SE. The computer algebra system Magma can calculate primary invariants (i.e. a homogeneous system of parameters) in an invariant ring of a finite group ...
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0answers
40 views

Compute a kind of symbolic integral

I have to handle a class of symbolic integral with the form, more precisely, When I set $u(x,t) = e^{-t}x^2(1-x)^2$, then how to compute \begin{equation} I = ...
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1answer
65 views

The fastest Gröbner basis algorithm available?

for my undergraduate thesis I'm (pseudo) replicating algebraic attack on certain cryptosystem using gröbner basis approach. The heart of original attack was F5/2 algorithm (since the cryptosystem is ...
2
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0answers
29 views

Problem with a notation of symbolic derivatives.

Let's say we have got a function $F(G(B)\cdot C)$, i.e function $F$, which is a function of a function $G$ and variable $C$; also function $G$ is a function of variable $B$. Now I want to obtain the ...
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1answer
28 views

Find the normal form of this function

A second order control theory function looks like: $$\text{H}_{(s)}=\frac{\text{K}_p}{\frac{1}{\omega_0^2}\cdot s^2+\frac{2\beta}{\omega_0}\cdot s+1}$$ Now I've got the function, with ...
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1answer
59 views

Two integrals from analysis

Let build a set $A$ by this rule: for $i$ from $0$ to $n - 1$ with probability of $\frac{1}{2}$ we add this number to set $A$. Then we generate set $B = A + A := \{a_1 + a_2: a_1 \in A, a_2 \in A\}$ ...
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1answer
168 views

Please, help to identify this numerical constant

I'm trying to find an answer to this question. Let $K(k)$ be the elliptic integral of the first kind and $K'=K(\sqrt{1-k^2})$. According to Abel's theorem (see this link) we know that if ...
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0answers
24 views

How to evaluate this definite integral

I want to obtain the symbollic expression for this integral: $\int^\infty_{-\infty} \, dx \, \left(\frac{y - x}{R^2 + (y-x)^2}\right)\, e^{-\frac{(x - \mu)^2}{4 s^2} - \frac{i k (y - x)^2}{2 R}}$, ...
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107 views

Max of symbolic value - Matlab, use in integral equation.

I'm studying probability and I have come across some integral equations, where the upper bound of integral is a function $f(x) = \text{max}(g(x), const.)$ for some function $g(x)$. My problem is with ...
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1answer
29 views

Computing Extensions of an Ideal in Singular or Macaulay2

Does Macaulay2 or Singular compute extensions of ideals under ring homomorphisms? Specifically, if $\phi:R\rightarrow S$ is a ring homomorphism (say polynomial rings over $\mathbb{Q}$ which can ...
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2answers
32 views

Programmatically derive a matrix form of quadratic equation [closed]

Is there a way to do that? For example from this equation: To this matrix form: We especially would like to get thos matrices circled-red. This is the code I have at the moment: ...
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2answers
111 views

How to represent this matlab code in mathematical notation?

I have this code in matlab: z = linspace(d1,d2,n)*W/t; I am wondering how to express this operation in mathematical notation? I was thinking of something like ...
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0answers
50 views

How do I symbolically compute $\int_{a}^{b} e^{x^2}(\textrm{erf}(x) - \textrm{erf(a)})\;\textrm{d}x$?

I want to symbolically write (in the form of a series), the integral of: $$ \int_{a}^{b} e^{x^2}(\textrm{erf}(x) - \textrm{erf(a)})\;\textrm{d}x, \text{where }\{x, a, b\} \subset \mathbb{R} $$ The ...
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3answers
53 views

What does this symbol mean $f(A \cap B)?$

What does $f(A \cap B)?$ mean. Is it a set, function , polynomial, etc? What are the characteristics in its structure? what does this mean in detail?
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0answers
81 views

What is the easiest to use software to draw Latex embeddable contour diagrams? [closed]

I need to draw a few diagrams of integration contours for complex integrals. What is the easiest to use software on which I can achieve this? Particular things I need, draw a zig-zag line to denote ...
4
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0answers
46 views

Linear algebra machinery for differentiation of families of functions.

So I know that since differentiation is linear, for many types of functions we can represent it using linear algebra. Famous examples include polynomials, if we represent them with their coefficients ...
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1answer
33 views

I am having trouble with formal mathematical notations.

I am having trouble with formal mathematical notations. What does this mean? $$f(\vec x) \to max : \text{find }\vec x^* \text{ so that} \ \forall \vec x^* \in M:f(\vec x) \le f(\vec x^*)=f^*$$ How ...
2
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2answers
115 views

Indefinite integral that Wolfram Alpha can't solve

Does anybody know the indefinite integral problems that Wolfram Alpha can not solve but human can solve by using elementary functions? (The meaning of "solve" here is to represent primitive function ...
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0answers
28 views

Symbolic solution to a non-linear equation

Is it possible to solve following univarate ($y$) equation symbolically: $$ a_{2} \left(- \frac{b_{1} y + d_{1}}{2 a_{1}} - \frac{1}{2 a_{1}} \sqrt{- 4 a_{1} c_{1} y^{2} - 4 a_{1} e_{1} y - 4 a_{1} ...
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2answers
153 views

Can I solve this integral with a squared sum in it?

Title says it all. By now I have tried by hand and I think that it is indeed solvable, but I can't handle the very long terms. I tried to run the thing through SAGEs integrator: ...
0
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0answers
79 views

How to solve a bi-quadratic equation with symbolic coefficients?

I have the following equation with the symbolic coefficients specified using syms which i have been trying to solve in MATLAB:- ...
0
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0answers
14 views

Implementing the incomplete gamma function under libmatheval

I am considering libmatheval for a task in C. The problem is I need the incomplete gamma function. 1) How hard is it to implement new functions in libmatheval? 2) Any instructions on how to? 3) ...
1
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1answer
264 views

How to convert the parametric equation into implicit form?

This problem is generated from another Green's theorem related question of mine. The original equation of the plane curve is not in rational parametric form. In order to calculate the symbolic ...
0
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2answers
51 views

Program to find Shortest Symbolic Expression

I was solving a physics problem using lots of replacements for some expressions to get a manageable equation. Finally I got my answer, but it looked more like a waterfall than an actual result : ...
3
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1answer
135 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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2answers
34 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 ...
4
votes
2answers
171 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 ...
0
votes
0answers
42 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 $∇.E = 0$ ...
0
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1answer
125 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 ...
2
votes
0answers
105 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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0answers
47 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}&= ...
0
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1answer
68 views

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

I recently came across an equation which says: $$\alpha_0+\alpha_1y^{*\beta_1}+\alpha_2\left(y-c\right)^{*\beta_2}+\alpha_3\left(y-1\right)^{*\beta_3}$$ ...
0
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1answer
46 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 ...
2
votes
3answers
92 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
2
votes
2answers
3k 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 ...
1
vote
2answers
118 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
819 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
35 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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votes
0answers
138 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 $X$