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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17 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 ...
3
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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
38 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
25 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 $B = A + A := \{a_1 + a_2: a_1 \in A, a_2 \in A\}$ ...
6
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1answer
158 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
22 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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0answers
57 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 ...
1
vote
1answer
21 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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votes
2answers
29 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
104 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 ...
4
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0answers
46 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 ...
0
votes
3answers
42 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?
2
votes
0answers
50 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
votes
0answers
40 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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votes
1answer
30 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
votes
2answers
107 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 ...
0
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0answers
27 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} ...
1
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2answers
138 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
64 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
9 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
211 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 ...
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2answers
44 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
votes
1answer
117 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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votes
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
149 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
votes
1answer
96 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
94 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
45 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
votes
1answer
54 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
votes
1answer
42 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
88 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
2k 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
106 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 ...
0
votes
1answer
667 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 ...
0
votes
1answer
32 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 ...
2
votes
0answers
121 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 $X$
1
vote
0answers
64 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
223 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 ...
11
votes
1answer
173 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 ...
0
votes
1answer
110 views

Simplifying with wxMaxima

I have this expression in wxMaxima: ...
2
votes
0answers
46 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
votes
1answer
46 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
80 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 ...
3
votes
0answers
211 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 ...
0
votes
1answer
201 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: ...
2
votes
1answer
107 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: $$ ...
1
vote
0answers
43 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.