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 ...
6
votes
3answers
73 views
Integral of a rational function: Proof of $\sqrt{C}\,\int_{0}^{+\infty }{{{y^2}\over{y^2\,C+y^4-2\,y^2+1}}\;\mathrm dy}= {{\pi}\over{2}}$?
I suspect that
$$\sqrt{C}\,\int_{0}^{+\infty }{{{y^2}\over{y^2\,C+y^4-2\,y^2+1}}\;\mathrm dy}=
{{\pi}\over{2}}$$
for $C>0$.
I tried $C=1$, $C=2$, $C=42$, and $C=\frac{1}{1000}$ with Wolfram ...
0
votes
0answers
36 views
Symbolic integration of vector norm
I'd like to symbolically integrate the expression $\int_0^1{\|r'\left(t\right)\|_2\,dt}$ where $r$ is a function $\mathbb{R} \rightarrow \mathbb{R}^2$ (so the expression is the arc length of the curve ...
1
vote
2answers
36 views
Solving symbolic equation from determinant numerically
In this problem: Intersection of conics using matrix representation , a situation arises where there are two matrices (for example:)
$$Q_1 = \begin{bmatrix}1 & 0 & 0\\0 & -1 & 0\\0 ...
1
vote
1answer
39 views
Assigning Interval on MATLAB Symbols
I have constant symbols such as
t = sym('t')
c = sym('c')
but I have to restrict these symbols with a constraint stating that t is between 0 and 1 (0 $\le$ t $\le$1). For c, 0 $\lt$ c $\lt$ 1 .
I ...
0
votes
1answer
53 views
Symbolic manipulations of integral equations
I was trying to learn about solving integral equations using symbolic algorithms. After a quick web search, I mostly found items like this Mathematica journal article that mostly focuses on how to use ...
0
votes
2answers
46 views
How to mathematically express square to not “lose” sign of a vector
I need to express force exerted on a body due to aerodynamic drag mathematically as vector in matrix form. Let $F_f$ be the exerted force, $k_{lf}$ the aerodynamic constant and $\vec{V} = [u, v, w]^T$ ...
2
votes
1answer
119 views
Computing inverse two-sided Laplace transform symbolically
How can I compute the inverse two-sided Laplace transform symbolically?
I know MATLAB has ilaplace[1], but that's just for a one-sided transform.
[1] ...
2
votes
1answer
128 views
Symbol for derivative in MAPLE
I am trying to use MAPLE to do some computations involving system of equations which terms are derivatives of functions.
When I type diff(alpha(x),x) it shows ...
2
votes
3answers
208 views
Symbolic Notation for Least Common Multiple
I am trying to write a proof for the least common multiple lcm(x, y), where lcm(x,y), x, and y are of course integers. What are the properties of lcm(x,y) written symbolically in mathematical logic ...
-1
votes
1answer
73 views
Need help figuring out $\frac{d}{dx}(x^2)|{x=3}$
Okay, I punched this into my new calculator:
$$\frac{d}{dx}(x^2)|{x=3}$$
and it all is equal to $6$. What is this called and/or what does it do?
1
vote
3answers
69 views
Find symbolic integral for expression containing multivariate polynomials
I'm looking for a way to symbolically integrate the following expression (the $k_i$ are integer constants):
Using a generalized form of the identity
I was able to express it without the ...
0
votes
1answer
57 views
Help me to understand the Gaussian blurring (2)
Here is an unknown luminosity function $f(x,y)$ and its integration results:
$$\begin{align*}
p_{i,j} &= \frac{1}{\Delta_{i,j}}\iint\limits_{D_{i,j}} \! f(x,y) \, dx \, dy,\\
\Delta_{i,j} &= ...
0
votes
1answer
40 views
Help me to understand the Gaussian blurring
Here is an unknown luminosity function $f(x,y)$ and its integration results:
$$p_{i,j}= \frac{\iint\limits_{D_{i,j}} \! f(x,y) \, dx \, dy}{\iint\limits_{D_{i,j}} \,dx\,dy}$$
I need to express the ...
1
vote
1answer
192 views
What is the $\lVert$ symbol?
I am trying to understand the quadratic equation below but cannot understand what the double bars stand for.
$$\lVert W_L LP' \rVert^2 + \sum_i W_{H,i}^2 \lVert p_i' - p_i\rVert$$
4
votes
1answer
126 views
Algorithms for symbolic definite integration?
What are the algorithms for symbolic definite integration? Apart from computing the antiderivative first.
What are the basic ideas behind such algorithms?
As far as I got it, the main idea behind ...
2
votes
2answers
118 views
Value of double product
What is
$$
\prod_{i=1}^n\prod_{j=1}^{n-i}i^2+j^2
$$
?
It feels like there should be some way to simplify this or calculate it more efficiently than iterating over each of the $\sim n^2/2$ points.
...
5
votes
2answers
180 views
How can I write an algorithm to perform the following calculation exactly? (references accepted)
Given natural numbers $N, K, m, C$, with $3^{m/3}K>C$, I want to be able to write an algorithm to exactly compute the number
$$ \left\lceil \log_3 \left(\frac{N}{3^{m/3}K-C}\right) \right\rceil $$
...
1
vote
0answers
82 views
Why are some integrals not analytically solvable? [duplicate]
Possible Duplicate:
How can you prove that a function has no closed form integral?
(Forgive my crude lingo)
Why do some integrals seem to be unsolvable; that is to say the indefinite ...
0
votes
0answers
42 views
Diagonalising a huge matrix of symbolic objects
I have to diagonalise this HUGE $9\times 9$ matrix with symbolic entries which are made up of three independent variables.
Can you please give me a reference as to how to do such a thing ...
1
vote
1answer
3k views
Is there a symbolic math package for octave?
I am using Octave (3.6) on Ubuntu 10.0.4 LTS. I want to do some research involving symbolic math. I was thinking of downloading sage (I just found about it today) - but thought I'd better ask in here ...
2
votes
1answer
166 views
Need help understanding finite fields / modulo for polynomials
I'm taking a class in finite fields and have not been able to conceptualize how modulo + finite fields works in polynomial space. I understand the basic premises of modular arithmetic, but can't work ...
1
vote
1answer
75 views
Maple help : How to use functions
I have a quadratic expression, which I process using the solve function in MAPLE, like so
quadformula := solve(p,x);
This displays the quadratic form of the ...
2
votes
2answers
111 views
Explicitly finding a cocycle in $H^3(S_3,\mathbb{Z}_3)$
I know that $H^3(S_3,\mathbb{Z}_3)\cong \mathbb{Z}_3$ (S_3 is the symmetric group for three elements). So this group is generated by any nontrivial cocycle. But I don't know how to explicitly find ...
1
vote
2answers
134 views
Express $I_{n}(x)=\int (x^{2}+1)^{(n-0.5)} dx$ with recursion
Let $I_{n}(x)=\int (x^{2}+1)^{(n-0.5)} dx$. I want to express $I_{n}(x)$ with earlier terms $\sum_{k\leq n} h_{k} I_{k}(x)$ where $h_{k}$ is a constant. I have no idea by which terms.
If I am going ...
2
votes
1answer
90 views
Computing contractions of ideals in Macaulay2
Does Macaulay2 compute contractions of ideals under ring homomorphisms. Specifically, if $R\subseteq S$ is a ring extension (say polynomial rings over $\mathbb{Q}$ which can be specified in M2) and ...
4
votes
1answer
308 views
Computing with ideals: over $K$ or over $\mathbb{Q}\subseteq K$? does it matter?
I'm beginning to learn to use SINGULAR, the computer algebra system (CAS) for commutative algebra.
NOTATION: If $K$ is a field of characteristic $0$, then $\mathbb{Q}\subseteq K$; otherwise ...
2
votes
1answer
255 views
Symbolic computation of the derivative of dot product of 2 vectors
If I have two vectors $a$ and $b$, whose components are time varying, for example
$$a=[a_x(t), a_y(t), a_z(t)]$$ $$b=[b_x(t), b_y(t), b_z(t)]$$ The dot product of these 2 vectors can be expressed as ...
0
votes
0answers
61 views
Mathematical software that handles symbolically the derivative of parametrically defined functions?
From M.S.'s question "A general formula for the n-th derivative of a parametrically defined function", the above question came to me.
I wasn't able to make Sage or Matlab doing something like the ...
4
votes
1answer
225 views
Series expansion for iterated function
I would like to find the MacLaurin expansion of an iterated function. Finding the first few terms is not hard, but it doesn't take long before Mathematica runs out of memory using the straightforward ...
4
votes
1answer
564 views
Computer algebra system to simplify huge rational functions (of order 100 Mbytes)
I have a huge rational function of three variables (which is of order ~100Mbytes if dumped to a text file) which I believe to be identically zero. Unfortunately, neither Mathematica nor Maple ...
8
votes
4answers
705 views
Easy ways to find partial fraction representation? (via a concrete example)
In a homework assignment (about generating functions) the students find themselves having to expand $\frac{3-7x+9x^{2}-3x^{3}}{\left(1-x\right)^{4}}$ intro partial fractions. Using some automated tool ...
1
vote
1answer
376 views
How to solve a symbolic non-linear vector equation?
I'm trying to find a solution to this symbolic non-linear vector equation:
...
4
votes
2answers
174 views
software for symbolic math plotter
I'm wondering if there is a plotting tool out there that will work in symbolic math?
For example, if I plot $x+y=a$ and $y=x$ on a chart, I should be able to click on the point of intersection to ...
9
votes
6answers
2k views
Online tools for doing symbolic mathematics
This question is similar to this one, but specifically relates to resources available strictly as on-line web apps. Examples include:
Wolfram Alpha
Sage Notebook
hicalc
not sure what this is; the ...
29
votes
3answers
685 views
How much does symbolic integration mean to mathematics?
(Before reading, I apologize for my poor English ability.)
I have enjoyed calculating some symbolic integrals as a hobby, and this has been one of the main source of my interest towards the vast ...
6
votes
1answer
292 views
Algorithms for Symbolic Manipulation
If you take a look at WolframAlpha, or other computer algebraic system, you will find that it is able to do symbolic manipulation like real humans.
For example, if you type in an integral, it can ...
3
votes
1answer
139 views
How to factorize $4x^4+12x^{10/3} y^{2/3}+ \dots $?
Does anyone know how to factorize the following expression:
$$4x^4+12x^{10/3} y^{2/3}+33x^{8/3} y^{4/3}+46x^2 y^2+33x^{4/3} y^{8/3}+12x^{2/3} y^{10/3}+4 y^4$$
?
3
votes
1answer
142 views
Reduce the number of operations on a simple expression
Lets say I take a computation that involves only addition and multiplication:
(a+b)*(c+d)
which can be done in many other ways, eg.
...
8
votes
5answers
771 views
symbolic computation program/software
What is your recommended symbolic computation program/software for free and commercial respectively?
What are its strength and weakness? For example, efficiency, comprehensiveness, etc
Thanks!
