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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28 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 ...
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14 views

Translate the selected argument into symbolic Form

Translate the selected argument into symbolic form, using the letters in the order in which they are listed. Then use indirect proof and the eighteen rules of inference to derive the conclusion. ...
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42 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
27 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 ...
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1answer
34 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 * ...
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1answer
63 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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53 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 ...
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56 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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33 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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16 views

Solve two equations to have the same roots (perhaps with computer symbolically)

I have a function: $$ P(z) \equiv (\cos(k_1 z) - d_1)(\cos(k_2 z) - d_2) $$ where $d_1$ and $d_2$ are both functions in $z$ and $k_1$ and $k_2$ are constants. I believe that there exists a function, ...
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66 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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31 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
18 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
34 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
22 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
39 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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59 views

Perturbation in Maple for ODE

I am working on doing a perturbation analysis for a model of opsin delivery in the eye. The ODE is VERY complicated ${\frac {d}{dt}}\eta \left( t \right) =1/2\,{\frac {-K_{{2}}kP_{{0}}+ \eta \left( ...
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1answer
48 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 ...
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1answer
32 views

how to set variables in mathematica

I have this optimization problem that Mathematica solves correctly: NMinimize[{x0^2 + x1^2 + x2^2, x0 - x1 + 2.0 x2 == 1.0, x0 + x1* + x2 == 0.0}, {x0, x1, x2}] {0.17748, {x0 -> 0.0739345, ...
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143 views

Test for equivalence of algebraic expressions

We are looking for the most efficient (most recent, or best) techniques to check if two algebraic expressions (elementary, Calculus-type functions) are equivalent (or if an expression is equivalent to ...
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1answer
42 views

If an ideal is made up by polynomials with disjoint variable parts, then those polynomials form a Grobner Basis.

I've been learning symbolic computation over the summer (just independent learning) and I'm at the section of my book about Grobner bases. There's an exercise I'd like to see a proof of, but have not ...
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1answer
119 views

Symbolic polynomial interpolation

I'm trying to create polynomials from some symbolic points to discretize derivations. This means I'm having data like $(a, \phi(a)),\ (b, \phi(b) ) $and $(c, \phi(c))$ and want to fit a second order ...
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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 ...
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169 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 ...
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2answers
45 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 ...
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1answer
96 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 ...
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1answer
79 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 ...
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89 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 $\vec{V} = [u, v, w]^T$ ...
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1answer
272 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] ...
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1answer
503 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 ...
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3answers
614 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 ...
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1answer
76 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?
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3answers
93 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 ...
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1answer
63 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} &= ...
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1answer
43 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 ...
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1answer
322 views

What is the $\lVert$ symbol?

I am trying to understand the quadratic equation below but cannot understand what the double bars stand for. $$\lVert W_L LP' \rVert^2 + \sum_i W_{H,i}^2 \lVert p_i' - p_i\rVert$$
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1answer
156 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 ...
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2answers
158 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. ...
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206 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 $$ \left\lceil \log_3 \left(\frac{N}{3^{m/3}K-C}\right) \right\rceil $$ ...
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83 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 ...
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55 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 ...
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1answer
6k 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 ...
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1answer
506 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 ...
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1answer
80 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 ...
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2answers
140 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 ...
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2answers
142 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 ...
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1answer
132 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 ...
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1answer
310 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 ...
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1answer
356 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 ...