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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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
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1answer
31 views

Simplifying with wxMaxima

I have this expression in wxMaxima: ...
2
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0answers
33 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
33 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
43 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
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0answers
41 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
63 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
74 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: $$ ...
0
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0answers
50 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 ...
1
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0answers
33 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.
1
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1answer
52 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 ...
1
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2answers
35 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
22 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 $p_1,p_2,p_3$?
0
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1answer
39 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 ...
0
votes
0answers
9 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
57 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 ...
3
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2answers
93 views

$1+n!=m^{2}$ for some n,m$\in\mathbb{N}$

I have no idea whether this is known or not and I couldn't find anything related on Google. While I was studying , I come up with this idea $1+n!=m^{2} $ for some $n,m\in\mathbb{N}$ $1+4!=5^{2}$ ...
1
vote
1answer
48 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
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0answers
69 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 ...
1
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0answers
83 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
37 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
124 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
62 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
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0answers
70 views

Closed-form expression of a definite integral

Does this definite integral admit a closed-form in terms of elementary functions? $$\int_0^{\infty } \frac{x}{\left(x^4+1\right) \left(2 x^2-2 \arctan\left(x^2\right)+\pi \right)} \, dx.$$
0
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1answer
70 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 ...
0
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0answers
19 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, ...
0
votes
2answers
95 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 $\frac{\pi^4}{90}$ ...
1
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1answer
52 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 ...
1
vote
1answer
23 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 $[1]$ ...
4
votes
0answers
98 views

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 ...
0
votes
1answer
40 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 ...
0
votes
1answer
27 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) ...
0
votes
2answers
49 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( ...
0
votes
0answers
96 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( ...
1
vote
1answer
71 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 ...
1
vote
1answer
37 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, ...
4
votes
0answers
170 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 ...
2
votes
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 ...
1
vote
1answer
183 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 ...
7
votes
3answers
145 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
231 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
46 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
124 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
95 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
101 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
328 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
725 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
866 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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votes
1answer
79 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
104 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 ...