Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).

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9
votes
1answer
265 views

Efficient way to solve equal sums $x_1^k+x_2^k+\dots+x_5^k=y_1^k+y_2^k+\dots+y_5^k$ with Mathematica?

I need to solve the system of equations, call it $S_1$, in the integers $$x_1x_2x_3x_4x_5 = y_1y_2y_3y_4y_5$$ $$x_1^k+x_2^k+\dots+x_5^k=y_1^k+y_2^k+\dots+y_5^k,\;\; k= 2,4,6$$ I used a very ...
9
votes
1answer
375 views

Mathematica implementation of Earth Movers Distance?

Has anyone implemented in Mathematica the Earth Mover's Distance (EMD)? A concept dating back to Monge 1871, used to compare histograms and images, e.g., the CIEDE2000 Color Difference algorithm. ...
8
votes
2answers
2k views

How do I work with Root objects?

I want to solve the trigonometric equation : $$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$ I tried Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x] It returns the ...
8
votes
2answers
656 views

How to solve a system of equations of the Vietnamese Mathematical Olympiad?

This is a system of equations of the Vietnamese Mathematical Olympiad 2013, the first day. Solve the system of equations $$\begin{cases} \sqrt{\sin^2 x + \dfrac{1}{\sin^2 x}} + \sqrt{\cos^2 y + ...
8
votes
3answers
991 views

Checking if the roots of a function are real

I'm trying to determine if the roots of a function are real. How would you do that? (In particular I'm interested in verifying that the roots of LegendreP[6, x] ...
8
votes
3answers
492 views

How do I make Reduce yield all solutions explicitly?

Say I want to do the following: Reduce[ x+y+z==1, {x,y,z}, Modulus -> 7 ] then I get a solution with parameters, C[1] : ...
8
votes
2answers
155 views

How to correct this, `f[a_] := FindRoot[eq == 0, {x, 0.5}]`, where `eq` contains a parameter $a$, without using `eq[a]`?

I want to solve an equation with a parameter $a$, and define the result as a function of $a$. It is something like this: ...
8
votes
2answers
763 views

Find the parameter values satisfying conditions for all roots of an equation

Hi I'm very new at Mathematica. My real problems concerns a much more difficult equation with many parameters, but I want to check that the method is good, so I made up a test equation. My test ...
8
votes
2answers
640 views

Number of iterations in NSolve

In Excel's solver, one can define how many iterations are to be done, to one's liking. I am wondering if this is possible to do with NSolve in Mathematica? Code ...
8
votes
2answers
748 views

How to find the maximum value of an integer that satisfies some inequality

Consider the following Mathematica expression: Reduce[2^j/(j + 1) <= 10, j, Integers] which outputs: ...
8
votes
2answers
267 views

Trouble getting FindInstance to return multiple results for certain constraints

I'm having a hard time getting FindInstance to return multiple results. Consider this simple example: ...
8
votes
3answers
627 views

Can Mathematica solve this sort of functional/differential equation?

I am looking for differentiable functions $f$ from the unit interval to itself that satisfy the following equation $\forall\:p \in \left( 0,1 \right)$: $$1-p-f(f(p))-f(p)f'(f(p))=0$$ Is there a way ...
8
votes
1answer
362 views

Complex valued 2+1D nonlinear PDE using NDSolve

I am trying to follow the main ideas presented in this question, applying it to my own problem, which is a complex, time-dependent, nonlinear PDE: $$i \frac{\partial \psi}{\partial t} = \left[ ...
8
votes
1answer
2k views

Solve Lagrange multipliers optimization problem

I have two nested solid figure, where $V(a,h,\tau)$ defines the volume and $A(a,h,t)$ defines the surface. The outer solid figure is parametrized in $a_s$,$h_s$ and $t_s$ (they share a common center). ...
8
votes
1answer
194 views

Unexpected behaviour of Solve applied to two equations in two variables

I have a simple Mathematica expression Solve[{a(a-1)Sqrt[1+a^2+b^2] == b(a^3-1), b(b-1)Sqrt[1+a^2+b^2] == a(b^3-1)}] which returns (on version 8.0, and also ...
7
votes
3answers
1k views

Finding the number of solutions to a diophantine equation

I want to count total number of the natural solutions (different from 0) of the equation $2x + 3y + z = 100$, but don't know how. How can I calculate it using Mathematica? I tried: ...
7
votes
3answers
1k views

First positive root

Simple question but problem with NSolve. I need help how to extract first positive root? For example: ...
7
votes
2answers
480 views

How do I solve this equation?

I want to solve the equation $$ f(f(-1)) = \sqrt{2} + g(f(2)), $$ where $$f(x) = \dfrac{a}{x^2} - 3x + 2, \quad g(x) = a\cdot \sin 2x$$ $a$ is unknown. The solution is $a \approx{-5.81}$. I tried ...
7
votes
4answers
387 views

Defining a Unique Domain for Solving Diophantine Equations

I am working on a research problem in discrete geometry to do with sphere packings, and believe it or not, I have been able to reduce it to finding the solutions to the Diophantine equation, $$n = ...
7
votes
5answers
300 views

Why is FindInstance finding non-instances?

Consider this example: FindInstance[Exists[{x, y}, x > 1 && y > 1 && x > Sqrt[x + y]], {x, y}] which finds values of $x$ and $y$ such ...
7
votes
3answers
368 views

1D quasicrystal: points on a line nearest to points on a lattice

I have a simple lattice / line manipulation: ...
7
votes
3answers
2k views

How to solve an overdetermined system in Mathematica

I would like to understand the reasons and find a way to avoid such behaviour of the Solve function in Mathematica 8. ...
7
votes
2answers
351 views

Finding all points of period n in an iterated map

I'm trying to implement an algorithm of Jenkinson and Pollicott to calculate the Hausdorff dimension of a Julia set for the map $f_c : z\mapsto z^2 + c$. It's described on page 40 of their paper, ...
7
votes
1answer
741 views

Handling failed FindRoot calls

I want to handle FindRoot calls which did not converge (e.g "thrown" error message FindRoot::cvmit) ...
7
votes
2answers
401 views

Is there any fast way to solve a quadratic matrix equation in Mathematica approximately?

Let the square nonsingular matrix $M$ is a given convergent matrix. What are the best scalar values for $\alpha$ and $\beta$ (in the real numbers domain), at which the following quadratic matrix ...
7
votes
2answers
2k views

Inverse of a complicated function

Mathematica is struggling to find the inverse of this function f(r): ...
7
votes
1answer
741 views

How to find the smallest root

I have a continuous, differentiable, monotonic, bounded function called F[t]. If t -> Infinity then ...
7
votes
2answers
192 views

Why does Solve and Sum give different answers when according to Table it is the same sequence?

I have been thinking about a piece of code today, but I don't understand why I get different outputs from two in my mind similar Mathematical sums. First I observe that the Table command for this: ...
7
votes
1answer
167 views

How can I only draw outer common tangent to two circles?

I have code worked for drawing common tangent lines to two circles(http://en.wikipedia.org/wiki/Tangent_lines_to_circles), now I want to delete the inner common tangent lines, how? ...
7
votes
3answers
465 views

NDSolve and {C, K, Slot} and other built-ins as a variable name

The following problem is an exploration of what causes the error "Input is not an ordinary differential equation" in Mathematica as it seems to have changed from version 8 to version 9. Specifically ...
7
votes
2answers
142 views

Behavior of Reduce with variables as domain

When using Reduce, I accidentally put a set of variables as the domain. To my surprise, it not only seems that Reduce expects ...
7
votes
1answer
189 views

How to plot inequalities taking into account that points must be integers and not reals?

I have solved with Mathematica 9 the following integer inequalities using Reduce: ...
7
votes
1answer
579 views

Getting an InterpolatingFunction from a ContourPlot

I have a function, say minimizeme[Ω_][β_][ϵ_] = ϵ^2 Ω - Log[2 (Cosh[2 β] + Cosh[2 β ϵ])]/(2 β); I want to find its critical points in $\epsilon$ for a given ...
7
votes
2answers
154 views

Is there a relatively quick way to solve my integer-valued equation?

This is a very simple problem. It can be solved by nested Forloops that exhaustively test every possible case, throwing out all non-solutions. Find all the ...
7
votes
1answer
397 views

Issue with the NDSolve code

With this procedure, one may determine an eigen-value function $R(a)$ for any given $\Xi$ (say 0, 25, 50, 75, 100) ...
7
votes
1answer
564 views

Using Mathematica to help to determine the consistency of and numerically solve systems of non-linear equations

The formal problem The question I am about to ask is applicable to many scientific and engineering problems. In short, I am bout to ask for pointers and practical advice for Mathematica beginners who ...
7
votes
1answer
129 views

How to find the positive region of this function?

I'm new-ish to Mathematica and I'm using it to learn the basics of derivative trading (for fun not for trading!). I've defined a simple function to calculate the pay off of a trading on a call. I have ...
7
votes
0answers
400 views

Creating and using an explicit piecewise function in a convenient way

I have a set of data points that define a function in the form curvePts = {data1,data2,...} where ...
7
votes
0answers
178 views

What Method options does FindInstance accept?

While answering Trouble getting FindInstance to return multiple results for certain constraints it became clear that for this problem FindInstance would be better ...
6
votes
4answers
391 views

Am I missing anything? Solving Equations

I want to know what $ a^4+b^4+c^4 $ would be when $ a+b+c=1, a^2+b^2+c^2=2, a^3+b^3+c^3=3. $ I tried ...
6
votes
3answers
391 views

Efficient code for solve this equation

We have $a*b*c=-1$, $\frac{a^2}{c}+\frac{b}{c^2}=1$, $a^2 b+a c^2+b^2 c=t$ What's the value of $a^5 c+a b^5+b c^5$? I tried ...
6
votes
3answers
375 views

Why don't I get numeric values from this Solve?

Solve[ a^2 + b^2 == c^2 && a < 100 && b < 100 && c < 100, {a, b, c}, Integers] gives me this result ...
6
votes
2answers
575 views

Solve an equation in $\mathbb{R}^+$

How can I solve this equation (both numerically and literally) only in the positive reals $\mathbb{R}^+$? Solve[x == (v0 - (A CD t v0^2 ρ)/(4m)) Cos[θ] t, t] And ...
6
votes
5answers
4k views

How to get rid of warnings when using Solve on an equation with inexact coefficients?

When I solve this equation in Mathematica 8, I can get the right answer, but with some uncomfortable warnings. Equation: ...
6
votes
2answers
401 views

How to work out the parameter in a definite integration which has an exact value while the integration doesn't have an analytical solution?

Here is the equation I'm trying to solve: NIntegrate[1/(E^(1/(λ T)) - 1), {λ, 200, 220}] == 1000 T is the parameter I'm ...
6
votes
3answers
975 views

Why won't Mathematica Solve a set of two equations for one variable?

For example, if I try to Solve this set of equations Solve[y == 3 x + 5 && y == -x + 7, {x, y}] Mathematica gives the right values for ...
6
votes
3answers
399 views

Plotting $\omega(k_x, k_z)$ in $(\omega, k)$ plane with assumption of $k^2 = k_x^2 + k_z^2$

I'm currently studying atmospheric-gravity waves and their dispersion relations. For analysis I need to plot the dispersion function: \begin{equation} \omega^4 - \omega^2\cdot C_s^2(k_x^2 + ...
6
votes
1answer
525 views

What are the algorithm details of FindRoot?

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system". But I ...
6
votes
3answers
628 views

Arithmetic operation on the value returned by Solve

I want to modify the value that is returned by Solve. Example: SolC1 = Solve[Sin[ π x / L] == 1, x] {{x -> L/2}} I need to add n to x so that x becomes ...
6
votes
2answers
1k views

NDSolve with vectors

I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ...