# Tagged Questions

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

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### Strange result of Reduce and ForAll

In the question Can Mathematica tell me if a polynomial has all real roots?, quite a few of interesting answers were given. I wanted to add another one, using quantors, and observed some strange ...
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### Why does Mathematica struggle with solving this equation?

Consider the evaluation of the following expression In[20]:= Reduce[ 1000 * 1.0609^t == 1500, t] ...
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### How can we plot the complex roots of an equation?

If we'd like to display the $n$ roots of a polynomial on the complex plane as points, how can we do this? For example, if we have the equation $x^3 + x^2 + x + 1$, how can we plot the 3 roots as ...
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### 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: ...
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### Finding “Maxima” and “Minima” on a B-Spline

I need to find the "Maxima" and "Minima" on a B-Spline or more correct the points where the 2nd components of the derivate equal zero. For example: ...
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### How to get exact roots of this polynomial?

The equation $$64x^7 -112x^5 -8x^4 +56x^3 +8x^2 -7x - 1 = 0$$ has seven solutions $x = 1$, $x = -\dfrac{1}{2}$ and $x = \cos \dfrac{2n\pi}{11}$, where $n$ runs from $1$ to $5$. With ...
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### 1D quasicrystal: points on a line nearest to points on a lattice

I have a simple lattice / line manipulation: ...
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### NDEigensystem returns incorrect eigenvalues for 2D coulomb problem, eigenfunctions contain discontinuity

I posted a similar question a short time ago regarding the 3D Coulomb problem. Jens' excellent answer to this thread allowed me to obtain the correct eigenvalues and eigenenergies for that system. I ...
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### Trying to fit an unknown extreme distribution

First up, I'm quite new to Mathematica so any hints on better code would be greatly appreciated. I have some histogram frequency data from an unknown distribution that I'm trying to fit. Here's the ...
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I have a parametric equation of two ellipses as follow $\begin{cases} x=a_1 \text{sin$\theta $}+b_1 \text{cos$\theta $}+c_1 \\ y=d_1 \text{sin$\theta $}+e_1 \text{cos$\theta }+f_1 \\ \end{cases}... 2answers 633 views ### Is there a way to symbolically invert a piecewise function I have a piecewise function that is continuous and strictly monotonic, like this: f[t_] = Piecewise[{{t/4, t < 0}, {t/2, t < 3}, {3/2 + (t - 3)*3, True}}] ... 1answer 492 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. ... 1answer 353 views ### Does NRoots own an abstract counterpart? If not, can we write one? We know when solving linear algebra equations, despite its abstract syntax, LinearSolve is much faster compared to Solve: ... 2answers 1k 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 $$\begin{cases} \sqrt{\sin^2 x + \dfrac{1}{\sin^2 x}} + \sqrt{\cos^2 y + \dfrac{... 3answers 323 views ### Problems Computing (in a reasonable amount of time) Solutions to a System of Inequalities For my Cryptography research I am interested in finding solutions to the following inequalities in terms of r and s, where p is some fixed constant.$$\begin{align} 2^{p - s + 4} + 2^{p - r} + ... 3answers 463 views ### Reduce can't reduce an equation without appropriate assumptions When there are three unknowns (x, y, z), Mathematica can solve it: ... 3answers 400 views ### Bug: Wrong results from NSolve on coupled polynomials. WorkingPrecision->Automatic fails OP UPDATE: I received an email from WR on 1-18-2016: "...It does appear that the NSolve function is not behaving properly in this case and I have forwarded an incident report to our developers with ... 2answers 692 views ### Mathematica isn't sure whether a sum of two positives is positive or not Mathematica is not able to tell whether a summation of two positive expressions is positive or not. Which is very strange. My three symbolic arguments,x$,$y$, and$z$, are all real numbers bounded ... 2answers 386 views ### How can I only draw outer common tangent to two circles? I have code worked for drawing common tangent lines to two circles(http://en.wikipedia.org/wiki/Tangent_lines_to_circles), now I want to delete the inner common tangent lines, how? ... 1answer 737 views ### Mathematica not honoring the distributive property of multiplication? ... 1answer 289 views ### Efficient way to solve equal sums$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 ... 1answer 237 views ### NDEigensystem cannot solve numerically the 3D Coulomb problem, while DSolve returns the right answer After having derived by hand the eigenvalues and eigenfunctions for the 3D and 2D hydrogen atom, I want to solve the systems numerically using Mathematica. I need to do this because my next step is to ... 1answer 852 views ### Find roots of polynomial in field extension$GF(2^n)$? How can I find roots of polynomial in extension field$GF(2^n)$? 4answers 772 views ### How many times do the two given curves intersect at the origin? I'm reading/studying on my own a book about algebraic curves. I'm trying to find a way for Mathematica help me with the following (the book, ISBN: 038731802X, allows me to use any CAS / program. ... 3answers 209 views ### How to find the solutions to$a+b+c+d=60$? How can I find all the solutions to: $$a+b+c+d=60\quad (0\leq a,b,c,d\leq 30,\; a,b,c,d\in\mathbb N)$$ I've tried to use Solve[], but it says that there are more ... 6answers 834 views ### Can Mathematica tell me if a polynomial has all real roots? I am trying on this polynomial, ... 4answers 833 views ### Finding the roots of Hypergeometric1F1[] I am trying to find the roots, Î», for this equation: Hypergeometric1F1[1/4 (2 - Â Î» /Î²), n + 1, Î²] for certain ... 4answers 282 views ### How to find the next root larger than a specified value, numerically? I would want to have a general-purpose, reasonably robust method of finding the next numerical root above a specific value of x. I'm stumped by the fact ... 3answers 537 views ### Using NSolve in the complex plane I am trying to find numerical values for$\Im\ e^{\frac{1}{2} +i\ y} = \Im\ \zeta(\frac{1}{2} +i\ y)$for a given range. I have tried: ... 5answers 804 views ### Create filling between two trig functions Working with trig functions, period, amplitude, etc. I found a worksheet at a calculus website, with some nice questions related to interpreting trig functions, at least, they provide some "fun" ... 3answers 2k 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 ... 3answers 983 views ### Using FindInstance to Prove No Solutions Exist For a small amount of background, I am currently working on an undergraduate research project in Combinatorial Geometry and I'm working on a case analysis for embedding spherical simplicial 2-... 3answers 300 views ### Labeling solutions of an Eigenvalue equation involving Bessel functions I'm solving the SchrÃ¶dinger equation for a particle in an annular geometry with hard wall boundary conditions and I've reduced it to the following equation: $$J_m(k\,R_1)\,Y_m(k\,R_2) - J_m(k\,R_2)\,... 2answers 278 views ### How can I get the solutions of x^n-x-t=0 in hypergeometric form? x^3-x-t=0 has three roots that can be expressed in hypergeometric form, for example$$x_1=-1-\frac{t}{2}{_2F_1\left(\frac{1}{3},\frac{2}{3};\frac{3}{2};\frac{27t^2}{4} \right)}+\frac{3t^2}{8} {... 2answers 749 views ### Solving/Reducing equations in$\mathbb{Z}/p\mathbb{Z}$I was trying to find all the numbers$n$for which$2^n=n\mod 10^k$using Mathematica. My first try: Reduce[2^n == n, n, Modulus -> 100] However, I receive ... 2answers 1k views ### Implement the Bisection algorithm elegantly and easily Description: Rencently, I have finished my course Numerical Analysis, so I'd like to implement many algorithm that I have learned from that course.By this practice, I hope that I can improve my ... 1answer 207 views ### Using Solve to solve the equation$x^{1/3}=-1\$

I am curious why this command returned no answers: Solve[x^(1/3) == -1, x] Gives this output: (* {} *) I was able to get ...
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### Inverse of a complicated function

Mathematica is struggling to find the inverse of this function f(r): ...