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

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0
votes
1answer
128 views

Numerical rule evaluation -> {True, False} to deviation of target equation

I solve some equations numerically with FindRoot[] returning a quadruple {1,2,3,4}. Because the solver sometimes do not find any roots depending on parameterization of these equations I select only ...
5
votes
2answers
1k views

Error (NSolve::ifun) when using NSolve, I need help interpreting the error

I wrote the following code to observe how the solutions to the equation $(e^{i a})^2 = e^{i b}$ varied as $b$ varied between 0 and $2\pi$ ...
18
votes
6answers
4k views

About multi-root search in Mathematica for transcendental equations

I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range? Perhaps ...
2
votes
3answers
823 views

Finding roots of nontrivial equation

I am trying to solve the following nontrivial equation: ...
2
votes
2answers
118 views

Solving an equation and finding a couple of results given that they are integer

My problem is to find all solutions to an equation with 2 variables between two values that define the range of my search. e.g., $(x+y-y²)/(1-y-x²)=0$ with solutions ${x,y} \in \mathbb{Z}$.
7
votes
1answer
829 views

How to find the smallest root

I have a continuous, differentiable, monotonic, bounded function called F[t]. If t -> Infinity then ...
4
votes
4answers
2k views

Solving complex equations

I feel like I am missing a basic, but key point when using Mathematica's Solve or Reduce. ...
1
vote
3answers
870 views

Conditional expression

How do I evaluate a conditional expression in order to convert the solutions that are in terms of $x$ to a new variable $c$ depending on $x$? The conventional method I have been using with eliminate ...
5
votes
1answer
525 views

Solving recurrence relation using Mathematica defined in a piecewise way

I have a recurrence relation defined as following: RSolve[ { p[0] == p0, p[1] == λ p[0]/μ, p[i + 1] == λ p[i]/(2 μ) }, p[i], i ] Note that the relation ...
17
votes
2answers
4k views

Can Reduce *really* not solve for x here?

Sometimes I get the feeling I'm just flailing blindly with Mathematica. Is solving for $x$ in the equation $$ \frac{\cosh (x/2)}{x} = \sqrt{2} $$ really beyond the scope of Mathematica? I try to ...
6
votes
2answers
1k views

How to invert an integral equation

There have been numerous times when I've needed to invert an integral equation, i.e. I have something like $$f(x) = g_1(x)\int_{0}^x g_2(x') dx'$$ for arbitrary functions $g_1$ and $g_2$, and ...
4
votes
1answer
78 views

Trouble using FindInstance with MatrixRank

I'm really confused about what's going wrong with my call to FindInstance: ...
19
votes
2answers
881 views

Using the Krylov method for Solve: Speeding up a SparseArray calculation

I'm trying to implement this Total Variation Regularized Numerical Differentiation (TVDiff) code in MMA (which I found through this SO answer): essentially I want to differentiate noisy data. The full ...
8
votes
2answers
694 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 ...
4
votes
2answers
855 views

Solving inequalities for positive Integers

Consider the following; ...
10
votes
1answer
631 views

Find roots of polynomial in field extension $GF(2^n)$?

How can I find roots of polynomial in extension field $GF(2^n)$?
9
votes
1answer
398 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. ...
4
votes
4answers
944 views

recursively solve equation and saving the values

I am new to Mathematica. I am trying to recursively solve an equation and saving the values into a Table. Since I need the real solutions only I use ...
10
votes
3answers
329 views

FindInstance with a Diophantine equation seems to go on forever

I tried to find a non-trivial integer solution to the equation $$2012^2=a^2+b^2+c^2+d^2+e^2$$ with Mathematica but the computation takes minutes; I might be doing something wrong. ...
12
votes
1answer
185 views

Solve[ ] with Method -> Reduce gives a different result than Reduce[ ]

Why does Solve[Sqrt[x + Sqrt[x]] - Sqrt[x - Sqrt[x]] == m Sqrt[x/(x + Sqrt[x])], x, Reals, Method -> Reduce] give a different result than ...
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). ...
7
votes
1answer
803 views

Handling failed FindRoot calls

I want to handle FindRoot calls which did not converge (e.g "thrown" error message FindRoot::cvmit) ...
4
votes
3answers
1k views

Backsubstituting solution into FindRoot

I am trying to solve a system of equations which is dependent to an parameter alpha. So I iterate over alpha via a ...
4
votes
2answers
1k views

How to find regions that satisfy this inequality?

I am new to Mathematica and would like to find the set $$\{ (x,y) \in \mathbb{R}^2: (3x+y\exp(xy))(x-a) + (6y + x \exp(xy))(y-b) < 0 \}$$ for some constants $a$ and $b$. How can I do ...
5
votes
2answers
353 views

Equation solving with GroebnerBasis

I have a system of quadratic equations defined below ...
2
votes
1answer
1k views

Solve in terms of specific variables

As part of my physics homework (which I do not need the answer for, as I did it by hand, and got the correct $$\frac{m_1 g-m_2 g \sin(\theta)}{-m_1-m_2}$$ as the answer) I would have liked to have ...
4
votes
2answers
639 views

How to solve for an Z-Score of a T-Distribution?

I'm looking for the Z-Score for a distribution, where the integrated area sums up to 0.90. Unfortunately I always get an error from Mathematica, ...
6
votes
2answers
2k views

How can I get Mathematica to solve an equation with multiple variables?

How can I get mathematica to solve the non-homogeneous differential equation with undetermined coefficients listed below? Solve $\ y''(t)+3y'(t) = 2t^4 $, using: $\ y_p(t) = ...
6
votes
2answers
480 views

Very long Refine/Solve batch run - is my code broken, or just complicated?

So I'm trying to run some Mathematica code in batch mode from my university cluster. Specifically, I'm trying to find the equilibria of a system of ordinary differential equations. Inspired by the ...
2
votes
1answer
1k views

Mathematica Can't Evaluate This?

I am trying to find the inverse function of $\frac{\ln{x}}{x^2}$ in Mathematica. I am using the Solve[] function to find the inverse (yes, I know about ...
2
votes
2answers
2k views

Root finding in Mathematica

I am new to Mathematica. I have used the WolframAlpha online calculator to find roots of equations (listed under the heading Root in the output generated in ...
9
votes
2answers
1k views

RootSearch for complex or multiple equations

First the background. I'm trying to solve for the roots of a rather messy complex equation. This is not the exact equation, but it's a decent (simpler) stand in: ...
3
votes
1answer
255 views

Result of Reduce contains duplicate terms

On my system, the result of this: f[x_] := 2 Sin[x] + Sin[x]^2; Reduce[f'[x] == 0, x] contains the following expression twice: ...
6
votes
3answers
695 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 ...
15
votes
3answers
766 views

Using results of Reduce

Suppose I have function f: f[x_, y_] := 50000 + x 30000 + y 35000; Now I want to find the x and y when f[]<=200000. I use Reduce: ...
13
votes
2answers
874 views

Suppressing negative roots in Mathematica

Problem Using Mathematica's Solve operator can sometimes lead to an output involving a positive and negative root (say when solving for a variable such as ...
7
votes
1answer
644 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
5answers
328 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 ...
9
votes
2answers
9k views

Figuring when the minute and hour hand coincide on a clock

I would like to list all possible times in a 12-hour period, where the hour hand overlaps the minute hand completely. This is really a question about three distinct things - to be done in Mathematica ...
43
votes
8answers
2k views

Updating Wagon's FindAllCrossings2D[] function

Stan Wagon's Mathematica in Action (second edition; I haven't read the third edition and I'm hoping to eventually see it), demonstrates a nifty function called ...