Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
31
votes
7answers
896 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 ...
30
votes
2answers
732 views
What is the difference between Reduce and Solve?
Solve and Reduce both can be used for solving equations.
Just by operating them, I know there is little difference between them.
But, the only thing I know is that there is little difference, and I ...
18
votes
2answers
2k views
Marking points of intersection between two curves
I'm trying to illustrate the solutions numerically and graphically for an equation such as Tan[x] == x. I think I did everything ok except I wanted to mark each ...
16
votes
2answers
2k 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 ...
16
votes
1answer
315 views
The Orbit and Perigee of the Flamsteed comet
Historical context
This year we have the 330-th anniversary of the Battle of Vienna - one of the great formative events of European history, it took place on September 12, 1683.
Kara Mustafa, Grand ...
16
votes
1answer
307 views
Why does repeating an equation help in FindRoot?
I'm trying to understand this behavior of FindRoot. Consider a sample function (the one I'm actually interested in is far more complicated, but has similar issues) ...
15
votes
3answers
382 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:
...
14
votes
2answers
478 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 ...
14
votes
1answer
241 views
Strange behaviour of Reduce for Mod[x,1]
For every integer $x$ the equation Mod[x, 1] == 0 holds. While
Simplify[Mod[x, 1] == 0, Element[x,Integers]]
gives ...
14
votes
1answer
418 views
Bug in Solve (Mathematica 9)
Just came across the strangest bug under both Mathematica 9.0.0 and 9.0.1. If one enters:
Solve[m == p Sin[x] && -Pi/2 < x < Pi/2, x]
... then ...
12
votes
2answers
453 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 ...
12
votes
2answers
432 views
How do I split up a curve into segments of equal length?
I have a curve that is defined as f[x] and what I'm attempting to do is to divide the curve into equal straight lengths for a number of segments of my choosing that I've defined as nSeg.
I've created ...
11
votes
4answers
356 views
How to make a Line[] with no end?
I'm trying to do this:
In this graph, the secant points are aproximated in order to become the tangent, it seems I need some kind of function which plots a line based on two points and it's points ...
11
votes
2answers
367 views
NSolve gives additional solutions that don't satisfy the equations!
I am trying to solve the following polynomial equations in Mathematica:
...
11
votes
2answers
444 views
Google Code Jam: Mountain View code review
After participating in Google Code Jam 2012 Round 2, it occurred to me that the Mountain View problem boiled down to solving a set of linear inequalities, which could be done in Mathematica. I've only ...
11
votes
1answer
137 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
...
11
votes
2answers
411 views
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 ...
10
votes
6answers
2k 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 ...
10
votes
3answers
221 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.
...
10
votes
3answers
218 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.
$$\begin{align}
2^{p - s + 4} + 2^{p - r} + ...
10
votes
1answer
113 views
FindInstance returns Indeterminate in version 9, but not in 8
Here is a trivial system of equations in three unknowns for which FindInstance obtains a solution:
...
10
votes
1answer
344 views
Find roots of polynomial in field extension $GF(2^n)$?
How can I find roots of polynomial in extension field $GF(2^n)$?
9
votes
2answers
3k views
Figuring when the minute and hour hand coincide on a clock
I would like to list all possible times in a 12-hour period, where the hour hand overlaps the minute hand completely. This is really a question about three distinct things - to be done in Mathematica ...
8
votes
2answers
230 views
Is there a way to use functions like Prime[n] within Solve[]?
I'm trying to see if a number can be written as the sum of two prime numbers. Ideally, I would like to use
Solve[Prime[n] + Prime[m] == 100, {n, m}]
But that ...
8
votes
2answers
432 views
How to solve a system of equations of the Vietnamese Mathematical Olympiad?
This is a system of equations of the Vietnamese Mathematical Olympiad 2013, the first day. Solve the system of equations
$$\begin{cases}
\sqrt{\sin^2 x + \dfrac{1}{\sin^2 x}} + \sqrt{\cos^2 y + ...
8
votes
5answers
329 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" ...
8
votes
3answers
399 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 ...
8
votes
3answers
2k views
Assign the results from a Solve to variable(s)
I understand Mathematica can't assign the results of a Solve to the unknowns because there may be more than 1 solution. How can I assign the 4 values of following result to variables?
8
votes
2answers
247 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
1answer
380 views
How do I find all the solutions of three simultaneous equations within a given box?
Sometimes, one needs to find all the solutions of three simultaneous nonlinear equations in three unknowns
$$\begin{align*}f(x,y,z)&=0\\g(x,y,z)&=0\\h(x,y,z)&=0\end{align*}$$
within a ...
8
votes
2answers
293 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
155 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
2answers
520 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:
...
8
votes
1answer
177 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 ...
8
votes
1answer
903 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
0answers
326 views
Proving inequalities with Mathematica
Question summary: I would like to learn some tips and tricks on how to prove inequalities with Mathematica.
I'm studying various inequalities in triangle that have the form $R+ar + bs\geq 0$, where ...
7
votes
3answers
899 views
Finding unit tangent, normal, and binormal vectors for a given r(t)
For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$.
I've got Mathematica, but I've never used it before and I'm not sure how to coerce ...
7
votes
3answers
534 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
4answers
262 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
4answers
436 views
Finding the roots of Hypergeometric1F1[]
I am trying to find the roots, λ, for this equation:
Hypergeometric1F1[1/4 (2 - λ /β), n + 1, β]
for certain ...
7
votes
5answers
193 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
2answers
324 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 ...
7
votes
3answers
446 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] ...
7
votes
3answers
255 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] :
...
7
votes
2answers
870 views
FindRoot Domain restriction
I am solving a system of four non-linear equations in four variables using FindRoot. I have some sense of the relationship between the variables so I don't want Mathematica to do its computations in ...
7
votes
2answers
229 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
2answers
674 views
Inverse of a complicated function
Mathematica is struggling to find the inverse of this function f(r):
...
7
votes
1answer
438 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
478 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 ...
7
votes
3answers
297 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 ...
