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

learn more… | top users | synonyms (5)

10
votes
3answers
755 views

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: ...
14
votes
2answers
451 views

Determining the default Method used in optimization and root-finding algorithms

Is it possible to extract the Method which is used in functions like NMinimize, FindRoot, ...
14
votes
3answers
1k views

NSolve gives additional solutions that don't satisfy the equations!

I am trying to solve the following polynomial equations in Mathematica: ...
12
votes
2answers
12k 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
3answers
1k 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
625 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
4answers
625 views

Solving $L=\frac{3}{2} \sqrt{4 \pi ^2 A^2+W^2}-\frac{\sqrt{5 W \sqrt{4 \pi ^2 A^2+W^2}+6 \pi ^2 A^2+3 W^2}}{\sqrt{2}}+\frac{3 W}{2}$ for $W$

When I solve the aforementioned equation for $W$ or $A$ on Mathematica I get a long and ugly equation in return, namely one of the solutions for $W$ is: (attempt to read at your own health) ...
3
votes
2answers
735 views

All possible solutions to the Matrix Equation (free variables appearing)

I am attempting to solve a system of linear equations using LinearSolve[] . In my case, the number of unknowns are more than constraints. I learnt that LinearSolve ...
9
votes
5answers
6k 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: ...
5
votes
2answers
285 views

Counting Real roots

I'm interested on how to count the number of real roots of a random polynomials in an instant, how to put the result in a table and how to plot it in a graph.I generated 1 million random polynomials ...
4
votes
1answer
271 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
0
votes
1answer
179 views

How can I obtain the complex root of an equation with FindRoot

I want to obtain the complex roots of some equations that are similar,but each of them has a different condition. this difference is the value of α in these ...
7
votes
3answers
533 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 ...
5
votes
4answers
2k views

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 ...
4
votes
3answers
383 views

Finding parameters making real part of eigenvalues vanish

I have the following $\;3\times3$ matrix: $\left( \begin{array}{ccc} 0.04 -0.4 b & 0 & 0.04 -0.4 b \\ 0 & -0.08-1.2 b & -0.06-0.9 b \\ 1.04 -0.4 b & 2.08 -0.8 b & 0 ...
4
votes
1answer
2k views

Finding the Minimum value of an interpolating function

I can't seem to use FindMinValue to find the min. value of a curve represented by an interpolating function. For instance the below code generates an interpolating ...
4
votes
4answers
3k views

Solving complex equations

I feel like I am missing a basic, but key point when using Mathematica's Solve or Reduce. ...
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 ...
3
votes
1answer
627 views

Solving a differential equation with initial conditions

I want to get a solution to an ordinary differential equation with imposed initial conditions. I'm confused about why my following code doesn't work: ...
1
vote
1answer
146 views

Eliminate z from two equations in x, y, z and plot y as a function of x [closed]

I have this equation to begin with: $$1 - 3 x y = 5 z - 2 x $$ I want to solve this equation for $z(x,y)$, then plug $z(x,y)$ I plug $z$ inside a second equation: $$ y = 7 x z - \frac{z}{x} $$ ...
0
votes
2answers
114 views

Gaps in plots of equation solution from parameter

I'm trying to plot solution of system of equations as a function of parameter ...
14
votes
3answers
717 views

How can I simulate this toggle mechanism?

I've been introduced to Mathematica very recently. Basically, I haven't actually "solved" anything in my Mathematica lifetime, but I've done some simulations. With my fractional knowledge, I tried ...
6
votes
2answers
2k 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
2answers
198 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: ...
4
votes
1answer
2k views

Solve system of equations related to perspective projection

I'm trying to solve system of equations. I have 4 points before perspective projection and after and I whant to obtain matrix of perspective projection $m_{i,j}$ ($x,y,u,v$ are known , $m_{i,j}$ ...
2
votes
1answer
3k views

Forcing FindRoot to return only real solutions

FindRoot documentation reports that if the equation and the initial point are reals, the solutions are searched in the real domain. However, in the following case I ...
11
votes
1answer
303 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: ...
8
votes
1answer
922 views

Handling failed FindRoot calls

I want to handle FindRoot calls which did not converge (e.g "thrown" error message FindRoot::cvmit) ...
3
votes
2answers
1k views

How can I solve an equation with symbolic coefficients?

I want to try to solve the following a x^(17/6) - b x^2 - 1 == 0 where a and b are ...
1
vote
3answers
453 views

How to find intersection points of lines?

Considering I have three functions f1 = -x + 1; f2 = x - 1; f3 = x + 3; How can I find the intersection points of this functions? Thanks. This didn't work ...
15
votes
1answer
415 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 ...
13
votes
1answer
312 views

ToNumberField won't recognize Root as an explicit algebraic number

Bug fixed in 10.0.0 In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an ...
13
votes
2answers
426 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 ...
12
votes
1answer
289 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: ...
9
votes
0answers
102 views

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 ...
9
votes
4answers
734 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 ...
8
votes
2answers
4k views

Inverse of a complicated function

Mathematica is struggling to find the inverse of this function f(r): ...
5
votes
2answers
525 views

Find all roots in range

Is there any way to check for all roots in a range? Jens' findAllRoots function is pretty good, but runs at approx. 10% of roots missed when I ran a quick check on ...
4
votes
1answer
617 views

How do I use RSolve to solve a system of recurrence relations?

I am trying to solve a system of recurrence relations as follows. ...
3
votes
1answer
1k views

NDSolve does not respond

For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
3
votes
1answer
674 views

Solving Simultaneous Equations

I am trying to solve two equations that take the form: $W_0 \sqrt{1+\left(\dfrac{z}{\lambda\,\pi\, W_{0}^2}\right)}=W_1\;\,\quad \ldots(1)$ $W_0\sqrt{1+\left( \dfrac{z+0.1}{\lambda\, \pi\, ...
3
votes
2answers
3k views

How to convert a system of parametric equations to a normal equation?

For example, I have a system of parametric equations (R is a constant number) : ...
2
votes
1answer
470 views

FindRoot giving false roots with Bessel Functions

I have read in some places about the errors associated with FindRoot, but the closest thing I can find on this website seems to be due to the imaginary unit. I am dealing with what should be a ...
1
vote
1answer
416 views

How do I get all possible solutions in an underdetermined system? [duplicate]

I have two problems which I'd like to solve with Mathematica. If I have a system of two equations with three unknowns, how can I get to list all possible solutions for the unknowns? Here is what I ...
1
vote
1answer
590 views

Using previous two solutions as a start point in FindRoot

I need to solve a sequence of equations and I want the starting point of each new FindRoot to be the solution of the earlier FindRoot, increased or decreased by a a bit in the following way: Some ...
0
votes
1answer
360 views

How to use `FindRoot` to solve an equation containing a parameter?

I'm trying to derive some of the results of the following paper: Electrodynamics of semiconductor-coated noble metal nanoshells, JT Manassah - Physical Review A In the paper there is matrix $\mathbf ...
8
votes
2answers
946 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 ...
6
votes
2answers
186 views

What are the Method options Solve command accepts?

What are the Method options Solve command accepts? Solve has the Method option, however documentation contains no methods that it accepts...
4
votes
3answers
222 views

Why the inequality does not take into account the domain?

I have this inequality: Reduce[(4000-1000k)/(k-4) < 0] and the answer is k ∈ Reals I would expect ...