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

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8
votes
2answers
957 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 ...
5
votes
2answers
320 views

Why doesn't Roots work on a certain quartic polynomial equation?

In everything that follows I am using Roots to get the solutions to the equations. I start off with this equation: $$ \frac{A}{3}x^4 - x^2 + 2ax - b^2 = 0$$ Now ...
4
votes
3answers
229 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 ...
4
votes
1answer
363 views

Eliminating functions from system of PDE in Mathematica

Mathematica users, Let's see an example of three PDEs: How can I eliminate variables q1[x,y,z] and q2[x,y,z] from a system of ...
3
votes
1answer
436 views

Solution given by Wolfram Alpha but not _Mathematica_

Why will Mathematica not give a soluion to Solve[Log[x] == Log[j, Log[j, x]], j], but Wolfram Alpha will?
3
votes
3answers
824 views

How can I solve Tan[t] - t == F[x] for t as a function of x?

How can I solve the equation Tan[t] - t = Ax, where A is a constant for t[x]? I know that ...
2
votes
3answers
335 views

Points of Intersection

How to numerically find points of intersection between pair of curves (Here,a circle and a parabola) ? Finding it a bit messy as, for a point on one curve, slope of the other is involved. ...
2
votes
1answer
1k views

NDSolve two PDE plus one ODE, together

I have a couple of PDE (time and space/length) that are correctly managed by NDSolve, but to which I’m adding an ODE on which the acc “accumulates”, through time, a ...
2
votes
1answer
1k views

Solve matrix equation A*X=X*B using LeastSquares

I want to solve matrix equation A*X=X*B using LeastSquares method, but it is suited for equation like A*X=B. All matrices are 3x3 ...
1
vote
1answer
85 views

How to speed or help Solve[] when it is stuck?

The code below generates a system of equations that I need to Solve[] for {c[5], c[6], c[7], c[8]} in terms of {c[1], c[2], c[3], c[4]}. ...
1
vote
1answer
171 views

Solving systems of equations

So I have a set of equations like 12 of them but 13 variables. However I would like to find the numerical value of the roots for the maximum value of a particular variable. I don't know how to do that ...
1
vote
1answer
106 views

Applying N to the roots found by Solve gives complex numbers when the roots are real [closed]

I have a function which is f(x) = x^3 - 5 x^2 - x + 1. When I solve for x to find the zeros ...
1
vote
2answers
236 views

Mathematica can't minimize a function

Mathematica seems not to be able to minimize this univariate function over integer arguments, $r>2, r \in \mathbb{Z}$. ...
1
vote
1answer
302 views

General form of a linear transformation

Let $v_1 = \begin{bmatrix} 2 \\ -1 \end{bmatrix}$ and $v_2=\begin{bmatrix} 1 \\ -1 \end{bmatrix}$ and let $A= \begin{bmatrix} 3 & 2 \\ -2 & 1 \end{bmatrix}$ be a matrix for $T\colon \Bbb ...
1
vote
3answers
154 views

automatic processing of numerical results in `Plot`

First I want to solve an equation $F(x,y)=0$ for $y$ by supplying a value of $x$. (suppose obtaining the analytic form of $y(x)$ is too difficult) Then I want to plot root $y$ (numerically calculated) ...
1
vote
1answer
539 views

How to guess initial complex value for FindRoot

I have to solve a transcendental equation for a parameter, say $\beta$. Now, the $\beta$ has a range from $ik$ to $k$ where $i$ is the usual imaginary root $\sqrt{-1}$ and $k$ is a real number. ...
1
vote
2answers
280 views

Is there a better way to get the eight points of intersection?

I want to get the eight points of intersection from the equations 2 Abs[x] + Abs[y] == 1 and Abs[x] + 2 Abs[y] == 1. To solve ...
1
vote
2answers
392 views

solving for one solution to a system of polynomials

I'm trying to solve a system of equations: ...
0
votes
1answer
143 views

How to solve this nonlinear 2 by 2 equations?

I have a equation (x^2 + q1^2 - y^2)/2*(x + q1 - y) + (1 - 2*a)*q + 2*F = 2*(1 - a)*c[q] in q(variable) with parameters q1,a,F and function c(in variable q also, and I define it outside Solve so I can ...
-2
votes
1answer
66 views

Solve For X inside arc-cos function (with division) [closed]

Very basic but I've been stuck for more than 12 hours trying to solver this equation 20=360/(arccos(X/3200)*2) Can anyone solve X? and explain what exactly you ...
22
votes
2answers
1k 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 ...
12
votes
2answers
3k 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 ...
19
votes
1answer
1k 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 ...
10
votes
3answers
522 views

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

I have a simple lattice / line manipulation: ...
19
votes
4answers
886 views

Hightlight all the self-intersections of a Lissajous figure

This graph–also known as a Lissajous figure–contains so many self-intersections.How can I highlight them? ...
14
votes
1answer
269 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 ...
11
votes
3answers
592 views

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 ...
10
votes
1answer
1k 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 ...
8
votes
3answers
195 views

How to solve for the intersection points of two ellipses?

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 \\ ...
8
votes
4answers
706 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. ...
6
votes
3answers
2k 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 ...
8
votes
1answer
198 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
1answer
436 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) ...
6
votes
2answers
822 views

Solution of equation with power series (perturbation)

So I need to use Mathematica to find the solution of $y=x- \epsilon \sin(2y)$ as a power series in terms of $\epsilon$. I'd assume I'd need to create an equation $f=x-y- \epsilon \sin(2y)$, then ...
4
votes
4answers
716 views

An easier way to find the properties of an ellipse from its equation?

In this Q&A about fitting an ellipse to a set of points, there are multiple answers that generated general equations of the ellipse, like this one by @ubpdqn: However, the steps to find out the ...
4
votes
1answer
588 views

How to solve this equation with integers as a solution?

I want to solve the equation $$x^y + y = y^x + x$$ with $x$, $y$ are integer numbers. I tried Solve[x^y + y == y^x + x, {x, y}, Integers] How to solve the ...
4
votes
3answers
493 views

Symbolic derivative of $n$-term product

I want to determine the relationship that must exist between the $x_i$ and $y_i$ such that $$ \frac{\partial}{\partial\theta} \prod_{i=1}^n \frac{f(x_i,\theta)}{f(y_i,\theta)} = 0, $$ where $$ ...
4
votes
3answers
462 views

How to obtain a fixed number of solutions to $x+y=1$?

How to obtain a fixed number of solutions to $x+y=1$? For example, I want 4 solutions: $(1,0),(2,-1),(3,-2),(-2,3)$ I want to do this also on bigger equations such as $x+y+...=1$ and then I want to ...
3
votes
2answers
336 views

Tweaking Solve for systems of polynomial equations

I am trying to solve the following system of $6$ quadratic equations in $6$ variables: ...
12
votes
2answers
677 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 ...
12
votes
1answer
208 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 ...
12
votes
2answers
1k 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 ...
11
votes
1answer
440 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. ...
9
votes
3answers
401 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
1answer
155 views

Using a Mathematica index as a DiscreteVariable in NDSolve when solving a coupled set of ordinary differential equations

Context Since the explanation below of the problem to be solved is lengthy, let me preamble this by saying that I have code that works to solve the problem, but I don't know whether (1) it's ...
7
votes
1answer
1k views

How to find the smallest root

I have a continuous, differentiable, monotonic, bounded function called F[t]. If t -> Infinity then ...
5
votes
1answer
2k views

Solving a system of linear equations modulo n

I have a system of linear equations $$ a+b+c \equiv 31 \pmod{54} $$ $$ 4a+2b+c \equiv 3 \pmod{54} $$ $$ 9a+3b+c \equiv 11 \pmod{54} $$ What should I input (I'm using ...
5
votes
1answer
2k views

finding poles of a function

Is there a command to find the poles of a function $f=f(z)$? example: let $$f(z) = \frac{1}{z^2-1}$$ then we know that the poles are at $z=\pm 1$ but is there a special command in mathematica to do ...
4
votes
1answer
279 views

How can I tell why Mathematica returns no solution to this system of nonlinear equations?

I'm trying to solve a system of 12 equations and 12 unknowns with the code below. ...
4
votes
3answers
894 views

Solving Integrals

Here's a problem that I don't understand. f[x_] := Exp[Cos[3*x]] g[x_] := (1/3)*x^3 - x^2 + 2 When I try to find the limit: ...