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Questions tagged [equation-solving]

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

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Reduce[Sin[x]==0,x] splitting odd and even multiples of Pi

as from Title, I'm wondering why Mathematica does not automatically give a single, simple solution for the problem Reduce[Sin[x] == 0, x] for which I obtain the ...
Luca Ferroglio's user avatar
11 votes
0 answers
121 views

Eliminate variable with partially documented Solve feature Solve[eqns,vars,elims]. Robust?

The Eliminating Variables section on Manipulating Equations and Inequalities documentation quotes an otherwise undocumented feature for Solve ...
rhermans's user avatar
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8 votes
0 answers
275 views

Spurious DSolve Solution

Bug introduced in 8.0.4 or earlier, persisting through 13.2. DSolve quickly returns solutions to the following PDE (which is the homogeneous portion of the PDE in ...
bbgodfrey's user avatar
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7 votes
0 answers
2k views

Does NSolve find all solutions?

Is the solution set returned by NSolve usually complete? Can I assume that there are no more solutions than what it returns? Consider systems of equations e.g. ...
Szabolcs's user avatar
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7 votes
0 answers
264 views

Strange behaviour of NotElement in Reduce

Bug introduced in 8.0 or earlier and fixed in 11.0.0. Confirmed, as bug, by WRI: [CASE:3527549] I have observed curious behaviour on domains supplied to NotElement...
kirma's user avatar
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7 votes
0 answers
3k views

Solve huge symbolic system of linear equations

I have a system of 76 symbolic linear equations (i.e. some coefficients are symbolic) with a sparse coefficient matrix. However, neither Solve[] nor ...
Stanislav Poslavsky's user avatar
6 votes
0 answers
149 views

Solving a matrix pencil (quadratic eigenvalue) problem with Mathematica

According to Wikipedia The matrix pencil of degree $\ell$ is the matrix-valued function defined on the complex numbers $L(k) = \sum_{i=0}^{\ell} k^{i} A_{i}$. Here $A_{\ell}$ are non-zero $n\times n$...
Rob's user avatar
  • 423
6 votes
0 answers
254 views

Finding periodic cycles of a function

Given a function f[{x,y}] it is rather simple to use, for example, NSolve to find periodic points of period $n$. We simply take ...
math's user avatar
  • 713
6 votes
0 answers
56 views

Limitations in using Reduce for Integer systems

The System For example, when solving the following system using Reduce in Integers: ...
Vepir's user avatar
  • 622
6 votes
0 answers
98 views

When does Root have a third argument

In Mathematica "11.0.1 for Microsoft Windows (64-bit) (September 20, 2016)", Root[#^4 + 1 &, 2]; actually has three arguments, as can be seen from ...
bbgodfrey's user avatar
  • 60k
6 votes
0 answers
388 views

Solving a nasty equation

Here's an equation that I need to solve for $t_k$ $$ \theta_0 = \tan^{-1}\left(\frac{2(w_x - m)}{p - g {t_k}^2 - 2 t_k w_y}\right) - {\frac{1} {r}} \left( \left(\frac{m}{t_k}\right)^2 + \left( \frac{...
soBinary's user avatar
  • 161
5 votes
0 answers
68 views

Making Intersection of 3 Lines Calculation More Efficient

So I managed to optimize the calculation a little for looking for 3 line intersections in equally spaced points around a circle by only checking one "wedge" of the circle, ignoring ...
Auri Crystal's user avatar
5 votes
0 answers
76 views

How to get an asymptotic of the real-valued branch of the inverse function?

Consider function $f:\mathbb R^+\to\mathbb R^+$, defined as $f(x) = x + x^2\left(1 + \log x\right)$. I need to find an asymptotic approximation of its inverse function $f^{\small(-1)}\!:\mathbb R^+\to\...
Vladimir Reshetnikov's user avatar
5 votes
0 answers
223 views

Incorrect result by DSolve

For real $x$ consider the trivial equation $$|y'(x)|=-|x|.$$ Since the left side is always positive and the right always negative, there is no solution. Let's try ...
JHT's user avatar
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5 votes
0 answers
582 views

How does NSolve find the roots to an equation?

I'm using NSolve to find the roots to a transcendental equation. For this, I need to specify a bounded region where roots are searched. What I want to know is how <...
Turbotanten's user avatar
5 votes
0 answers
1k views

Solving a system of differential algebraic equations (DAE)

I am trying to solve a system of 8 differential algebraic equations, where equations 3 and 5 are differential equations and the rest are constraints which need to be satisfied. Also I only know the ...
Branka's user avatar
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5 votes
0 answers
168 views

Find regions in which the roots of a third degree polynomial are real

I have to find the roots of a third degree polynomial in $\phi$ that depends from 3 parameters, namely $t,s,w\in \mathbb R$. In order to do that I've used the command ...
Claretta's user avatar
  • 283
5 votes
0 answers
314 views

How to find an algebraic representation

I want to find matrix representation of some algebra (Clifford algebra Cl(3,1) in this case). Here is an example, which I would like to get and then extend to higher dimensional matrices. Suppose we ...
Acus's user avatar
  • 3,474
5 votes
0 answers
341 views

Method of characteristics, recursion formulas

I'm helping a friend out with a problem. He needs to plot out the solution to a water surge in a pipeline. I have all the parameters set and I've put the equations in Mathematica, but I can't get the ...
dingo_d's user avatar
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5 votes
0 answers
141 views

Reduce doesn't solve this equations with condition

Reduce[{4==Abs[-1+2 Cos[2A]+2 Cos[2B]+2 Cos[2(A+B)]]},{A,B},Reals] worked well, but ...
matrix42's user avatar
  • 6,697
5 votes
0 answers
619 views

Suggestions for solving a large linear system

I have a system of $\approx 200,000$ linear equations in $\approx 40,000$ variables (with rational coefficients) and I would like to determine the dimension of the solution space, which I know to be ...
José Figueroa-O'Farrill's user avatar
5 votes
0 answers
115 views

Using quantifiers with free indices as declarative conditions in equation solving

This is a toy example: Is there a way to rewrite Reduce[{Norm@{c[1], c[2], c[3]} == 1, 0 <= c[1] < c[2] < c[3]}, {c[1], c[2], c[3]}] ...
Dr. belisarius's user avatar
4 votes
1 answer
139 views

Finding real solution(s) to a complex equation

I have a matrix matA defined as ...
Zubin's user avatar
  • 415
4 votes
0 answers
231 views

Constructing a Lyapunov function for this system?

This question seems interesting but I cant figure out how to apply Micahel E2's solution to my system: How to write that Lyapunov function? My system is very simple, I already have a working Lyapunov ...
Math's user avatar
  • 445
4 votes
0 answers
227 views

Finding Coefficients in a Perturbation Problem related to Chaotic Dynamics

I am trying to reproduce the results from this paper: Chaotic dynamics of a suspended string in a gravitational background with magnetic field I am currently stuck with finding the coefficients. First ...
codebpr's user avatar
  • 713
4 votes
0 answers
119 views

Solving or Minimizing the Norm of the matrix equation $M^TAM - M^TB - B^TM =C$

I am trying to solve the matrix equation $M^TAM - M^TB - B^TM=C$ where I know A, B and C. My unknown matrix is M which has the special form that all the rows and columns sum to zero. i.e. I have four ...
1729taxi's user avatar
  • 717
4 votes
0 answers
86 views

Force Solve to respect unit system

I give Solve quantities in FPS and it returns resulting quantities in SI, necessitating that I add an entire section to my workflow where I pick apart the solution ...
Matt Murphy's user avatar
4 votes
0 answers
180 views

Indicate Unit Vectors in Solve

I'm solving a system defined by two rays. The rays originate from two points {x,y,z} and {x,y,z-h}. They go in directions (unit ...
Brent's user avatar
  • 141
4 votes
0 answers
155 views

DSolve, NDSolve with WhenEvent Give Incorrect Solution for Simple ODE

NDSolve Results On the course of addressing question 181974, I encountered the following problem. ...
bbgodfrey's user avatar
  • 60k
4 votes
0 answers
182 views

Discordance in plots

Let us solve the system with Floors ...
user64494's user avatar
4 votes
0 answers
63 views

A simple expression on which `Reduce` fails

The conditions in x ∉ Integers && y ∈ Integers && y == -(1/2) + x/2 are inconsistent but Reduce does not solve ...
Michael E2's user avatar
  • 228k
4 votes
0 answers
258 views

Why does Reduce[x + 1/x == 1/x, x] give the result x == 0, instead of the result False?

Why does Reduce[x + 1/x == 1/x, x] give the result x == 0 instead of the result False? There is no value of x that causes ...
Jason Zimba's user avatar
4 votes
0 answers
114 views

Order of evaluation of FunctionDomain, Reduce, Solve, etc

For the input (mine is much more complicated, this is a toy example): x/x /. x -> 0 the output of 1 (as opposed to ...
Aharon Naiman's user avatar
4 votes
0 answers
529 views

Homotopy Continuation solution of system of polynomials

I have very large systems (>20) of polynomial (max degree 3) equations that I would like to find a solution to. I'm not interested in all solutions as presumably there are too many (a huge number ...
physioConfusio's user avatar
4 votes
0 answers
121 views

Why does Solve work in v9.0.1 but not in v10.3.1

I want to solve the following DE $$ P'=k(M-P)P, P[0]=53.08, P[50]=23.192, P[100]=76.212.$$ The Mathematica command is ...
xpaul's user avatar
  • 251
4 votes
0 answers
390 views

Complex boundary conditions and NDEigensystem

I am having difficulties implementing a Neumann value when numerically solving the Navier equation using NDEigensystem. The Navier equation is given by $\nabla^2 \vec u + (p^2 - 1) \nabla(\nabla\...
Red's user avatar
  • 53
4 votes
0 answers
467 views

Extending Bresenham's algorithm for subpixel rendering

Original Bresenham's line drawing algorithm it limited to drawing lines between two integer pixel positions and does not allow subpixel rendering. However with my reformulation of this algorithm as a ...
Alexey Popkov's user avatar
4 votes
0 answers
371 views

Stability analysis of transcendental equation (stability crossing curves)

I am working with a non-linear delay system with three scalar delays. After taking the Laplace transform of the linearized system, the characteristic function is a transcendental equation with three ...
Bruno Pace's user avatar
4 votes
0 answers
329 views

Solving Thue equations

A Thue equation is a 2-variable homogeneous integer polynomial of degree at least 3. It's well-known that such equations have only finitely many solutions over the integers. I'm trying to solve some ...
Charles's user avatar
  • 1,329
4 votes
0 answers
419 views

Am I entering this 2-variable recurrence correctly?

I'm trying to solve this recurrence with two variables. RSolve[g[d, n] == 1 + g[d - 1, n] + g[d - 1, n - 1] && g[d, 0] == g[0, n] == 0, g[d, n], {d, n}] ...
tba's user avatar
  • 555
4 votes
0 answers
176 views

Symbolic solution to ODE, pure InverseFunction not evaluated

I'm new to Mathematica and I don't understand why in the solution of the following ODE, the #1 in the pure function is not immediately replaced by the corresponding ...
malumno's user avatar
  • 339
3 votes
0 answers
63 views

Can I use FindInstance to prove an algebraic identity?

This question arose from a [now removed] MathOverflow discussion, where a Null result from a FindInstance query was used to prove that $f(x_1,x_2,\ldots x_n)\neq 0$ has no solution in $\mathbb{R}$. My ...
Carlo Beenakker's user avatar
3 votes
0 answers
81 views

Simplifying formula for a real-valued root of the quartic

I have a minimization problem which reduces a 4th degree polynomial with a real valued root. It's easy to get explicit formula for this root, but formula involves imaginary parts which always cancel ...
Yaroslav Bulatov's user avatar
3 votes
0 answers
38 views

Numerically solve a non-differential equation with InterpolatingFunction as output

I have some a function that I need to solve numerically over an entire domain (Ideally I would like an InterpolatingFunction object as output), which does not include any derivatives. I have found a ...
jamman2000's user avatar
3 votes
0 answers
80 views

How to improve this code?

The aim of my work is to find a value for the complex constant $\omega$. In order to do that I solve the below system of differential equations with a manual shooting method: I first solve the system ...
mattiav27's user avatar
  • 6,434
3 votes
0 answers
65 views

Different output to Solve command in Mathematica changing a variable for a subscripted variable

I have a system of equations that is solved with the Solve command in Mathematica 10.2, when one of the variables is changed for a subscripted variable the answer is not the same, the difference is ...
Miguel Angel Alvarez Ballester's user avatar
3 votes
0 answers
257 views

Errors Using FindFit and FindRoot

I'm trying to fit the following equation to data: where and x and y are the dimensionless variables x=V/Vr and y=Ir/(2*I0). n=1 and I'm trying to find Vr and R. The blue is an example of the curve ...
mlt's user avatar
  • 31
3 votes
0 answers
152 views

Unexpected Behavior of Parametric Sensitivity in ParametricNDSolveValue

Bug introduced in 10.4 or earlier and continuing through 11.3 Submitted as CASE:3916971 While exploring alternative methods of solving 33538, I encountered difficulties with the parametric ...
bbgodfrey's user avatar
  • 60k
3 votes
0 answers
136 views

Solving Monster Equations with Mathematica

I would like to solve the following equations in Mathematica. Here are the formulas: $u=0.5$ $\alpha=0.5$ $\epsilon_0=0.1$ $\epsilon_1=0.1$ $f_0(y)=\mbox{Gaussian density with mean -1 and ...
Seyhmus Güngören's user avatar
3 votes
0 answers
182 views

Replace all (/.) parameters with equation or condition rather than single values

Suppose that one wants to calculate the surface charge density of a polarized dielectric ellipsoid, prolate ellipsoid with long and short axes as $a$ and $c$ where $a$ is parallel to the $z$ axis. $a$ ...
O_o's user avatar
  • 259

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