Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
878
questions with no upvoted or accepted answers
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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 ...
- 211
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
...
- 35.2k
8
votes
0
answers
275
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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 ...
- 59.7k
7
votes
0
answers
2k
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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. ...
- 231k
7
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0
answers
264
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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...
- 18.3k
7
votes
0
answers
3k
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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 ...
6
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0
answers
247
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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 ...
- 713
6
votes
0
answers
55
views
Limitations in using Reduce for Integer systems
The System
For example, when solving the following system using Reduce in Integers:
...
- 622
6
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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
...
- 59.7k
6
votes
0
answers
385
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Solving a nasty equation
Here's an equation that I need to solve for $t_k$
$$
\theta_0 = \tan^{-1}\left(\frac{2(w_x - m)}{p - g {t_k}^2 - 2 t_k w_y}\right) - {\frac{1}
{r}}
\left( \left(\frac{m}{t_k}\right)^2 +
\left( \frac{...
- 161
5
votes
0
answers
331
views
5
votes
0
answers
64
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Making Intersection of 3 Lines Calculation More Efficient
So I managed to optimize the calculation a little for looking for 3 line intersections in equally spaced points around a circle by only checking one "wedge" of the circle, ignoring ...
- 63
5
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0
answers
75
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How to get an asymptotic of the real-valued branch of the inverse function?
Consider function $f:\mathbb R^+\to\mathbb R^+$, defined as $f(x) = x + x^2\left(1 + \log x\right)$. I need to find an asymptotic approximation of its inverse function $f^{\small(-1)}\!:\mathbb R^+\to\...
- 7,058
5
votes
0
answers
221
views
Incorrect result by DSolve
For real $x$ consider the trivial equation
$$|y'(x)|=-|x|.$$
Since the left side is always positive and the right always negative, there is no solution.
Let's try
...
- 1,005
5
votes
0
answers
559
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 <...
- 691
5
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0
answers
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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 ...
- 51
5
votes
0
answers
168
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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 ...
- 283
5
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0
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313
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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 ...
- 3,104
5
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0
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339
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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 ...
- 637
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
...
- 6,625
5
votes
0
answers
609
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 ...
5
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0
answers
115
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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]}]
...
- 115k
4
votes
0
answers
201
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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 ...
- 435
4
votes
0
answers
225
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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 ...
- 689
4
votes
0
answers
117
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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 ...
- 717
4
votes
0
answers
81
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 ...
- 191
4
votes
0
answers
166
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 ...
- 141
4
votes
0
answers
155
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DSolve, NDSolve with WhenEvent Give Incorrect Solution for Simple ODE
NDSolve Results
On the course of addressing question 181974, I encountered the following problem.
...
- 59.7k
4
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0
answers
182
views
4
votes
0
answers
62
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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 ...
- 226k
4
votes
0
answers
255
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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 ...
- 151
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 ...
- 1,131
4
votes
0
answers
518
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 ...
- 107
4
votes
0
answers
121
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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
...
- 251
4
votes
0
answers
388
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\...
- 53
4
votes
0
answers
460
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 ...
- 60.8k
4
votes
0
answers
370
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 ...
- 41
4
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0
answers
327
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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 ...
- 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}]
...
- 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 ...
- 339
3
votes
0
answers
58
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 ...
- 913
3
votes
0
answers
76
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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 ...
- 6,807
3
votes
0
answers
36
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 ...
- 31
3
votes
0
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78
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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 ...
- 6,266
3
votes
0
answers
63
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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 ...
3
votes
0
answers
248
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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 ...
- 31
3
votes
0
answers
151
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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 ...
- 59.7k
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 ...
- 2,405
3
votes
0
answers
181
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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. $a$ ...
- 259
3
votes
0
answers
556
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Solve PDE over time-dependent region
I have some experience with C++ programming, but I am quite new to Mathematica and I think the latter requires a different mindset which I am still not used to.
I would like to simulate the effect ...
- 83