15 votes
Accepted

How to solve this trig equation with Mathematica?

...
chyanog's user avatar
  • 15.6k
13 votes
Accepted

Why is the difference in the behavior of Solve?

Use Trace[Solve[...], TraceInternal -> True] to observe the difference between cases with Tan and ...
Domen's user avatar
  • 25.1k
13 votes
Accepted

Why is Mathematica showing a root twice from Reduce or Solve?

This is a bug. A subdivision method happens to subdivide very close to a root, and the same root gets found in both branches (due to numerical tolerance). The code was not checking for that, it will ...
Adam Strzebonski's user avatar
12 votes
Accepted

The Poincaré Sections of Yang-Mills-Higgs System

I'm currently co-developing an interactive tool for extracting Poincaré sections from Hamiltonian systems. I've got a preliminary version up and running, so feel free to use it. It's available on the ...
E. Chan-López's user avatar
11 votes

All solutions that satisfy $ x_{1}^{5}+x_{2}^{5}+x_{3}^{5}+x_{4}^{5}-x_{5}^{5}=0 $

I am a bit surprised that not a Mathematica solution with a statement "I don't think Mathematica is suited for this kind of problem." is accepted. I do believe that Mathematica is well ...
yarchik's user avatar
  • 18.4k
11 votes

Weakness in Reduce and Solve and FindInstance

$Version (* "14.0.0 for Mac OS X ARM (64-bit) (December 13, 2023)" *) Clear["Global`*"]; eqn = 2 ArcCos[Sin[Pi*x]] == Pi*Cos[ArcSin[x + 1]]; ...
Bob Hanlon's user avatar
  • 158k
10 votes
Accepted

Solve for equation that just above 10000 degree

Define the equation exactly, without summing explicitly: ...
Roman's user avatar
  • 47.5k
10 votes
Accepted

Reasoning about rational numbers

Assuming[Element[x, PositiveRationals], Simplify@Element[2*x, PositiveRationals]] ...
Nasser's user avatar
  • 144k
10 votes
Accepted

How to find the analytical expression of function f [x] for such a composite function?

...
Bob Hanlon's user avatar
  • 158k
10 votes
Accepted

Why can't NSolve solve for the obvious zeros?

This shows the step that rejects the root (note that Rationalize is applied to g[x] internally): ...
Michael E2's user avatar
  • 236k
10 votes
Accepted

Solving a polynomial via NSolve

Remember that when you write something like ar with no space between, it is treated as a variable named ar instead of ...
ydd's user avatar
  • 3,738
10 votes

The Poincaré Sections of Yang-Mills-Higgs System

If we take icv from your second example and define Hamiltonian as ...
Alex Trounev's user avatar
  • 44.7k
10 votes
Accepted

All solutions that satisfy $ x_{1}^{5}+x_{2}^{5}+x_{3}^{5}+x_{4}^{5}-x_{5}^{5}=0 $

I don't think Mathematica is suited for this kind of problem. Here's a C code that can solve it in 10 seconds on my laptop: ...
Roman's user avatar
  • 47.5k
9 votes
Accepted

NSolve doesn't find all solutions in a range

Add Reals. ...
cvgmt's user avatar
  • 73k
9 votes
Accepted

Projecting the stationary points of a function below its 3D Plot

Use ContourPlot or ContourPlot3D to draw V'[r]==0 and set the range of ...
herbertfederer's user avatar
8 votes
Accepted

Solving $e^{-t \epsilon } \text{csch}(t) \sinh (t-t \epsilon )=\epsilon$ for small $\epsilon$

Asymptotic analysis along the lines of @Roland's answer reveals that the root of $$e^{-t \epsilon } \text{csch}(t) \sinh (t-t \epsilon ) = \epsilon$$ as $\epsilon\rightarrow 0$ is at $t \sim \frac{1}{...
QuantumDot's user avatar
  • 19.7k
8 votes

Why can't NSolve solve for the obvious zeros?

I could not find why NSolve fail. Could be a bug? I tried FunctionExpand but that did not help. As a workaround, use Solve? <...
Nasser's user avatar
  • 144k
8 votes
Accepted

How can this equation with logarithms not be solved?

Add Reals. Reduce[{Log[a, b] + Log[b, a] == 5/2, a^b == b^a, a > 0, b > 0, t == a/b}, t, {a, b},Reals] ...
cvgmt's user avatar
  • 73k
8 votes
Accepted

What's wrong with a simple equation-solving task?

First of all the system works corectly while you make unjustified reductions. Expressions w - 1/(w (1 - e)) and z can be ...
Artes's user avatar
  • 57.3k
8 votes

How to draw the trajectory of the circumscribed rectangle of an ellipse and determine the area range of the rectangle?

The radius of the Monge circle is Sqrt[a^2 + b^2]. By the symmetric,one of the diogonal of the rectangle is pt and ...
cvgmt's user avatar
  • 73k
8 votes

Cannot solve this polynomial equation

...
Bob Hanlon's user avatar
  • 158k
8 votes

Projecting the stationary points of a function below its 3D Plot

Perhaps this is a starting point (assuming the OP code): ...
ubpdqn's user avatar
  • 60.8k
8 votes
Accepted

How many real solutions does $a^{a^{a^x}}=b^{b^{b^x}}$ have?

Beginning with the equation eq = a^(a^(a^x)) == b^(b^(b^x)) set b -> a^c with c > 1. <...
bbgodfrey's user avatar
  • 61.5k
8 votes

Basins of attraction using Newton-Raphson method for nonlinear system

modified Try ...
Ulrich Neumann's user avatar
8 votes

Basins of attraction using Newton-Raphson method for nonlinear system

The simplest way is to use FindRoot with option Method -> {"Newton", "StepControl" -> Automatic} and ...
Alex Trounev's user avatar
  • 44.7k
8 votes
Accepted

Finding the maximum of NDSolve's result

Try this: FindRoot[(D[T[t], t] /. s) == 0, {t, 20}] (* {t -> 17.9042} *) or this: ...
Alexei Boulbitch's user avatar
7 votes
Accepted

Is there a way to divide associations by key?

a = <|A -> 2.02015, B -> 1.98025|>; b = <|B -> 0.538000, A -> 0.462000|>; Merge[{a, b}, Apply[Divide]]
lericr's user avatar
  • 28.2k
7 votes
Accepted

Getting a series expansion for implicitly defined function

Here's a step-by-step way to discover @Roman's first two terms: ...
Michael E2's user avatar
  • 236k
7 votes
Accepted

Minimize is returning unevaluated for a simple positive integer domain problem

You need to specify what you mean by "smallest solution". If it means that you want the smallest value of $x+y$, then you can do ...
Roman's user avatar
  • 47.5k
7 votes
Accepted

Find the zero crossing in data

$Version "13.3.0 for Microsoft Windows (64-bit) (June 3, 2023)" ...
cvgmt's user avatar
  • 73k

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