# 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 ...
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### 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 ...
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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 ...
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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. ...
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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...
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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 ...
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### 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 $n\times n$...
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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 ...
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### Limitations in using Reduce for Integer systems

The System For example, when solving the following system using Reduce in Integers: ...
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### 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 ...
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