# Rounding in the Characteristic Polynomial (using Sympy)¶

Copyright (C) 2019 Andreas Kloeckner

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In [2]:

```
import sympy as sp
sp.init_printing()
```

In [3]:

```
eps = sp.Symbol("epsilon")
lam = sp.Symbol("lambda")
```

In [4]:

```
m = sp.Matrix([[1, eps], [eps, 1]])
m
```

Out[4]:

$$\left[\begin{matrix}1 & \epsilon\\\epsilon & 1\end{matrix}\right]$$

In [5]:

```
m.charpoly(lam)
```

Out[5]:

$$\operatorname{PurePoly}{\left( - \epsilon^{2} + \lambda^{2} - 2 \lambda + 1, \lambda, domain=\mathbb{Z}\left[\epsilon\right] \right)}$$

Observe the occurrence of $(1-\epsilon^2)$ above.