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# Symbolic Computation
{:.no_toc}
<nav markdown="1" class="toc-class">
* TOC
{:toc}
</nav>
## Top
Questions to [David Rotermund](mailto:davrot@uni-bremen.de)
```shell
pip install sympy
```
||
|---|
|[Simplification](https://docs.sympy.org/latest/tutorials/intro-tutorial/simplification.html)|
|[Calculus](https://docs.sympy.org/latest/tutorials/intro-tutorial/calculus.html) |
|[Solvers](https://docs.sympy.org/latest/tutorials/intro-tutorial/solvers.html)|
## [Some examples](https://docs.sympy.org/latest/tutorials/intro-tutorial/intro.html#a-more-interesting-example)
### [Derivatives](https://docs.sympy.org/latest/tutorials/intro-tutorial/calculus.html#derivatives)
```python
import sympy
x, y = sympy.symbols("x y")
y = sympy.diff(sympy.sin(x) * sympy.exp(x), x)
print(y) # -> exp(x)*sin(x) + exp(x)*cos(x)
```
### [Integrals](https://docs.sympy.org/latest/tutorials/intro-tutorial/calculus.html#integrals)
```python
import sympy
x, y = sympy.symbols("x y")
y = sympy.integrate(sympy.cos(x), x)
print(y) # -> sin(x)
```
### [(Taylor) Series Expansion](https://docs.sympy.org/latest/tutorials/intro-tutorial/calculus.html#series-expansion)
```python
import sympy
x, y, z = sympy.symbols("x y z")
y = sympy.cos(x)
z = y.series(x, 0, 8) # around x = 0 , up order 7
print(z) # -> 1 - x**2/2 + x**4/24 - x**6/720 + O(x**8)
```
## [simplify](https://docs.sympy.org/latest/tutorials/intro-tutorial/simplification.html#simplify)
```python
import sympy
x, y, z = sympy.symbols("x y z")
y = sympy.simplify(sympy.sin(x) ** 2 + sympy.cos(x) ** 2)
print(y) # -> 1
```
## [Solving Equations Algebraically](https://docs.sympy.org/latest/tutorials/intro-tutorial/solvers.html)
> Recall from the [gotchas section](https://docs.sympy.org/latest/tutorials/intro-tutorial/gotchas.html#tutorial-gotchas-equals) of this tutorial that symbolic equations in SymPy are not represented by = or ==, but by Eq.
```python
import sympy
x, y, z = sympy.symbols("x y z")
z = sympy.Eq(x, y)
```
Output:
$$x=y$$