91 lines
2 KiB
Markdown
91 lines
2 KiB
Markdown
# Symbolic Computation
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{:.no_toc}
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<nav markdown="1" class="toc-class">
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* TOC
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{:toc}
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</nav>
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## Top
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Questions to [David Rotermund](mailto:davrot@uni-bremen.de)
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```shell
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pip install sympy
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```
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|[Simplification](https://docs.sympy.org/latest/tutorials/intro-tutorial/simplification.html)|
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|[Calculus](https://docs.sympy.org/latest/tutorials/intro-tutorial/calculus.html) |
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|[Solvers](https://docs.sympy.org/latest/tutorials/intro-tutorial/solvers.html)|
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## [Some examples](https://docs.sympy.org/latest/tutorials/intro-tutorial/intro.html#a-more-interesting-example)
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### [Derivatives](https://docs.sympy.org/latest/tutorials/intro-tutorial/calculus.html#derivatives)
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```python
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import sympy
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x, y = sympy.symbols("x y")
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y = sympy.diff(sympy.sin(x) * sympy.exp(x), x)
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print(y) # -> exp(x)*sin(x) + exp(x)*cos(x)
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```
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### [Integrals](https://docs.sympy.org/latest/tutorials/intro-tutorial/calculus.html#integrals)
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```python
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import sympy
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x, y = sympy.symbols("x y")
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y = sympy.integrate(sympy.cos(x), x)
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print(y) # -> sin(x)
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```
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### [(Taylor) Series Expansion](https://docs.sympy.org/latest/tutorials/intro-tutorial/calculus.html#series-expansion)
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```python
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import sympy
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x, y, z = sympy.symbols("x y z")
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y = sympy.cos(x)
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z = y.series(x, 0, 8) # around x = 0 , up order 7
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print(z) # -> 1 - x**2/2 + x**4/24 - x**6/720 + O(x**8)
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```
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## [simplify](https://docs.sympy.org/latest/tutorials/intro-tutorial/simplification.html#simplify)
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```python
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import sympy
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x, y, z = sympy.symbols("x y z")
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y = sympy.simplify(sympy.sin(x) ** 2 + sympy.cos(x) ** 2)
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print(y) # -> 1
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```
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## [Solving Equations Algebraically](https://docs.sympy.org/latest/tutorials/intro-tutorial/solvers.html)
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> 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.
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```python
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import sympy
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x, y, z = sympy.symbols("x y z")
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z = sympy.Eq(x, y)
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```
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Output:
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$$x=y$$
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