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Signed-off-by: David Rotermund <54365609+davrot@users.noreply.github.com>
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@ -61,7 +61,7 @@ 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) 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) ### [simplify](https://docs.sympy.org/latest/tutorials/intro-tutorial/simplification.html#simplify)
```python ```python
import sympy import sympy
@ -72,7 +72,11 @@ y = sympy.simplify(sympy.sin(x) ** 2 + sympy.cos(x) ** 2)
print(y) # -> 1 print(y) # -> 1
``` ```
## [Solving Equations Algebraically](https://docs.sympy.org/latest/tutorials/intro-tutorial/solvers.html) ### [Solving Equations Algebraically](https://docs.sympy.org/latest/tutorials/intro-tutorial/solvers.html)
```python
solveset(equation, variable=None, domain=S.Complexes)
```
> 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. > 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.
@ -89,3 +93,32 @@ Output:
$$x=y$$ $$x=y$$
```python
import sympy
x, y, z = sympy.symbols("x y z")
y = sympy.Eq(x**2 - x, 0)
z = sympy.solveset(y, x)
print(z) # -> {0, 1}
```
### [Solving Differential Equations](https://docs.sympy.org/latest/tutorials/intro-tutorial/solvers.html#solving-differential-equations)
```python
import sympy
# Undefined functions
f = sympy.symbols("f", cls=sympy.Function)
x = sympy.symbols("x")
diffeq = sympy.Eq(f(x).diff(x, x) - 2 * f(x).diff(x) + f(x), sympy.sin(x))
print(diffeq) # -> Eq(f(x) - 2*Derivative(f(x), x) + Derivative(f(x), (x, 2)), sin(x))
result = sympy.dsolve(diffeq, f(x))
print(result) # -> Eq(f(x), (C1 + C2*x)*exp(x) + cos(x)/2)
```