# Formulas

Formulas allow for using mathematical expressions for specifications. There are three different parameter types that support formulas:

* `Integer`
* `Number`
* `PhysicalQuantity`

The formula syntax is different for each parameter type and becomes richer wen traversing the list from top to bottom.

### Integer formulas

The Integer formula syntax allows any kind of mathematical expression that is valid Python syntax (including parentheses, e.g. `"(2 + 3*4) * 5**6"`) and which will result in an integer value. For that reason the Integer formula syntax forbids true division expressions by default (e.g. `4 / 2`, see [Patterns](https://dominik1123.gitbook.io/hanna/patterns#illegal-patterns)). Floor division however is allowed (`4 // 2`).

### Number formulas

The Number formula syntax extends the Integer formula syntax by true division as well as by references to a broad set of [numpy](https://pypi.org/project/numpy/) functions (and the constant `pi`). These can be used directly within the expressions: `(2 + 3) * 4 * sin(pi / 4)`. To see which numpy functions are available check `Number.np_members`.

### PhysicalQuantity formulas

The PhysicalQuantity formula syntax extends the Number formula syntax by the possibility to reference constants defined in [`scipy.constants.physical_constants`](https://docs.scipy.org/doc/scipy/reference/constants.html#scipy.constants.physical_constants). These constants can be refered to by their name using the syntax `{name of constant}`.

```python
class Particle(Configurable):
    rest_energy = PhysicalQuantity(unit='eV')
    
electron = Particle(ConfigTree(
    rest_energy='{electron mass} * {speed of light in vacuum}**2 [eV]'
))
```

### Fine control for the formula syntax

By default the formula syntax for all parameters is activated. You can deactivate it by setting e.g. `Integer.formulas = False`. If you want to deactivate on a per instance basis you can do so via `Integer(formulas=False)`. You can even customize what kind of formula syntax is allowed by providing a regular expression to `formulas`. This regular expression will be matched against the specified formula and raise a `ValueError` if the formula is invalid. If for example you want to allow only addition in the formulas for a specific Integer parameter you can do so via `Integer(formulas=r'^(\d+\s*\+\s*)*\d+$')`.


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