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# Formulate

Easy conversions between different styles of expressions. Formulate currently supports converting between ROOT and numexpr style expressions.

## Installation

Install formulate like any other Python package:

`pip install --user formulate`

or similar (use ``sudo`, ``virtualenv`, or ``conda`` if you wish).

## Usage

### Command line usage

```\$ python -m formulate --from-root '(A && B) || TMath::Sqrt(A)' --to-numexpr
(A & B) | sqrt(A)

\$ python -m formulate --from-numexpr '(A & B) | sqrt(A)' --to-root
(A && B) || TMath::Sqrt(A)

\$ python -m formulate --from-root '(A && B) || TMath::Sqrt(1.23) * e**1.2 + 5*pi' --variables
A
B

\$ python -m formulate --from-root '(A && B) || TMath::Sqrt(1.23) * e**1.2 + 5*pi' --named-constants
E
PI

\$ python -m formulate --from-root '(A && B) || TMath::Sqrt(1.23) * e**1.2 + 5*pi' --unnamed-constants
1.2
1.23
5```

### API

The most basic usage involves calling `from_\$BACKEND` and then `to_\$BACKEND`, for example when starting with a ROOT style expression:

```>>> import formulate
>>> momentum = formulate.from_root('TMath::Sqrt(X_PX**2 + X_PY**2 + X_PZ**2)')
>>> momentum
Expression<SQRT>(Expression<ADD>(Expression<POW>(Variable(X_PX), UnnamedConstant(2)), Expression<POW>(Variable(X_PY), UnnamedConstant(2)), Expression<POW>(Variable(X_PZ), UnnamedConstant(2))))
>>> momentum.to_numexpr()
'sqrt(((X_PX ** 2) + (X_PY ** 2) + (X_PZ ** 2)))'
>>> momentum.to_root()
'TMath::Sqrt(((X_PX ** 2) + (X_PY ** 2) + (X_PZ ** 2)))'```

Similarly, when starting with a `numexpr` style expression:

```>>> my_selection = formulate.from_numexpr('X_PT > 5 & (Mu_NHits > 3 | Mu_PT > 10)')
>>> my_selection.to_root()
'(X_PT > 5) && ((Mu_NHits > 3) || (Mu_PT > 10))'
>>> my_selection.to_numexpr()
'(X_PT > 5) & ((Mu_NHits > 3) | (Mu_PT > 10))'```

If the the type of expression isn't known in advance `formulate` can also auto detect it:

```>>> my_sum = formulate.from_auto('True + False')
>>> my_sum.to_root()
'true + false'
>>> my_sum.to_numexpr()
'True + False'```

### The `Expression` Object

When calling `from_*` the returned object is derived from `formulate.ExpressionComponent`. From this object you can inspect the expression to find it's dependencies:

```>>> my_check = formulate.from_auto('(X_THETA*TMath::DegToRad() > pi/4) && D_PE > 9.2')
>>> my_check.variables
{'D_PE', 'X_THETA'}
>>> my_check.named_constants
>>> my_check.unnamed_constants
{'4', '9.2'}```

Additionally `ExpressionComponent` s can be combined using both operators and `numpy` functions:

```>>> new_selection = (momentum > 100) and (my_check or (numpy.sqrt(my_sum) < 1))
>>> new_selection.to_numexpr()
'((X_THETA * 0.017453292519943295) > (3.141592653589793 / 4)) & (D_PE > 9.2)'```

As the `==` operator returns a new expression, it can't be used to check for equality. Instead the `.equivalent` method should be used:

TODO: Implement this using `expression.equivalent` !

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