# Welcome to pymbolic!¶

Pymbolic is a simple and extensible package for precise manipulation of
symbolic expressions in Python. It doesn’t try to compete with `sympy`

as
a computer algebra system. Pymbolic emphasizes providing an extensible
expression tree and a flexible, extensible way to manipulate it.

## A taste of `pymbolic`

¶

Follow along on a simple example. Let’s import `pymbolic`

and create a
symbol, *x* in this case.

```
>>> import pymbolic as pmbl
>>> x = pmbl.var("x")
>>> x
Variable('x')
```

Next, let’s create an expression using *x*:

```
>>> u = (x+1)**5
>>> u
Power(Sum((Variable('x'), 1)), 5)
>>> print u
(x + 1)**5
```

Note the two ways an expression can be printed, namely `repr()`

and
`str()`

. `pymbolic`

purposefully distinguishes the two.

`pymbolic`

does not perform any manipulations on expressions
you put in. It has a few of those built in, but that’s not really the point:

```
>>> print pmbl.differentiate(u, 'x')
5*(x + 1)**4
```

### Manipulating expressions¶

The point is for you to be able to easily write so-called *mappers* to
manipulate expressions. Suppose we would like all sums replaced by
products:

```
>>> from pymbolic.mapper import IdentityMapper
>>> class MyMapper(IdentityMapper):
... def map_sum(self, expr):
... return pmbl.primitives.Product(expr.children)
...
>>> print u
(x + 1)**5
>>> print MyMapper()(u)
(x*1)**5
```

### Custom Objects¶

You can also easily define your own objects to use inside an expression:

```
>>> from pymbolic.primitives import Expression
>>> class FancyOperator(Expression):
... def __init__(self, operand):
... self.operand = operand
...
... def __getinitargs__(self):
... return (self.operand,)
...
... mapper_method = "map_fancy_operator"
...
>>> u
Power(Sum((Variable('x'), 1)), 5)
>>> 17*FancyOperator(u)
Product((17, FancyOperator(Power(Sum((Variable('x'), 1)), 5))))
```

As a final example, we can now derive from *MyMapper* to multiply all
*FancyOperator* instances by 2.

```
>>> class MyMapper2(MyMapper):
... def map_fancy_operator(self, expr):
... return 2*FancyOperator(self.rec(expr.operand))
...
>>> MyMapper2()(FancyOperator(u))
Product((2, FancyOperator(Power(Product((Variable('x'), 1)), 5))))
```

## Pymbolic around the web¶

- download (via the package index)
- documentation
- source code via git (also bug tracker)