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
a computer algebra system. Pymbolic emphasizes providing an extensible
expression tree and a flexible, extensible way to manipulate it.
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
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
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
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¶
- Primitives (Basic Objects)
- Utilities for dealing with expressions
- Interoperability with other symbolic systems
- Geometric Algebra
- Why pymbolic when there’s already sympy?
- User-visible changes
- Frequently Asked Questions