From `2 * ( ( 9 / 6 ) + 6 * x )`

, you need to get to a tree like this:

* 2 + / * 9 6 6 x

The advantages of using Python syntax: you don't have to make a separate language for the purpose, the parser is built in, and so is the evaluator. Disadvantages: there's quite a lot of extra complexity in the parse tree that you don't need (you can avoid some of it by using the built-in `NodeVisitor`

and `NodeTransformer`

classes to do your work).

>>> import ast >>> a = ast.parse('x**2 + x', mode = 'eval') >>> ast.dump(a) "Expression(body=BinOp(left=BinOp(left=Name(id='x', ctx=Load()), op=Pow(), right = Num(n = 2)), op = Add(), right = Name(id = 'x', ctx = Load()))) "

Here's an example class that walks a Python parse tree and does recursive constant folding (for binary operations), to show you the kind of thing you can do fairly easily.

```
from ast import *
class FoldConstants(NodeTransformer):
def visit_BinOp(self, node):
self.generic_visit(node)
if isinstance(node.left, Num) and isinstance(node.right, Num):
expr = copy_location(Expression(node), node)
value = eval(compile(expr, '<string>', 'eval'))
return copy_location(Num(value), node)
else:
return node
>>> ast.dump(FoldConstants().visit(ast.parse('3**2 - 5 + x', mode='eval')))
"Expression(body=BinOp(left=Num(n=4), op=Add(), right=Name(id='x', ctx=Load())))"
```

Before we can carry out any symbolic operations, we need to create symbolic variables using SymPy’s Symbol function:,We can abbreviate the creation of multiple symbolic variables using the symbols function. For example, to create the symbolic variables x, y and z, we can use,In this section, we introduce some basic functionality of the SymPy (SYMbolic Python) library. In contrast to numerical computation (involving numbers), in symbolic calculation we are processing and transforming generic variables.,SymPy is capable of carrying out differentiation and integration of many functions:

```
import sympy
sympy.init_printing()
```

```
from sympy
import Symbol
x = Symbol('x')
type(x)
```

sympy.core.symbol.Symbol

```
y = Symbol('y')
2 * x - x
```

x + y + x + 10 * y

y + x - y + 10

What is SymPy? SymPy is a Python library for symbolic mathematics. It aims to be an alternative to systems such as Mathematica or Maple while keeping the code as simple as possible and easily extensible. SymPy is written entirely in Python and does not require any external libraries.,SymPy uses mpmath in the background, which makes it possible to perform computations using arbitrary-precision arithmetic. That way, some special constants, like , , (Infinity), are treated as symbols and can be evaluated with arbitrary precision:,In contrast to other Computer Algebra Systems, in SymPy you have to declare symbolic variables explicitly:,SymPy is also able to solve boolean equations, that is, to decide if a certain boolean expression is satisfiable or not. For this, we use the function satisfiable:

```
>>>
import sympy as sym
>>>
a = sym.Rational(1, 2)
>>>
a
1 / 2
>>>
a * 2
1
```

>>> sym.pi ** 2 pi ** 2 >>> sym.pi.evalf() 3.14159265358979 >>> (sym.pi + sym.exp(1)).evalf() 5.85987448204884

>>> sym.oo > 99999 True >>> sym.oo + 1 oo

```
>>> x = sym.Symbol('x') >>>
y = sym.Symbol('y')
```

>>> x + y + x - y 2 * x >>> (x + y) ** 2(x + y) ** 2

>>> sym.init_printing(use_unicode = False, wrap_line = True)

A Logical Not function results in negation of the Boolean argument. It returns True if its argument is False and returns False if True. The ~ operator performs the operation similar to Not function. It is shown in the example below −,In Mathematics, a matrix is a two dimensional array of numbers, symbols or expressions. Theory of matrix manipulation deals with performing arithmetic operations on matrix objects, subject to certain rules.,Sympy has powerful ability to simplify mathematical expressions. There are many functions in SymPy to perform various kinds of simplification. A general function called simplify() is there that attempts to arrive at the simplest form of an expression.,One of the most basic operations to be performed on a mathematical expression is substitution. The subs() function in SymPy replaces all occurrences of first parameter with second.

SymPy has one important prerequisite library named **mpmath**. It is a Python library for real and complex floating-point arithmetic with arbitrary precision. However, Python's package installer PIP installs it automatically when SymPy is installed as follows −

pip install sympy

Other Python distributions such as Anaconda, Enthought Canopy, etc., may have SymPy already bundled in it. To verify, you can type the following in the Python prompt −

```
>>>
import sympy
>>>
sympy.__version__
```

Symbolic computation refers to development of algorithms for manipulating mathematical expressions and other mathematical objects. Symbolic computation integrates mathematics with computer science to solve mathematical expressions using mathematical symbols. A Computer Algebra System (CAS) such as SymPy evaluates algebraic expressions exactly (not approximately) using the same symbols that are used in traditional manual method. For example, we calculate square root of a number using Python's math module as given below −

```
>>>
import math
>>>
print(math.sqrt(25), math.sqrt(7))
```

It is possible to simplify and show result of expression symbolically with the code snippet below −

```
>>>
import math
>>>
print(math.sqrt(12))
```

You need to use the below code snippet to execute the same using sympy −

# #sympy output >>> print(sympy.sqrt(12))