# Fractional math (token based)

Summary

This is includes a source transformation that converts integers literals that are followed by the `/` operator into instances of the Fraction class in the source using the tokenizer.

In a later section, we do something similar but using an Abstract Syntax Tree (AST) transformation, which is a more robust approach for this type of example.

Consider the following standard Python code:

```>>> x = 1/10
>>> for i in range(11):
...    print(i * x)
...
0.0
0.1
0.2
0.30000000000000004
0.4
0.5
0.6000000000000001
0.7000000000000001
0.8
0.9
1.0
```

This is quite surprising for beginners, not familiar with the limitations of representing floating point numbers.

However, we can “fix” this using an import hook that wraps integer, which are followed by a `/`, into a `Fraction` instance:

```> python -m ideas -a fractions_tok
The following initializing code from ideas is included:

from fractions import Fraction

Ideas Console version 0.0.38. [Python version: 3.7.9]

ideas> x =  1 / 10

ideas> for i in range(11):
...     print(i * x)
...
0
1/10
1/5
3/10
2/5
1/2
3/5
7/10
4/5
9/10
1

ideas> from ideas.session import config

ideas> config.show_changes = True

ideas> x = 1 / 10
new: x = Fraction(1) / 10

ideas>
```

This example was created after a similar example using AST transformation was created as a proof of concept. For more details about the difference, please have a look at the AST-based example.

Adds required import so that `Fraction` is a known object.