6.1.2 How Some Python Annoyances are Resolved in Sage

People who do research mathematics and use Python often run into a few problems:

Notation for exponentiation: ** versus ^. In Python, ^ means ``xor'', not exponentiation, so in Python we have
```
>>> 2^8
10
>>> 3^2
1
>>> 3**2
9
```
This might be easy for some people to get used to, but for a person used to typing LaTeX this appears odd; it is also inefficient for pure math research, since exclusive or is rarely used. For convenience, Sage pre-parses all command lines before passing them to Python, replacing instances of ^ that are not in strings with **:
```
sage: 2^8
256
sage: 3^2
9
sage: "3^2"
'3^2'
```
Integer division: The expression 2/3 has much different behavior in Python than in any standard math system. In Python, if and are ints then is also an int, namely the quotient of divided by . Therefore . This illustrates how Python is similar to C in many ways (arrays are also indexed starting at 0). There has been talk in the Python community about changing Python so 2/3 returns the floating point number 0.6666..., and making 2//3 return 0 .
We deal with this in the Sage interpreter, by wrapping integer literals in ZZ( ) and making division a constructor for rational numbers. For example:
```
sage: 2/3
2/3
sage: 2//3
0
sage: int(2)/int(3)
0
```
Long integers: Python has native support for arbitrary precision integers, in addition to C-int's. These are significantly slower than what GMP provides, and have the extremely annoying property that they print with an L at the end to distinguish them from int's (and this won't change any time soon). Sage also implements arbitrary precision integers, using the GMP C-library, and these print without an L.

Rather than modifying the Python interpreter (as I've heard some people have done for internal projects), we use the Python language exactly as is, and write a pre-parser for IPython so that the command line behavior of IPython is what a mathematician expects. This means any existing Python code can be used in Sage. However, one must still obey the standard Python rules when writing packages that will be imported into Sage.

Note: To install a random Python library that you find on the internet, follow the directions, but run sage -python instead of python. Very often this means typing sage -python setup.py install.

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