# diofant/diofant

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# Gotchas

Lets recall again, that Diofant is nothing more than a Python library, like :mod:`numpy` or even the Python standard library module :mod:`sys`. What this means is that Diofant does not add anything to the Python language. Limitations that are inherent in the language are also inherent in Diofant.

In this section we are trying to collect some things that could surprise newcomers.

## Numbers

To begin with, it should be clear for you, that if you type a numeric literal --- it will create a Python number of type :class:`int` or :class:`float`.

Diofant uses its own classes for numbers, for example :class:`~diofant.core.numbers.Integer` instead of :class:`int`. In most cases, Python numeric types will be correctly coersed to Diofant numbers during expression construction.

```>>> 3 + x**2
2
x  + 3
>>> type(_ - x**2)
<class 'diofant.core.numbers.Integer'>```

But if you use some arithmetic operators between two numerical literals, Python will evaluate such expression before Diofant has a chance to get to them.

```>>> x**(3/2)
1.5
x```

Tip

While working in the IPython console, you could use :class:`~diofant.interactive.session.IntegerDivisionWrapper` AST transformer to wrap all integer divisions with :class:`~diofant.core.numbers.Rational` automatically.

The universal solution is using correct Diofant numeric class to construct numbers explicitly. For example, :class:`~diofant.core.numbers.Rational` in the above example

```>>> x**Rational(3, 2)
3/2
x```

## Equality

You may think that `==`, which is used for equality testing in Python, is used for Diofant to test mathematical equality. This is not quite correct either. Let us see what happens when we use `==`.

```>>> (x + 1)**2 == x**2 + 2*x + 1
False```

But, (x + 1)^2 does equal x^2 + 2x + 1. What is going on here?

In Diofant, `==` represents structural equality testing and (x + 1)^2 and x^2 + 2x + 1 are not the same in this sense. One is the power and the other is the addition of three terms.

There is a separate class, called :class:`~diofant.core.relational.Eq`, which can be used to create a symbolic equation

```>>> Eq((x + 1)**2 - x**2, 2*x + 1)
2          2
- x  + (x + 1)  = 2⋅x + 1```

It is not always return a :class:`bool` object, like `==`, but you may use some simplification methods to prove (or disprove) equation.

```>>> expand(_)
true```

## Naming of Functions

Diofant uses different names for some mathematical functions than most computer algebra systems. In particular, the inverse trigonometric functions use the python names of :func:`~diofant.functions.elementary.trigonometric.asin`, :func:`~diofant.functions.elementary.trigonometric.acos` and so on instead of `arcsin` and `arccos`.