Gotchas¶

Lets recall again, that Diofant is nothing more than a Python library, like numpy or even the Python standard library module 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 int or float.

Diofant uses its own classes for numbers, for example Integer instead of 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 IntegerWrapper AST transformer to wrap all integer literals with Integer automatically.

The universal solution is using correct Diofant numeric class to construct numbers explicitely. For example, 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 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 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 asin(), acos() and so on instead of arcsin and arccos.