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
Wrapping the integer division with Fraction
is automatically enabled if you run Diofant as a module.
The universal solution is using correct Diofant numeric class to
construct numbers explicitly. 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
.