> Somewhat related, why should we use Integer(1) and not int(1)?
>

These create little sympy-landmines if you have to remember which things
give ints and which give Integers. e.g. Rational(2,3).q and
multiplicity(2,12) are ints so you have to be careful how you use them. If
all Integers are stored as ints then the consistency helps; but if
sometimes a Rational can be produced then you can't do things like `if
i.is_Integer` you have to do `if type(i) is int` or `if isinstance(i,
int)`.  SymPy can't anticipate what you are going to do with the
integer-like properties/return values but it can make your life a little
easier by making them consistent.

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