🐛 ZX PiExpression arithmetic not working properly

[burgholzer]

Environment information

Any version of the ZX library.

Description

The arithmetic for PiExpressions in the ZX package seems to be quite buggy in certain aspects.
For example

const auto beta = zx::PiRational(1, 2);

std::cout << beta * 2 << "\n";
std::cout << beta * 2. << "\n";

const auto betaExpr = zx::PiExpression{beta};
std::cout << betaExpr * 2. << "\n";
// std::cout << betaExpr * 2 << "\n"; // does not compile due to missing overload

yields

1/1
1/1
159154943/500000000

The last entry is completely unexpected.

So that's the one thing. This also means something like betaExpr / 2. will result in complete garbage.
Now, #482 adds support for divisions by integers (which allows to write the above as betaExpr / 2).
However, that revealed quite a problem in the way arithmetic expressions are handled.
Namely, that

const auto beta = zx::PiRational(-1, 2);
std::cout << (beta + beta) / 2 << "\n";  // and, if the above is fixed most likely also `(beta+beta)/2.` which currently returns garbage

prints

1/2

instead of the desired result of -1/2.
The reason for that is beta+beta evaluating to -1 which is 1 mod pi.

Expected behavior

I would expect division and multiplication by floating point numbers for PiExpression to work exactly as they do for PiRational.
Furthermore, I would expect moderately complex arithmetic expressions to produce the correct result.

How to Reproduce

Run the examples from above