Complex-valued variables

[projekter]

This is a first draft for the ideas mentioned in #212

[blegat]

Sorry for not following up on this, are you still interested ?

[projekter]

I am still interested, and if you also are, I'll go back and have a look at what I changed in the meantime (since I'm actively using those ideas locally for a package of mine) and update this request.

[blegat]

Ok, thanks, I'll have a look at the update

[projekter]

Now I updated this to my current state. And I also uploaded my current implementation of all this in DynamicPolynomials.
Note that I did not include an implementation of Base.abs2, as it is not clear whether this should be done as conj(z)*z or as real(z)^2+imag(z)^2, which will give entirely different representations.
Well... you could already debate this for real(z). If z = z_r + im*z_i, is this then z_r or rather (z+conj(z))/2? For polynomials/monomials, this will make a huge difference in how many terms there are.

[blegat]

I would add a shortcut here in case isreal(x) is true

[blegat]

Same for the three methods below

[projekter]

I added the shortcuts; my initial rationale for not doing so was that the checks themselves are not just a query of a flag, but instead an iteration over potentially all the involved variables, so this is not a super cheap operation.
There's also the question of the function contract: Now it may return either the same object (for a no-op) or a new operation. Since MP is abstract, we don't know whether the underlying implementations are immutable/have addresses.
I added an isreal/iscomplex check for monomial vectors as well to have this explicitly and updated this in DynamicPolynomials, where it can be done much more efficiently.

[projekter]

Whew, when trying to implement the tests, I needed to go on the current master. I hope I found all the necessary replacements to the new conventions. Locally, all the tests work apart from two broken ones. One is due to iszero not being implemented on MutableArithmetics.Zero (since I don't know much/anything about MA, I can't comment on this). The other one is due to a difficulty on parsing incomplete substitutions - which hopefully is not the standard case. This could be mitigated (though it's more a DynamicPolynomials issue), but at some conversion cost.

[projekter]

@blegat , is there something that still prevents this from being merged? Everything should be adapted for the current version, the test are working by now with the DP implementation (though you can always argue that there could be more tests), the functions are documented...

[blegat]

Thanks, no let's try to push this through the finish line.

[blegat]

Thanks for all the work, it's been a requested feature for a long time and the implementation looks neat. We can merge once ci passes