Make assumptions about indexed symbols

[normalhuman]

I think this should be possible to do:

>>> x = IndexedBase("x", positive=True)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/ubuntu/sympy/sympy/tensor/indexed.py", line 403, in __new__
    obj = Expr.__new__(cls, label, **kw_args)
TypeError: __new__() got an unexpected keyword argument 'positive'

Without assumptions, it's hard to do algebra with indexed symbols, e.g., get sqrt(x[1]**2) to simplify to x[1].

I understand that the class Indexed inherits from Expr, not from Symbol, and there are no assumptions on Expr. Still, we already have some quasi-assumptions on Indexed and IndexedBase in the form of is_commutative=True class property. And the objects of class Idx, which also inherits from Expr, have them in the form obj._assumptions["finite"] = True as seen here.

Could IndexedBase.__new__ parse and use the **kwargs that it accepts, instead of trying to pass them to Expr.__new__?

Optionally, maybe even Indexed.__new__ could do that, so an assumption can be added to a particular indexed object?

By the way, any attempt to pass **kwargs to Expr.__new__ is a potential bug because this method, inherited from Basic.__new__, does not accept any keyword arguments.

[Nirvan101]

Can I work on this?

[normalhuman]

Yes, you can.

[jlumpe]

@Nirvan101 any progress on this?

[PymZoR]

+1

[asmeurer]

Since it doesn't subclass from Symbol, it should reapply the logic in the Symbol constructor:

sympy/sympy/core/symbol.py

Lines 233 to 235 in cd98ba0

	is_commutative = fuzzy_bool(assumptions.get('commutative', True))
	assumptions['commutative'] = is_commutative
	obj._assumptions = StdFactKB(assumptions)

Specifically, create a StdFactKB from the assumptions that are passed in and set obj._assumptions to it.

[bsamseth]

As this had been open for a while, I've made a PR that I believe resolves this issue (#16085). I based the changes on @asmeurer's comment, and have reused the logic applied in Symbol.