Consider adding categorical variables

[arcondello]

Example

Say one wants to model choosing between four different stocks, each with an expected return and a volatility. One might currently model it like

model = Model()

expected_return = model.constant([...])
volatility = model.constant([...])

stock = model.integer(lower_bound=0, upper_bound=3)

stock_return = expected_return[stock]
stock_volatility = volatility[stock]

This works OK but stock isn't really modelling an integer variable in the sense that the ordering of the stocks in the relevant arrays does not hold any semantic meaning.

Feature Request

In such cases a user might wish to use a categorical variable. This might have a similar API

model = Model()

expected_return = model.constant([...])
volatility = model.constant([...])

stock = model.categorical(num_categories=4)

stock_return = expected_return[stock]
stock_volatility = volatility[stock]

but semantically the solver would not consider the variable to be ordered.

Other thoughts

This needs more thought, but something like

stock = model.categorical(["a", "b", "c"])  # takes values in [0, 1, 2] as usual
stock == stock.category("a")  # equivalent to stock == model.constant(0)

might be convenient. Or might just introduce a mess.