Add expression objects, convertible to LinearConstraints

[tlambert03]

this is now ready @funkey

from ilpy import Relation
from ilpy.expressions import Variable

u = Variable("u", index=0)
v = Variable("v", index=1)
e = Variable("e", index=2)

expr = 2 * u - 5 * v + e / 2 >= -3
print(expr)  # "2 * u - 5 * v + e / 2 >= -3"

constraint = expr.constraint()
assert constraint.get_value() == -3
assert constraint.get_relation() == Relation.GreaterEqual
assert constraint.get_coefficients() == {0: 2.0, 1: -5.0, 2: 0.5}

see funkelab/motile#30 for an example of how this could be used in motile

[tlambert03]

would appreciate a careful look at this function... which is responsible for reducing an expression to coefficients (even if a term appears multiple times or is nested inside parentheses)

[funkey]

Looks good to me!

[funkey]

Yes! For quadratic objectives!

[tlambert03]

yeah, I thought so. that raises another question: should the Expression.constraint() method be renamed to linear_constraint()? or should it simply be smart and return the right type of constraint given the expression? (i.e. autodetect whether it's a quadratic expression)

[tlambert03]

also, do you want that done in this PR? or should I switch it to a NotImplementedError for now and follow up in another PR?

[funkey]

NotImplementedError is totally fine for now.

[funkey]

I'd keep the constraint() instead of linear_constraint(). Future versions might return either, no need for the user to specify it.

[funkey]

Wonderful, I like it very much!

Only problem I have with it is that I want more of it now :)

Those are the things we could build on top of the expressions:

• conversion of expressions into objectives
• support for quadratic objectives (and maybe at some point quadratic constraints, which are not part of the C++ wrapper, yet)
• definitions of ranges (0 <= x <= 10 could be allowed)
• support for boolean expressions (x > 0 and y == 1 = z)

...but this is out of scope for this PR I'd say.

[funkey]

Looks good to me!