Concepts

polar-high's mental model is straightforward: everything is a polars DataFrame. Variables, parameters, expressions, constraints — all carry their index sets explicitly as frame columns, and the operations on them (*, +, Sum, Where, Lag) are just joins and group-bys under the hood.

If you have used Pyomo or JuMP, the data structures will feel familiar; the semantics will not. Read this section before the API reference. It will make better sense once the dim/join model clicks.

Reading order

1. Vars and Params — what an indexed variable actually is, what dims mean, how parameters merge.
2. Expressions — Sum, Where, Lag, broadcasting / inner-join rules and what they compile to.
3. Problem and Solve — Problem.add_cstr, row counts, how over= materializes rows, the Solution shape.
4. Duals and bases — accessing dual values, reduced costs, the live highspy.Highs instance.

One-liner glossary

Term	What it is
dim	A named index axis (e.g. "i", "t"). Always a column name in the underlying frame.
Var	A frame (*dims, col_id): one LP column per row.
Param	A frame (*dims, value): one numeric value per cell.
Expr	A list of _Terms, each a frame (*dims, col_id, coef).
over=	The index frame that defines the rows of a constraint family.
Sum(..., over=)	Group-by-sum: the listed dims disappear, the rest become open.
Where(..., frame)	Inner-join an Expr with a frame: filters rows and can introduce new open dims.
Lag(var, frame, time, lag)	Reference var at a shifted time index, joined via frame.