TODO

Somehow find a compromise between the Map of flat Rationals and a Trie of rationals - the trie would be the embodiment of our tuple-based lexicographic ordering.
- Implement operations discussed in main.pdf
Prove that

ReOptimize

Pushes unrestricted equations to restricted, by the err_x_+, err_x_- substitution
Checks new edit constraints, to see if their constant value can just be substituted
- takes coefficients from objective function during re-assignment? line 5-10 p. 18

Arithmetic Use Sites

Division

blandRatioPrimal (Rational b b) and blandRatioDual (b b b) - primal is "constant divided by coefficient", and dual is "objective coefficient divided by coefficient".
flatten (b b b and Rational b Rational) - magnify an equation's coefficients and constant.

FUNDEP CONFLICT: Rational b b (weighted bland ratios) vs. Rational b Rational (constant re-magnification)

Multiplication

substitute (b b b and Rational b b) - magnify an equation's coefficients and constant.

Substitution

substitute (b b b and Rational b Rational) - remove a b amount from an equation's coefficients and constant.

New Version

Tableau coefficients may be polymorphic, while the objective function should be constrained to Rational
There should be a class for Simplex and SimplexDual, which may change behavior based on the instance of the coefficient - weighted sets, for instance, require that we attempt one layer at a time.

Classes

HasName - LinVarName
HasStringName - String -- lossy info for Error and Slack variables
HasVariables - LinVarMap
HasCoefficients - b
HasConstant - Rational
SimplexPrimal
- nextBasicPrimal
- nextRowPrimal
  - implicit blandRatioPrimal
SimplexDual
- nextRowDual
- nextBasicDual
  - implicit blandRatioDual