-- | Common library for algebraic structures. Has the advantage of automatically inferring lots of useful structure, especially -- in the writing of linear programs. For example, here are several ways of writing @3 x - 4 y + z@: -- -- > gsum [3 *& x, (-4) *^ var y, var z] -- > linCombination [(3, x), (-4, y), (1, z)] -- > 3 *& x ^-^ 4 *& y ^+^ var z -- -- In addition, if we have two functions @f@ and @g@, we can construct linear combinations of those functions, using -- exactly the same syntax. Moreover, we can multiply functions with 'Double' coefficients by 'Rational' values successfully. -- This module is intended to offer as much generality as possible without getting in your way. module Data.Algebra ( -- * Algebraic structures Group(..), Ring(..), Field(..), Module(..), VectorSpace(..), Poly, varPoly, GroupRing, LinFunc, -- * Algebraic functions gsum, combination, evalPoly, -- ** Specialized methods on linear functions var, varSum, (*&), linCombination) where import Data.Algebra.Group import Data.Algebra.Ring import Data.Algebra.Field import Data.Algebra.Module