úÎ "• ½"      ! experimentalconal@conal.net experimental conal@conal.net, andygill@ku.eduLinear transformations/&maps. For now, represented as simple  functions. The ( instance for functions gives the usual 7 meaning for a vector space of linear transformations. Adds inner (dot) products Inner/ dot product  Vector space v over a scalar field s The zero vector Scale a vector  Add vectors Additive inverse 'Convenience. Maybe add methods later. # class VectorSpace s s => Scalar s Vector subtraction Vector divided by scalar Vector multiplied by scalar Linear interpolation between a (when t==0) and b (when t==1). DSquare of the length of a vector. Sometimes useful for efficiency.  See also  . Length of a vector. See also  . BVector in same direction as given one but with length of one. If ( given the zero vector, then return it.      experimentalconal@conal.net $Infinitely differentiable functions Tower of derivatives.  Warning, the " instance is missing its # (due to a   type constraint). Use  instead. Constant derivative tower. Derivative tower full of . ATower of derivatives of the identity function. Sometimes called the derivation variable or similar, but it's not really a variable. FEvery linear function has a constant derivative equal to the function  itself (as a linear map). ;Derivative tower for applying a bilinear function, such as  multiplication.  Chain rule. Specialized chain rule.    experimental conal@conal.net, andygill@ku.eduSubtract points Point plus vector Point minus vector ASquare of the distance between two points. Sometimes useful for  efficiency. See also  . 'Distance between two points. See also . !*Affine linear interpolation. Varies from p to p' as s varies  from 0 to 1. See also   (on vector spaces).  ! ! !$      !"#$%&'()*+vector-space-0.1.1Data.VectorSpaceData.DerivativeData.AffineSpaceData.NumInstancesbaseControl.Applicative:-* InnerSpace<.> VectorSpacezeroV*^^+^negateV^-^^/^*lerp magnitudeSq magnitude normalized:~>:>DdValdDerivdConstdZerodIdlinearD bilinearD@.>-< AffineSpace.-..+^.-^ distanceSqdistancealerp Applicativepure