úÎ &¶%      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$Infinitely differentiable functions (Tower of derivatives. Values look like b  b'  b''  ....  The type of an nth derivative is a :-* a :-* ... :-* b, where there  are n levels of a :-*, i.e.,  (a :-*)^n b.  Warning, the  instance is missing its   (due to a   type constraint). Use  instead. Derivative tower full of . Constant derivative tower. ATower of derivatives of the identity function. Sometimes called the derivation variable or similar, but it's not really a variable. EConvenient encapsulation of the chain rule. Combines value function @ and derivative function, to get a infinitely differentiability 8 function, which is then applied to a derivative tower. Specialized form of '(>*<)'', convenient for functions with scalar F values. Uses the more common view of derivatives as rate-of-change.    experimental conal@conal.net, andygill@ku.eduSubtract points Point plus vector Point minus vector ASquare of the distance between two points. Sometimes useful for  efficiency. See also . 'Distance between two points. See also . *Affine linear interpolation. Varies from p to p' as s varies  from 0 to 1. See also   (on vector spaces). !      !"#$%&'(vector-space-0.0.1Data.VectorSpaceData.DerivativeData.AffineSpaceData.NumInstancesbaseControl.Applicative:-* InnerSpace<.> VectorSpacezeroV*^^+^negateV^-^^/^*lerp magnitudeSq magnitude normalized::>:>DdZerodConstdId bilinearD>*<>-< AffineSpace.-..+^.-^ distanceSqdistancealerp Applicativepure