úÎIôE…U      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRST experimentalconal@conal.net experimental conal@conal.net, andygill@ku.eduGroup subtraction Additive group v. The zero element: identity for '(^+^)'  Add vectors Additive inverse  experimental conal@conal.net, andygill@ku.edu Vector divided by scalar Vector multiplied by scalar Linear interpolation between a (when t==0) and b (when t==1). DSquare of the length of a vector. Sometimes useful for efficiency.  See also  . Length of a vector. See also . BVector in same direction as given one but with length of one. If ( given the zero vector, then return it. Adds inner (dot) products. Inner/ dot product  Vector space v over a scalar field s . Extends   with scalar multiplication. Scale a vector      experimentalconal@conal.netLinear map type :Transform a linear map by transforming a linear function. :Transform a linear maps by transforming linear functions. :Transform a linear maps by transforming linear functions. Constant value as a linear map Map a linear function over a linear map. Apply a linear# binary function over linear maps. Apply a linear$ ternary function over linear maps. Identity linear map Compose linear maps Convenience function for " definitions. Both functions are  assumed linear. Domain of a linear map. Linear map as function )Function (assumed linear) as linear map.  experimentalconal@conal.netDSampled derivative. For avoiding an awkward typing problem related  to the two required   instances. Derivative tower full of . Constant derivative tower. "Map a linear# function over a derivative tower. #Apply a linear) binary function over derivative towers. $Apply a linear* ternary function over derivative towers. %4Differentiable identity function. Sometimes called the derivation variable or similar, but it's not really a variable. &FEvery linear function has a constant derivative equal to the function  itself (as a linear map). 'Differentiable version of U  (Differentiable version of V  )FDerivative tower for applying a binary function that distributes over A addition, such as multiplication. A bit weaker assumption than  bilinearity. ,Chain rule. See also '(>-<)'. -"Specialized chain rule. See also '(@.)' .$Infinitely differentiable functions /Tower of derivatives.  !"#$%&'()*+,-./01/01. !"#$%'(&),-*+ experimentalconal@conal.net2*Extract the value from a derivative tower 3/Extract the derivative from a derivative tower 4DSampled derivative. For avoiding an awkward typing problem related  to the two required   instances. 5Derivative tower full of . 6Constant derivative tower. 8Map a linear# function over a derivative tower. 9Apply a linear) binary function over derivative towers. :Apply a linear* ternary function over derivative towers. ;4Differentiable 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). =Differentiable version of U  >Differentiable version of V  ?FDerivative tower for applying a binary function that distributes over A addition, such as multiplication. A bit weaker assumption than  bilinearity. @ Chain rule. ASpecialized chain rule. B$Infinitely differentiable functions CTower of derivatives. 23456789:;<=>?@ABCC234B56789:;=><?@A experimentalconal@conal.netD$Normalized normal vector. See also cross. E-Cross product of various forms of 3D vectors G-Cross product of various forms of 2D vectors IHomogeneous triple JHomogeneous pair K Singleton L9Thing with a normal vector (not necessarily normalized). DEFGHIJKLM LMDKJIGHEF experimental conal@conal.net, andygill@ku.eduNPoint minus vector OASquare of the distance between two points. Sometimes useful for  efficiency. See also P. P'Distance between two points. See also O. Q*Affine linear interpolation. Varies from p to p' as s varies  from 0 to 1. See also  (on vector spaces). SSubtract points TPoint plus vector NOPQRSTRSTNOPQW    !"#$%&'()*+,-./0123456789:;<;<)*+,-./01234789:=>?@ABCDEFGHIJKLM N OPvector-space-0.2.0Data.AdditiveGroupData.VectorSpaceData.LinearMapData.MaclaurinData.Derivative Data.CrossData.AffineSpaceData.NumInstancesbase Data.Tuple^-^ AdditiveGroupzeroV^+^negateV^/^*lerp magnitudeSq magnitude normalized InnerSpace<.> VectorSpace*^:-*inLinL2inL3pureLfmapL<$>*liftL2liftL3idL.*linearKLMapDomlapplylinear derivativeAtdZeropureDfmapD<$>>liftD2liftD3idDlinearDfstDsndDdistrib**^<*.>@.>-<:~>:>powVal derivativenormal HasCross3cross3 HasCross2cross2ThreeTwoOne HasNormal normalVec.-^ distanceSqdistancealerp AffineSpace.-..+^fstsnd