úÎ8\47?      !"#$%&'()*+,-./0123456789:;<=>  experimentalconal@conal.net?@ABC experimental conal@conal.net, andygill@ku.edu1Monoid under group addition. Alternative to the Sum in   Data.Monoid , which uses D instead of . Additive group v. The zero element: identity for '(^+^)'  Add vectors Additive inverse Group subtraction Sum over several vectors  experimental conal@conal.net, andygill@ku.edu Adds inner (dot) products. Inner/ dot product  Vector space v over a scalar field s . Extends   with scalar multiplication. Scale a vector Vector divided by scalar Vector multiplied by scalar Linear interpolation between a (when t==0) and b (when t==1). DSquare of the length of a vector. Sometimes useful for efficiency.  See also . Length of a vector. See also . BVector in same direction as given one but with length of one. If ( given the zero vector, then return it.        experimentalconal@conal.net *Representation of the canonical basis for v  Interpret basis rep as a vector Extract coordinates AExperimental version. More elegant definitions, and friendly to % infinite-dimensional vector spaces. Linear combination EFG experimentalconal@conal.net=Linear map, represented as a memo-trie from basis to values. )Function (assumed linear) as linear map.  Apply a linear map to a vector.  experimentalconal@conal.net$Infinitely differentiable functions Tower of derivatives. H I!Derivative tower full of . "Constant derivative tower. #$Map a linear# function over a derivative tower. %Apply a linear) binary function over derivative towers. &Apply a linear* ternary function over derivative towers. '4Differentiable identity function. Sometimes called the derivation variable or similar, but it's not really a variable. (FEvery linear function has a constant derivative equal to the function  itself (as a linear map). )Differentiable version of J *Differentiable version of K +FDerivative tower for applying a binary function that distributes over A addition, such as multiplication. A bit weaker assumption than  bilinearity. ,"Specialized chain rule. See also '(@.)' L !"#$%&'()*+,  !"#$%&')*(+,  !"#$%&'()*+,  experimentalconal@conal.net !"#$%&'()*+, experimentalconal@conal.net--Cross product of various forms of 3D vectors ./-Cross product of various forms of 2D vectors 01Homogeneous triple 2Homogeneous pair 3 Singleton 49Thing with a normal vector (not necessarily normalized). 56$Normalized normal vector. See also cross. MNOP -./0123456 456321/0-. -../001234556 experimental conal@conal.net, andygill@ku.edu78Associated vector space 9Subtract 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). 789:;<=>789:;<=>789:89:;<=>Q      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSHMTUMTVWXYZ[\vector-space-0.5.2Data.AdditiveGroupData.VectorSpace Data.BasisData.LinearMapData.Maclaurin Data.CrossData.AffineSpaceData.NumInstancesData.DerivativeSum AdditiveGroupzeroV^+^negateV^-^sumV InnerSpace<.> VectorSpaceScalar*^^/^*lerp magnitudeSq magnitude normalizedHasBasisBasis basisValue decompose decompose' linearCombo recompose:-*linearlapply:~>:>powVal derivativedZeropureDfmapD<$>>liftD2liftD3idDlinearDfstDsndDdistrib>-< HasCross3cross3 HasCross2cross2ThreeTwoOne HasNormal normalVecnormal AffineSpaceDiff.-..+^.-^ distanceSqdistancealerpnoOvnoFunlift2lift3lift4baseGHC.NumNumdecomp2unnest3nest3D Data.TuplefstsndsqrpairDtripleDunpairD untripleD