úÎ8^4,@      !"#$%&'()*+,-./0123456789:;<=>?  experimentalconal@conal.net@ABCD experimental conal@conal.net, andygill@ku.edu1Monoid under group addition. Alternative to the Sum in   Data.Monoid , which uses E instead of . Additive group v. The zero element: identity for '(^+^)'  Add vectors Additive inverse Group subtraction Sum over several vectors  experimental conal@conal.net, andygill@ku.edu Adds inner (dot) products. Inner/ dot product  Vector space v over a scalar field s . Extends   with scalar multiplication. Scale a vector Vector divided by scalar Vector multiplied by scalar Linear interpolation between a (when t==0) and b (when t==1). DSquare of the length of a vector. Sometimes useful for efficiency.  See also . Length of a vector. See also . BVector in same direction as given one but with length of one. If ( given the zero vector, then return it.        experimentalconal@conal.net *Representation of the canonical basis for v  Interpret basis rep as a vector Extract coordinates AExperimental version. More elegant definitions, and friendly to % infinite-dimensional vector spaces. Linear combination FGH experimentalconal@conal.net=Linear map, represented as a memo-trie from basis to values. )Function (assumed linear) as linear map.  Apply a linear map to a vector. Compose linear maps  experimentalconal@conal.net$Infinitely differentiable functions Tower of derivatives. I!"J#Constant derivative tower. $%Map a linear# function over a derivative tower. &Apply a linear) binary function over derivative towers. 'Apply a linear* ternary function over derivative towers. (4Differentiable identity function. Sometimes called the derivation variable or similar, but it's not really a variable. )FEvery linear function has a constant derivative equal to the function  itself (as a linear map). *Differentiable version of K +Differentiable version of L ,FDerivative tower for applying a binary function that distributes over A addition, such as multiplication. A bit weaker assumption than  bilinearity. -"Specialized chain rule. See also '(@.)' M !"#$%&'()*+,- !"!"#$%&'(*+),- !"!"#$%&'()*+,-  experimentalconal@conal.net !"#$%&'()*+,- experimentalconal@conal.net.-Cross product of various forms of 3D vectors /0-Cross product of various forms of 2D vectors 12Homogeneous triple 3Homogeneous pair 4 Singleton 59Thing with a normal vector (not necessarily normalized). 67$Normalized normal vector. See also cross. NOPQ ./01234567 56743201./ .//0112345667 experimental conal@conal.net, andygill@ku.edu89Associated vector space :Subtract 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). 89:;<=>?89:;<=>?89:;9:;<=>?R      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTINUVNUWXYZ[\]vector-space-0.5.3Data.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:-*linearlapplyidLcompL:~>:>powVal derivativepureDfmapD<$>>liftD2liftD3idDlinearDfstDsndDdistrib>-< HasCross3cross3 HasCross2cross2ThreeTwoOne HasNormal normalVecnormal AffineSpaceDiff.-..+^.-^ distanceSqdistancealerpnoOvnoFunlift2lift3lift4baseGHC.NumNumdecomp2unnest3nest3D Data.TuplefstsndsqrpairDtripleDunpairD untripleD