úÎ8;4>      !"#$%&'()*+,-./0123456789:;<=  experimentalconal@conal.net>?@AB experimental conal@conal.net, andygill@ku.edu1Monoid under group addition. Alternative to the Sum in   Data.Monoid , which uses C instead of . DAdditive group v. The zero element: identity for '(^+^)'  Add vectors Additive inverse Group subtraction Sum over several vectors  experimental conal@conal.net, andygill@ku.edu Adds inner (dot) products. Inner/ dot product  Vector space v over a scalar field s . Extends   with scalar multiplication. Scale a vector Vector divided by scalar Vector multiplied by scalar Linear interpolation between a (when t==0) and b (when t==1). DSquare of the length of a vector. Sometimes useful for efficiency.  See also . Length of a vector. See also . BVector in same direction as given one but with length of one. If ( given the zero vector, then return it.       experimentalconal@conal.net *Representation of the canonical basis for v  Interpret basis rep as a vector Extract coordinates AExperimental version. More elegant definitions, and friendly to % infinite-dimensional vector spaces. Linear combination EFG experimentalconal@conal.net=Linear map, represented as a memo-trie from basis to values. )Function (assumed linear) as linear map.  Apply a linear map to a vector.  experimentalconal@conal.net$Infinitely differentiable functions Tower of derivatives. HI 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 !"#$%&'()*+ experimentalconal@conal.net,-Cross product of various forms of 3D vectors -.-Cross product of various forms of 2D vectors /0Homogeneous triple 1Homogeneous pair 2 Singleton 39Thing with a normal vector (not necessarily normalized). 45$Normalized normal vector. See also cross. MNOP ,-./012345 345210./,- ,--.//0123445 experimental conal@conal.net, andygill@ku.edu67Associated vector space 8Subtract points 9Point 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). 6789:;<=6789:;<=6789789:;<=Q     !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNO PQRSHMTUMTVWXYZ[\vector-space-0.5.1Data.AdditiveGroupData.VectorSpace Data.BasisData.LinearMapData.Maclaurin Data.CrossData.AffineSpaceData.NumInstancesData.DerivativeSum AdditiveGroupzeroV^+^negateV^-^sumV InnerSpace<.> VectorSpaceScalar*^^/^*lerp magnitudeSq magnitude normalizedHasBasisBasis basisValue decompose decompose' linearCombo recompose:-*linearlapply:~>:>powVal derivativedZeropureDfmapD<$>>liftD2liftD3idDlinearDfstDsndDdistrib>-< HasCross3cross3 HasCross2cross2ThreeTwoOne HasNormal normalVecnormal AffineSpaceAVector.-..+^.-^ distanceSqdistancealerpnoOvnoFunlift2lift3lift4baseGHC.NumNumdecomp2unnest3nest3D Data.TuplefstsndsqrpairDtripleDunpairD untripleD