úÎH(B±S      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQR  experimentalconal@conal.netSTUVW experimental conal@conal.net, andygill@ku.edu 1Monoid under group addition. Alternative to the Sum in   Data.Monoid , which uses X instead of . Additive group v. The zero element: identity for '(^+^)'  Add vectors Additive inverse Group subtraction Sum over several vectors &Application a unary function inside a  'Application a binary function inside a  Y     experimental conal@conal.net, andygill@ku.edu Adds inner (dot) products. Inner/ dot product  Vector space v. 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 Z[\ experimental conal@conal.net, andygill@ku.eduAssociated 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 ". $*Affine linear interpolation. Varies from p to p' as s varies  from 0 to 1. See also  (on vector spaces).  !"#$ !"#$  !"#$ experimentalconal@conal.net%?Linear map, represented as an optional memo-trie from basis to  values, where ]' means the zero map (an optimization). ^_`aAn optional additive value b&)Function (assumed linear) as linear map. c'()* Apply a linear map to a vector. +*Evaluate a linear map on a basis element. d Handy for * and '(*.*)'. ,Identity linear map -Compose linear maps ./0e19Apply a linear function to each element of a linear map.  liftL f l == linear f *.* l, but works more efficiently. 2CApply a linear binary function (not to be confused with a bilinear , function) to each element of a linear map. 3EApply a linear ternary function (not to be confused with a trilinear , function) to each element of a linear map. f%&'()*+,-./0123%&*+,-'()./0123%&'()*+,-./0123 experimentalconal@conal.net4$Infinitely differentiable functions 5Tower of derivatives. 678g9Constant derivative tower. :Map a linear# function over a derivative tower. ;Map a linear# function over a derivative tower. <Apply a linear) binary function over derivative towers. =Apply a linear* ternary function over derivative towers. >4Differentiable identity function. Sometimes called the derivation variable or similar, but it's not really a variable. ?FEvery linear function has a constant derivative equal to the function  itself (as a linear map). @Differentiable version of h ADifferentiable version of i BFDerivative tower for applying a binary function that distributes over A addition, such as multiplication. A bit weaker assumption than > bilinearity. Is bilinearity necessary for correctness here? C"Specialized chain rule. See also '(@.)' jDASample the derivative at a basis element. Optimized for partial 6 application to save work for non-scalar derivatives. EFGH456789:;<=>?@ABCDEFGH5678D49:;<=>@A?BCEFGH456786789:;<=>?@ABCDEFGH  experimentalconal@conal.net456789:;<=>?@ABCDEFGH experimentalconal@conal.net I-Cross product of various forms of 3D vectors JK-Cross product of various forms of 2D vectors LMHomogeneous triple NHomogeneous pair O Singleton P9Thing with a normal vector (not necessarily normalized). QR$Normalized normal vector. See also cross. IJKLMNOPQR PQRONMKLIJ IJJKLLMNOPQQRk      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefgahijklmnopqd\arsartuvvector-space-0.7.3Data.AdditiveGroupData.VectorSpace Data.BasisData.AffineSpaceData.LinearMapData.Maclaurin Data.CrossData.NumInstancesData.DerivativeSumgetSum AdditiveGroupzeroV^+^negateV^-^sumVinSuminSum2 InnerSpace<.> VectorSpaceScalar*^^/^*lerp magnitudeSq magnitude normalizedHasBasisBasis basisValue decompose decompose' linearCombo recompose AffineSpaceDiff.-..+^.-^ distanceSqdistancealerp:-*linearinLMapinLMap2inLMap3lapplyatBasisidL*.*liftMSliftMS2liftMS3liftLliftL2liftL3:~>:>DpowVal derivativepureDfmapD<$>>liftD2liftD3idDlinearDfstDsndDdistrib>-< derivAtBasispairDunpairDtripleD untripleD HasCross3cross3 HasCross2cross2ThreeTwoOne HasNormal normalVecnormalnoOvnoFunlift2lift3lift4baseGHC.NumNum~>decomp2unnest3nest3 Data.MaybeNothingLMapunLMapLMap'MSumjsumatZlapply'fromMS Data.Tuplefstsndsqr