úÎ6H2J=      !"#$%&'()*+,-./0123456789:;<  experimentalconal@conal.net=>?@A experimental conal@conal.net, andygill@ku.eduAdditive group v. The zero element: identity for '(^+^)'  Add vectors Additive inverse Group subtraction Sum over several vectors  experimental conal@conal.net, andygill@ku.edu Adds inner (dot) products. Inner/ dot product  Vector space v over a scalar field s . Extends   with scalar multiplication. Scale a vector Vector divided by scalar Vector multiplied by scalar Linear interpolation between a (when t==0) and b (when t==1). DSquare of the length of a vector. Sometimes useful for efficiency.  See also . Length of a vector. See also . BVector in same direction as given one but with length of one. If ( given the zero vector, then return it.        experimentalconal@conal.net *Representation of the canonical basis for v  Interpret basis rep as a vector Extract coordinates AExperimental version. More elegant definitions, and friendly to % infinite-dimensional vector spaces. Linear combination BCD experimentalconal@conal.net=Linear map, represented as a memo-trie from basis to values. )Function (assumed linear) as linear map.  Apply a linear map to a vector.  experimentalconal@conal.net$Infinitely differentiable functions Tower of derivatives. EFDerivative tower full of . Constant derivative tower. !"Map a linear# function over a derivative tower. #Apply a linear) binary function over derivative towers. $Apply a linear* ternary function over derivative towers. %4Differentiable identity function. Sometimes called the derivation variable or similar, but it's not really a variable. &FEvery linear function has a constant derivative equal to the function  itself (as a linear map). 'Differentiable version of G (Differentiable version of H )FDerivative tower for applying a binary function that distributes over A addition, such as multiplication. A bit weaker assumption than  bilinearity. *"Specialized chain rule. See also '(@.)' I !"#$%&'()* !"#$%'(&)* !"#$%&'()*  experimentalconal@conal.net !"#$%&'()* experimentalconal@conal.net+-Cross product of various forms of 3D vectors ,--Cross product of various forms of 2D vectors ./Homogeneous triple 0Homogeneous pair 1 Singleton 29Thing with a normal vector (not necessarily normalized). 34$Normalized normal vector. See also cross. JKLM +,-./01234 23410/-.+, +,,-../012334 experimental conal@conal.net, andygill@ku.edu56Associated vector space 7Subtract points 8Point plus vector 9Point 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). 56789:;<56789:;<56786789:;<N     !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOGPQRPQSTUVWXYvector-space-0.5Data.AdditiveGroupData.VectorSpace Data.BasisData.LinearMapData.Maclaurin Data.CrossData.AffineSpaceData.NumInstancesData.Derivative AdditiveGroupzeroV^+^negateV^-^sumV InnerSpace<.> VectorSpaceScalar*^^/^*lerp magnitudeSq magnitude normalizedHasBasisBasis basisValue decompose decompose' linearCombo recompose:-*linearlapply:~>:>powVal derivativedZeropureDfmapD<$>>liftD2liftD3idDlinearDfstDsndDdistrib>-< HasCross3cross3 HasCross2cross2ThreeTwoOne HasNormal normalVecnormal AffineSpaceAVector.-..+^.-^ distanceSqdistancealerpnoOvnoFunlift2lift3lift4decomp2unnest3nest3Dbase Data.TuplefstsndsqrpairDtripleDunpairD untripleD