úÎI•DyP      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEF G H I J K L M N O  experimentalconal@conal.netPQRST experimental conal@conal.net, andygill@ku.eduAdditive group v. The zero element: identity for '(^+^)'  Add vectors Additive inverse Group subtraction Sum over several vectors  experimental conal@conal.net, andygill@ku.edu Adds inner (dot) products. Inner/ dot product  Vector space v over a scalar field s . Extends   with scalar multiplication. Scale a vector Vector divided by scalar Vector multiplied by scalar Linear interpolation between a (when t==0) and b (when t==1). DSquare of the length of a vector. Sometimes useful for efficiency.  See also . Length of a vector. See also  . BVector in same direction as given one but with length of one. If ( given the zero vector, then return it.        experimentalconal@conal.net *Representation of the canonical basis for v  Interpret basis rep as a vector Extract coordinates AExperimental version. More elegant definitions, and friendly to % infinite-dimensional vector spaces. Linear combination /Turn a basis decomposition back into a vector. UVW experimentalconal@conal.netCLinear map, represented a as a memo function from basis to values. )Function (assumed linear) as linear map.  Apply a linear map to a vector.  experimentalconal@conal.net$Infinitely differentiable functions Tower of derivatives. XYDerivative 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. $4Differentiable identity function. Sometimes called the derivation variable or similar, but it's not really a variable. %FEvery linear function has a constant derivative equal to the function  itself (as a linear map). &Differentiable version of Z 'Differentiable version of [ (FDerivative tower for applying a binary function that distributes over A addition, such as multiplication. A bit weaker assumption than  bilinearity. )"Specialized chain rule. See also '(@.)' \ !"#$%&'() !"#$&'%() !"#$%&'()  experimentalconal@conal.net !"#$%&'() experimentalconal@conal.net*-Cross product of various forms of 3D vectors +,-Cross product of various forms of 2D vectors -.Homogeneous triple /Homogeneous pair 0 Singleton 19Thing with a normal vector (not necessarily normalized). 23$Normalized normal vector. See also cross. ]^_` *+,-./0123 1230/.,-*+ *++,--./01223 experimental conal@conal.net, andygill@ku.edu45Subtract points 6Point plus vector 7Point minus vector 8ASquare of the distance between two points. Sometimes useful for  efficiency. See also 9. 9'Distance between two points. See also 8. :*Affine linear interpolation. Varies from p to p' as s varies  from 0 to 1. See also   (on vector spaces). 456789:456789:45656789: 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 AVector multiplied by scalar BLinear interpolation between a (when t==0) and b (when t==1). CDSquare of the length of a vector. Sometimes useful for efficiency.  See also D. DLength of a vector. See also C. EBVector in same direction as given one but with length of one. If ( given the zero vector, then return it. ;<=>?@ABCDE =>?@A;<BCDE ;<<=>?>?@ABCDE  experimentalconal@conal.net FG*Representation of the canonical basis for v H Interpret basis rep as a vector IExtract coordinates JAExperimental version. More elegant definitions, and friendly to % infinite-dimensional vector spaces. KLinear combination LabcFGHIJKLFGHIJKLFGHIJGHIJKL  experimentalconal@conal.netM=Linear map, represented as a memo-trie from basis to values. N)Function (assumed linear) as linear map. O Apply a linear map to a vector. MNOMNOMNOd  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGH    ! " # $ % & I J K L MNOPQIRSTRSUVWXYZ N O P[vector-space-0.4.1Data.AdditiveGroupData.VectorSpace Data.BasisData.LinearMapData.Maclaurin Data.CrossData.AffineSpaceData.AVectorSpace Data.ABasisData.ALinearMapData.NumInstancesData.Derivative AdditiveGroupzeroV^+^negateV^-^sumV InnerSpace<.> VectorSpace*^^/^*lerp magnitudeSq magnitude normalizedHasBasisBasis basisValue decompose decompose' linearCombo recompose:-*linearlapply:~>:>powVal derivativedZeropureDfmapD<$>>liftD2liftD3idDlinearDfstDsndDdistrib>-< HasCross3cross3 HasCross2cross2ThreeTwoOne HasNormal normalVecnormal AffineSpace.-..+^.-^ distanceSqdistancealerpScalarnoOvnoFunlift2lift3lift4decomp2unnest3nest3Dbase Data.TuplefstsndsqrpairDtripleDunpairD untripleD