úÎ0Œ,é8      !"#$%&'()*+,-./01234567  experimentalconal@conal.net89:;< experimental conal@conal.net, andygill@ku.eduAdditive group v. The zero element: identity for '(^+^)'  Add vectors Additive inverse Group subtraction Sum over several vectors  experimental conal@conal.net, andygill@ku.edu Adds inner (dot) products. Inner/ dot product  Vector space v over a scalar field s . Extends   with scalar multiplication. Scale a vector Vector divided by scalar Vector multiplied by scalar Linear interpolation between a (when t==0) and b (when t==1). DSquare of the length of a vector. Sometimes useful for efficiency.  See also . Length of a vector. See also  . BVector in same direction as given one but with length of one. If ( given the zero vector, then return it.        experimentalconal@conal.net=>? experimentalconal@conal.netCLinear map, represented a as a memo function from basis to values. )Function (assumed linear) as linear map.  Apply a linear map to a vector.  experimentalconal@conal.net$Infinitely differentiable functions Tower of derivatives. @ADerivative 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). #FDerivative tower for applying a binary function that distributes over A addition, such as multiplication. A bit weaker assumption than  bilinearity. $%&"Specialized chain rule. See also '(@.)' B !"#$%& !"#&$% !"#$%&  experimentalconal@conal.net !"#$%& experimentalconal@conal.net'-Cross product of various forms of 3D vectors ()-Cross product of various forms of 2D vectors *+Homogeneous triple ,Homogeneous pair - Singleton .9Thing with a normal vector (not necessarily normalized). /0$Normalized normal vector. See also cross. CDEF '()*+,-./0 ./0-,+)*'( '(()**+,-.//0 experimental conal@conal.net, andygill@ku.edu12Subtract points 3Point plus vector 4Point minus vector 5ASquare of the distance between two points. Sometimes useful for  efficiency. See also 6. 6'Distance between two points. See also 5. 7*Affine linear interpolation. Varies from p to p' as s varies  from 0 to 1. See also   (on vector spaces). 12345671234567123234567G     !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJBKLMNOPvector-space-0.3.1Data.AdditiveGroupData.VectorSpace Data.BasisData.LinearMapData.Maclaurin Data.CrossData.AffineSpaceData.NumInstancesData.Derivative AdditiveGroupzeroV^+^negateV^-^sumV InnerSpace<.> VectorSpace*^^/^*lerp magnitudeSq magnitude normalizedHasBasisBasis basisValue decompose:-*linearlapply:~>:>powVal derivativedZeropureDfmapD<$>>liftD2liftD3idDlinearDdistrib**^<*.>>-< HasCross3cross3 HasCross2cross2ThreeTwoOne HasNormal normalVecnormal AffineSpace.-..+^.-^ distanceSqdistancealerpnoOvnoFunlift2lift3lift4decomp2unnest3nest3DsqrpairDtripleDunpairD untripleD