718      !"#$%&'()*+,-./01234567  experimentalconal@conal.net Safe-Inferred89:;<=>?@ABCDEFGHIJK89:;<=>?@ABCDEFGHIJK experimental conal@conal.net, andygill@ku.eduNoneAdditive group v. The zero element: identity for '(^+^)'  Add vectors Additive inverse Group subtraction Sum over several vectors LMNOPQR LMNOPQR experimental conal@conal.net, andygill@ku.eduNone 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.  STUVWXYZ[\]^     STUVWXYZ[\]^ experimentalconal@conal.netNone _`abcde_`abcde experimentalconal@conal.netNoneCLinear 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.netNone $Infinitely differentiable functions Tower of derivatives. Derivative tower full of . Constant derivative tower. Map a linear# function over a derivative tower. Map a linear# function over a derivative tower. Apply a linear) binary function over derivative towers. Apply a linear* ternary function over derivative towers. !4Differentiable identity function. Sometimes called the derivation variable or similar, but it's not really a variable. "FEvery linear function has a constant derivative equal to the function  itself (as a linear map). #FDerivative tower for applying a binary function that distributes over A addition, such as multiplication. A bit weaker assumption than  bilinearity. &"Specialized chain rule. See also '(@.)' fg !"#$%&hijklmnopq !"#$%& !"#&$%fg !"#$%&hijklmnopq  experimentalconal@conal.netNone !"#$%& experimentalconal@conal.netNone'-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$Normalized normal vector. See also cross. '()*+,-./0rstuvwxyz{|} '()*+,-./0 ./0-,+)*'('()*+,-./0rstuvwxyz{|} experimental conal@conal.net, andygill@ku.eduNone2Subtract points 3Point plus vector 4Point minus vector 5ASquare of the distance between two points. Sometimes useful for  efficiency. See also 6. 6'Distance between two points. See also 5. 7*Affine linear interpolation. Varies from p to p' as s varies  from 0 to 1. See also   (on vector spaces). 1234567~123456712345671234567~     !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopBqrstuvwxyz{|}~vector-space-0.3Data.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<$>>liftD2liftD3idDlinearDdistrib**^<*.>>-< HasCross3cross3 HasCross2cross2ThreeTwoOne HasNormal normalVecnormal AffineSpace.-..+^.-^ distanceSqdistancealerpnoOvnoFunlift2lift3lift4$fFloating(,,,)$fFractional(,,,) $fNum(,,,)$fFloating(,,)$fFractional(,,) $fNum(,,) $fFloating(,)$fFractional(,)$fNum(,)$fFloating(->)$fFractional(->) $fNum(->) $fShow(->) $fOrd(->)$fEq(->)$fAdditiveGroup:->:$fAdditiveGroup(->)$fAdditiveGroup(,,)$fAdditiveGroup(,)$fAdditiveGroupComplex$fAdditiveGroupFloat$fAdditiveGroupDouble$fVectorSpace:->:s$fVectorSpace(->)s$fInnerSpace(,,)s$fVectorSpace(,,)s$fInnerSpace(,)s$fVectorSpace(,)s$fInnerSpaceComplexs$fVectorSpaceComplexs$fInnerSpaceFloatFloat$fVectorSpaceFloatFloat$fInnerSpaceDoubleDouble$fVectorSpaceDoubleDoubledecomp2unnest3nest3$fHasBasis(,,)s$fHasBasis(,)s$fHasBasisDoubleDouble$fHasBasisFloatFloatDsqr $fFloating:>$fFractional:>$fNum:>$fInnerSpace:>:>$fVectorSpace:>:>$fAdditiveGroup:>$fOrd:>$fEq:>$fShow:>pairDtripleDunpairD untripleD$fHasNormal(,,) $fHasNormal:> $fHasCross3:>$fHasCross3(,,)$fHasNormal(,)$fHasNormal:>0 $fHasCross2:>$fHasCross2(,)$fAffineSpaceFloatFloatFloat$fAffineSpaceDoubleDoubleDouble