!ȑI      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                                  ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                                                                                                                                                                   ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~-(C) 2013-2015 Edward Kmett and Anthony Cowley BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portableSafe4<linearSerialize a linear type.linearDeserialize a linear type.(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portableSafe89linear4Requires and provides a default definition such that  =  linearAn involutive ringlinear;Conjugate a value. This defaults to the trivial involution.conjugate (1 :+ 2) 1.0 :+ (-2.0) conjugate 11(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafe@%linearDProvides a fairly subjective test to see if a quantity is near zero.nearZero (1e-11 :: Double)FalsenearZero (1e-17 :: Double)TruenearZero (1e-5 :: Float)FalsenearZero (1e-7 :: Float)True&linear%Determine if a quantity is near zero.(linear  a  1e-12)linear  a  1e-6*linear  a  1e-12+linear  a  1e-6%&%&(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafeB(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable Trustworthy 8>HSUVXZR.linear8A vector is an additive group with additional structure./linearThe zero vector0linearCompute the sum of two vectorsV2 1 2 ^+^ V2 3 4V2 4 61linear*Compute the difference between two vectorsV2 4 5 ^-^ V2 3 1V2 1 42linear)Linearly interpolate between two vectors.3linearApply a function to merge the  'non-zero'< components of two vectors, unioning the rest of the values.)For a dense vector this is equivalent to .*For a sparse vector this is equivalent to .4linear2Apply a function to the components of two vectors.)For a dense vector this is equivalent to .*For a sparse vector this is equivalent to .5linear Basis element8linear Compute the negation of a vectornegated (V2 2 4) V2 (-2) (-4)9linearSum over multiple vectorssumV [V2 1 1, V2 3 4]V2 4 5:linearCompute the left scalar product 2 *^ V2 3 4V2 6 8;linear Compute the right scalar product V2 3 4 ^* 2V2 6 8<linear*Compute division by a scalar on the right.=lineartProduce a default basis for a vector space. If the dimensionality of the vector space is not statically known, see >.>linearMProduce a default basis for a vector space from which the argument is drawn.?linear0Produce a diagonal (scale) matrix from a vector.scaled (V2 2 3)V2 (V2 2 0) (V2 0 3)@linearCreate a unit vector.unit _x :: V2 IntV2 1 0Alinear%Outer (tensor) product of two vectors./0134256789:;<=>?@A./013425678;:<9=>?A@0616:7;7<7(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portable Trustworthy8h[ Tlinear,Free and sparse inner product/metric spaces.UlinearMCompute the inner product of two vectors or (equivalently) convert a vector f a into a covector f a -> a.V2 1 2 `dot` V2 3 411VlineargCompute the squared norm. The name quadrance arises from Norman J. Wildberger's rational trigonometry.Wlinear'Compute the quadrance of the differenceXlinear:Compute the distance between two vectors in a metric spaceYlinear.Compute the norm of a vector in a metric spaceZlinear)Convert a non-zero vector to unit vector.[linear Normalize a T functor to have unit Y4. This function does not change the functor if its Y is 0 or 1.\linear project u v computes the projection of v onto u. TUVWXYZ[\ TUVWXYZ[\(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portable Trustworthy-.278=>?@AGHIMSUVXkvghijklmnopqrstuvwghirnouvstwjklmpq(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portable Trustworthy.24567:=?@AHMVXqlinear)A space that has at least 1 basis vector .linear V1 2 ^._x2V1 2 & _x .~ 3V1 3linearA 1-dimensional vectorpure 1 :: V1 IntV1 1 V1 2 + V1 3V1 5 V1 2 * V1 3V1 6 sum (V1 2)2 (C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portable Trustworthy.27:=?@AHSVX{linear6A space that distinguishes 2 orthogonal basis vectors  and , but may have more.linear V2 1 2 ^._y2V2 1 2 & _y .~ 3V2 1 3linearA 2-dimensional vectorpure 1 :: V2 IntV2 1 1V2 1 2 + V2 3 4V2 4 6V2 1 2 * V2 3 4V2 3 8 sum (V2 1 2)3linear V2 1 2 ^. _yxV2 2 1linear*the counter-clockwise perpendicular vectorperp $ V2 10 20 V2 (-20) 10linearDThe Z-component of the cross product of two vectors in the XY-plane.crossZ (V2 1 0) (V2 0 1)1 (C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portable Trustworthy.27:=?@AHSVXAlinear7A space that distinguishes 3 orthogonal basis vectors: , , and B. (It may have more)BlinearV3 1 2 3 ^. _z3DlinearA 3-dimensional vectorPlinear cross productQlinearscalar triple productABCDEFGHIJKLMNOPQDEPQABCFGHIJKLMNO (C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portable Trustworthy.27:=?@AHSVXlinear4A space that distinguishes orthogonal basis vectors , , B, . (It may have more.)linearV4 1 2 3 4 ^._w4linearA 4-dimensional vector.linear^Convert a 3-dimensional affine vector into a 4-dimensional homogeneous vector, i.e. sets the w coordinate to 0.linear]Convert a 3-dimensional affine point into a 4-dimensional homogeneous vector, i.e. sets the w coordinate to 1.lineargConvert 4-dimensional projective coordinates to a 3-dimensional point. This operation may be denoted, &euclidean [x:y:z:w] = (x/w, y/w, z/w)/ where the projective, homogenous, coordinate  [x:y:z:w]/ is one of many associated with a single point (x/w, y/w, z/w).MABCFGHIJKLMNOMABCFGHIJKLMNO (C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portable Trustworthy.27:=?@AHVXlinearA 0-dimensional vectorpure 1 :: V0 IntV0V0 + V0V0 (C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portable Trustworthy.27:=?@AHQVX8linear0A vector space that includes the basis elements =, >, 9 and :<linear0A vector space that includes the basis elements = and >?linear Quaternionslinear$quadrance of the imaginary componentElinearnorm of the imaginary componentFlinearraise a ? to a scalar powerlinear0Helper for calculating with specific branch cutslinear0Helper for calculating with specific branch cutsGlinear with a specified branch cut.Hlinear with a specified branch cut.Ilinear with a specified branch cut.Jlinear with a specified branch cut.Klinear with a specified branch cut.Llinear with a specified branch cut.Mlinear7Spherical linear interpolation between two quaternions.NlinearApply a rotation to a vector.OlinearO axis theta builds a ? representing a rotation of theta radians about axis.8:9;<=>?@ABCDEFGHIJKLMNO?@<=>8:9;ABCDMGHIJKLEFNO(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portable Trustworthy&'.7:=?@AHVXlinear'Describe how two lines pass each other.linear2The lines are coplanar (parallel or intersecting).linear9The lines pass each other clockwise (right-handed screw)linear@The lines pass each other counterclockwise (left-handed screw).linear7Plcker coordinates for lines in a 3-dimensional space.linearGiven a pair of points represented by homogeneous coordinates generate Plcker coordinates for the line through them, directed from the second towards the first.linearGiven a pair of 3D points, generate Plcker coordinates for the line through them, directed from the second towards the first.linearOThese elements form a basis for the Plcker space, or the Grassmanian manifold Gr(2,V4).  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a linearOThese elements form a basis for the Plcker space, or the Grassmanian manifold Gr(2,V4).  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a linearOThese elements form a basis for the Plcker space, or the Grassmanian manifold Gr(2,V4).  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a linearOThese elements form a basis for the Plcker space, or the Grassmanian manifold Gr(2,V4).  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a linearOThese elements form a basis for the Plcker space, or the Grassmanian manifold Gr(2,V4).  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a linearOThese elements form a basis for the Plcker space, or the Grassmanian manifold Gr(2,V4).  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a  ::  ( a) a linearZThese elements form an alternate basis for the Plcker space, or the Grassmanian manifold Gr(2,V4).  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a linearZThese elements form an alternate basis for the Plcker space, or the Grassmanian manifold Gr(2,V4).  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a linearZThese elements form an alternate basis for the Plcker space, or the Grassmanian manifold Gr(2,V4).  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a linearZThese elements form an alternate basis for the Plcker space, or the Grassmanian manifold Gr(2,V4).  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a linearZThese elements form an alternate basis for the Plcker space, or the Grassmanian manifold Gr(2,V4).  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a linearZThese elements form an alternate basis for the Plcker space, or the Grassmanian manifold Gr(2,V4).  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a  ::  a =>  ( a) a linearValid Plcker coordinates p will have  p  0PThat said, floating point makes a mockery of this claim, so you may want to use &.linearaThis isn't th actual metric because this bilinear form gives rise to an isotropic quadratic spacelinearsChecks if the line is near-isotropic (isotropic vectors in this quadratic space represent lines in real 3d space).linear4Checks if two lines intersect (or nearly intersect).linear%Check how two lines pass each other.  passes l1 l2 describes l2 when looking down l1.linear!Checks if two lines are parallel.linearQRepresent a Plcker coordinate as a pair of 3-tuples, typically denoted U and V.linearKChecks if two lines coincide in space. In other words, undirected equality.linearFChecks if two lines coincide in space, and have the same orientation.linear7The minimum squared distance of a line from the origin.linear0The point where a line is closest to the origin.linearNot all 6-dimensional points correspond to a line in 3D. This predicate tests that a Plcker coordinate lies on the Grassmann manifold, and does indeed represent a 3D line.%%5(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portableSafe-8HUV*linearCompute the trace of a matrixtrace (V2 (V2 a b) (V2 c d))a + dlinear Compute the diagonal of a matrixdiagonal (V2 (V2 a b) (V2 c d))V2 a dlinear Compute the  /http://mathworld.wolfram.com/FrobeniusNorm.htmlFrobenius norm of a matrix.(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portableSafe&'linearWhen lines are represented as Plcker coordinates, we have the ability to check for both directed and undirected equality. Undirected equality between s (or a  and a R) checks that the two lines coincide in 3D space. Directed equality, between two s, checks that two lines coincide in 3D, and have the same direction. To accomodate these two notions of equality, we use an  instance on the  data type.For example, to check the directed equality between two lines, p1 and p2 , we write, Ray p1 == Ray p2.(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portable Trustworthy HSVXXg6linear*A 4x4 matrix with row-major representationlinear*A 4x3 matrix with row-major representationlinear*A 4x2 matrix with row-major representationlinear*A 3x4 matrix with row-major representationlinear*A 3x3 matrix with row-major representation linear*A 3x2 matrix with row-major representation linear*A 2x4 matrix with row-major representation linear*A 2x3 matrix with row-major representation linear*A 2x2 matrix with row-major representation linearThis is a generalization of " to work over any corepresentable .   ::  f =>  s t a b ->  (f s) (f t) (f a) (f b) 6In practice it is used to access a column of a matrix.V2 (V3 1 2 3) (V3 4 5 6) ^._xV3 1 2 3$V2 (V3 1 2 3) (V3 4 5 6) ^.column _xV2 1 4linearTMatrix product. This can compute any combination of sparse and dense multiplication.:V2 (V3 1 2 3) (V3 4 5 6) !*! V3 (V2 1 2) (V2 3 4) (V2 4 5)V2 (V2 19 25) (V2 43 58)SV2 (fromList [(1,2)]) (fromList [(2,3)]) !*! fromList [(1,V3 0 0 1), (2, V3 0 0 5)]V2 (V3 0 0 2) (V3 0 0 15)linearEntry-wise matrix addition.5V2 (V3 1 2 3) (V3 4 5 6) !+! V2 (V3 7 8 9) (V3 1 2 3)V2 (V3 8 10 12) (V3 5 7 9)linearEntry-wise matrix subtraction.5V2 (V3 1 2 3) (V3 4 5 6) !-! V2 (V3 7 8 9) (V3 1 2 3)!V2 (V3 (-6) (-6) (-6)) (V3 3 3 3)linearMatrix * column vector$V2 (V3 1 2 3) (V3 4 5 6) !* V3 7 8 9 V2 50 122linearRow vector * matrix"V2 1 2 *! V2 (V3 3 4 5) (V3 6 7 8) V3 15 18 21linearScalar-matrix product5 *!! V2 (V2 1 2) (V2 3 4)V2 (V2 5 10) (V2 15 20)linearMatrix-scalar productV2 (V2 1 2) (V2 3 4) !!* 5V2 (V2 5 10) (V2 15 20)linearMatrix-scalar divisionlinear*Hermitian conjugate or conjugate transpose:adjoint (V2 (V2 (1 :+ 2) (3 :+ 4)) (V2 (5 :+ 6) (7 :+ 8)))LV2 (V2 (1.0 :+ (-2.0)) (5.0 :+ (-6.0))) (V2 (3.0 :+ (-4.0)) (7.0 :+ (-8.0)))linear$Build a rotation matrix from a unit ?.linearOBuild a transformation matrix from a rotation matrix and a translation vector.linear>Build a transformation matrix from a rotation expressed as a ? and a translation vector.linearAConvert from a 4x3 matrix to a 4x4 matrix, extending it with the  [ 0 0 0 1 ] column vectorlinearUConvert a 3x3 matrix to a 4x4 matrix extending it with 0's in the new row and column.linear-The identity matrix for any dimension vector.identity :: M44 Int6V4 (V4 1 0 0 0) (V4 0 1 0 0) (V4 0 0 1 0) (V4 0 0 0 1)identity :: V3 (V3 Int)#V3 (V3 1 0 0) (V3 0 1 0) (V3 0 0 1)linearbExtract the translation vector (first three entries of the last column) from a 3x4 or 4x4 matrix.linear]Extract a 2x2 matrix from a matrix of higher dimensions by dropping excess rows and columns.linear]Extract a 2x3 matrix from a matrix of higher dimensions by dropping excess rows and columns. linear]Extract a 2x4 matrix from a matrix of higher dimensions by dropping excess rows and columns.!linear]Extract a 3x2 matrix from a matrix of higher dimensions by dropping excess rows and columns."linear]Extract a 3x3 matrix from a matrix of higher dimensions by dropping excess rows and columns.#linear]Extract a 3x4 matrix from a matrix of higher dimensions by dropping excess rows and columns.$linear]Extract a 4x2 matrix from a matrix of higher dimensions by dropping excess rows and columns.%linear]Extract a 4x3 matrix from a matrix of higher dimensions by dropping excess rows and columns.&linear]Extract a 4x4 matrix from a matrix of higher dimensions by dropping excess rows and columns.'linear2x2 matrix determinant.det22 (V2 (V2 a b) (V2 c d)) a * d - b * c(linear3x3 matrix determinant.+det33 (V3 (V3 a b c) (V3 d e f) (V3 g h i))?a * (e * i - f * h) - d * (b * i - c * h) + g * (b * f - c * e))linear4x4 matrix determinant.*linear2x2 matrix inverse.inv22 $ V2 (V2 1 2) (V2 3 4)"V2 (V2 (-2.0) 1.0) (V2 1.5 (-0.5))+linear3x3 matrix inverse.+inv33 $ V3 (V3 1 2 4) (V3 4 2 2) (V3 1 1 1)CV3 (V3 0.0 0.5 (-1.0)) (V3 (-0.5) (-0.75) 3.5) (V3 0.5 0.25 (-1.5)),linear, is just an alias for  )transpose (V3 (V2 1 2) (V2 3 4) (V2 5 6))V2 (V3 1 3 5) (V3 2 4 6)-linear4x4 matrix inverse..linearTCompute the (L, U) decomposition of a square matrix using Crout's algorithm. The  of the vectors must be ./linearcCompute the (L, U) decomposition of a square matrix using Crout's algorithm, using the vector's j instance to provide an index.0linearcSolve a linear system with a lower-triangular matrix of coefficients with forwards substitution.1linearwSolve a linear system with a lower-triangular matrix of coefficients with forwards substitution, using the vector's j! instance to provide an index.2lineareSolve a linear system with an upper-triangular matrix of coefficients with backwards substitution.3linearySolve a linear system with an upper-triangular matrix of coefficients with backwards substitution, using the vector's j! instance to provide an index.4linear,Solve a linear system with LU decomposition.5linear@Solve a linear system with LU decomposition, using the vector's j! instance to provide an index.6linear&Invert a matrix with LU decomposition.7linear:Invert a matrix with LU decomposition, using the vector's j! instance to provide an index.8linear;Compute the determinant of a matrix using LU decomposition.9linearRCompute the determinant of a matrix using LU decomposition, using the vector's j instance to provide an index.9      !"#$%&'()*+,-./01234567899     '()*+-, !"#$%&./012345678976677777(C) 2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portableNonew:linearBuild a look at view matrix;linear7Build a matrix for a symmetric perspective-view frustum<linear#Build an inverse perspective matrix=linear+Build a perspective matrix per the classic  glFrustum arguments.?linearTBuild a matrix for a symmetric perspective-view frustum with a far plane at infiniteAlinearBuild an orthographic perspective matrix from 6 clipping planes. This matrix takes the region delimited by these planes and maps it to normalized device coordinates between [-1,1]<This call is designed to mimic the parameters to the OpenGL glOrtho_ call, so it has a slightly strange convention: Notably: the near and far planes are negated. Consequently: A l r b t n f !*  l b (-n) 1 =  (-1) (-1) (-1) 1 A l r b t n f !*  r t (-f) 1 =  1 1 1 1  Examples:"ortho 1 2 3 4 5 6 !* V4 1 3 (-5) 1V4 (-1.0) (-1.0) (-1.0) 1.0"ortho 1 2 3 4 5 6 !* V4 2 4 (-6) 1V4 1.0 1.0 1.0 1.0BlinearGBuild an inverse orthographic perspective matrix from 6 clipping planes :linearEyelinearCenterlinearUp;linearFOV (y direction, in radians)linear Aspect ratiolinear Near planelinear Far plane<linearFOV (y direction, in radians)linear Aspect ratiolinear Near planelinear Far plane=linearLeftlinearRightlinearBottomlinearToplinearNearlinearFar>linearLeftlinearRightlinearBottomlinearToplinearNearlinearFar?linearFOV (y direction, in radians)linear Aspect Ratiolinear Near plane@linearFOV (y direction, in radians)linear Aspect Ratiolinear Near planeAlinearLeftlinearRightlinearBottomlinearToplinearNearlinearFarBlinearLeftlinearRightlinearBottomlinearToplinearNearlinearFar :;<=>?@AB :;<?@=>AB BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableNone=>?@A{&Clinear.A coassociative counital coalgebra over a ringFlinear)An associative unital algebra over a ring CDEFGHIJKL FGHCDEIJKL BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableNone=>?@A~f^linearILinear functionals from elements of an (infinite) free module to a scalar^_`a^_`aa0 BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable Trustworthy124567=>?@AHMSVX llinearJA handy wrapper to help distinguish points from vectors at the type levelnlinearwAn affine space is roughly a vector space in which we have forgotten or at least pretend to have forgotten the origin. `a .+^ (b .-. a) = b@ (a .+^ u) .+^ v = a .+^ (u ^+^ v)@ (a .-. b) ^+^ v = (a .+^ v) .-. q@plinear9Get the difference between two points as a vector offset.qlinearAdd a vector offset to a point.rlinear&Subtract a vector offset from a point.slinearDCompute the quadrance of the difference (the square of the distance)tlinear.Distance between two points in an affine spacezlinearVector spaces have origins.{linearFAn isomorphism between points and vectors, given a reference point.lmnrqpostuvwxyz{nrqpostlmuvwxyz{p6q6r6(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portableNone%&./0134256789:;<=>?@ATUVWXYZ[\ABCDEFGHIJKLMNOPQ8:9;<=>?@ABCDEFGHIJKLMNO      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKL^_`a !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                     ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                                                                                                                                                                     ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                                      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnnopqrstuvwxyz{|}~   "linear-1.21-8koDM2CeTPQEICbCH921MULinear.V Linear.BinaryLinear.ConjugateLinear.EpsilonLinear.Instances Linear.Vector Linear.Metric Linear.V1 Linear.V2 Linear.V3 Linear.V4 Linear.V0Linear.QuaternionLinear.Plucker Linear.TraceLinear.Plucker.Coincides Linear.MatrixLinear.ProjectionLinear.AlgebraLinear.Covector Linear.AffineLinear'reflection-2.1.5-4qtfUoYSp3c7gqYGlkI3YXData.Reflectionint putLinear getLinearTrivialConjugate Conjugate conjugate$fTrivialConjugateCDouble$fTrivialConjugateCFloat$fTrivialConjugateFloat$fTrivialConjugateDouble$fTrivialConjugateWord8$fTrivialConjugateWord16$fTrivialConjugateWord32$fTrivialConjugateWord64$fTrivialConjugateWord$fTrivialConjugateInt8$fTrivialConjugateInt16$fTrivialConjugateInt32$fTrivialConjugateInt64$fTrivialConjugateInt$fTrivialConjugateInteger$fConjugateComplex$fConjugateCDouble$fConjugateCFloat$fConjugateFloat$fConjugateDouble$fConjugateWord8$fConjugateWord16$fConjugateWord32$fConjugateWord64$fConjugateWord$fConjugateInt8$fConjugateInt16$fConjugateInt32$fConjugateInt64$fConjugateInt$fConjugateIntegerEpsilonnearZero$fEpsilonComplex$fEpsilonCDouble$fEpsilonCFloat$fEpsilonDouble$fEpsilonFloat$fMonadFixComplex$fMonadZipComplexAdditivezero^+^^-^lerpliftU2liftI2EelnegatedsumV*^^*^/basisbasisForscaledunitouter$fGAdditivePar1 $fGAdditiveM1$fGAdditive:*: $fGAdditiveU1$fAdditiveIdentity$fAdditiveComplex $fAdditive->$fAdditiveHashMap $fAdditiveMap$fAdditiveIntMap $fAdditive[]$fAdditiveMaybe$fAdditiveVector$fAdditiveZipList$fAdditiveCompose$fAdditiveProduct$fGAdditiveRec1$fGAdditive:.:Metricdot quadranceqddistancenormsignorm normalizeproject$fMetricVector$fMetricHashMap $fMetricMap$fMetricIntMap$fMetricZipList $fMetricMaybe $fMetric[]$fMetricIdentity$fMetricCompose$fMetricProductVtoVectorFiniteSizetoVfromVDim reflectDim_V_V'dim reifyDimNatreifyVectorNatreifyDim reifyVector fromVector $fDimNatn $fField19VVaa $fField18VVaa $fField17VVaa $fField16VVaa $fField15VVaa $fField14VVaa $fField13VVaa $fField12VVaa $fField11VVaa $fField10VVaa $fField9VVaa $fField8VVaa $fField7VVaa $fField6VVaa $fField5VVaa $fField4VVaa $fField3VVaa $fField2VVaa $fField1VVaa$fVectorVectorV$fMVectorMVectorV$fUnboxV$fRead1V$fShow1V$fOrd1V$fEq1V $fSerializeV $fBinaryV $fSerialV $fSerial1V$fDataV $fBoundedV $fEachVVab $fMonadFixV $fMonadZipV$fIxedV$fRepresentableV $fMetricV $fEpsilonV $fStorableV $fHashable1V $fHashableV$fDistributiveV $fFloatingV $fFractionalV$fNumV 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