!ny       !"#$%&'()*+,-./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 opqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~-(C) 2013-2015 Edward Kmett and Anthony Cowley BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portableSafe1linearSerialize 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-portableSafe87 linear4Requires 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>0%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> provisionalportableSafe@3(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable Trustworthy 8>HSUVXW.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 Trustworthy8e Qlinear,Free and sparse inner product/metric spaces.RlinearMCompute 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 411SlineargCompute the squared norm. The name quadrance arises from Norman J. Wildberger's rational trigonometry.Tlinear'Compute the quadrance of the differenceUlinear:Compute the distance between two vectors in a metric spaceVlinear.Compute the norm of a vector in a metric spaceWlinear)Convert a non-zero vector to unit vector.Xlinear Normalize a Q functor to have unit V4. This function does not change the functor if its V is 0 or 1.Ylinear project u v computes the projection of v onto u. QRSTUVWXY QRSTUVWXY(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portable Trustworthy-.278=>?@AGHIMSUVXhbcdefghijklmnopqrbcdmijpqnorefghkl(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portable Trustworthy.24567:=?@AHMVXo linear)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:=?@AHSVXxlinear6A 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:=?@AHSVX.2linear7A space that distinguishes 3 orthogonal basis vectors: , , and 3. (It may have more)3linearV3 1 2 3 ^. _z35linearA 3-dimensional vectorAlinear cross productBlinearscalar triple product23456789:;<=>?@AB56AB234789:;<=>?@ (C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portable Trustworthy.27:=?@AHSVX{linear4A space that distinguishes orthogonal basis vectors , , 3, |. (It may have more.)|linearV4 1 2 3 4 ^._w4~linearA 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).M234789:;<=>?@{|}~M~234789:;<=>?{|}@ (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:=?@AHQVXr linear0A vector space that includes the basis elements %, &, ! and "$linear0A vector space that includes the basis elements % and &'linear Quaternionslinear$quadrance of the imaginary component-linearnorm of the imaginary component.linearraise a ' to a scalar powerlinear0Helper for calculating with specific branch cutslinear0Helper for calculating with specific branch cuts/linear with a specified branch cut.0linear with a specified branch cut.1linear with a specified branch cut.2linear with a specified branch cut.3linear with a specified branch cut.4linear with a specified branch cut.5linear7Spherical linear interpolation between two quaternions.6linearApply a rotation to a vector.7linear7 axis theta builds a ' representing a rotation of theta radians about axis. "!#$%&'()*+,-./01234567'($%& "!#)*+,5/01234-.67(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portable Trustworthy&'.7:=?@AHVX;olinear'Describe how two lines pass each other.plinear2The lines are coplanar (parallel or intersecting).qlinear9The lines pass each other clockwise (right-handed screw)rlinear@The lines pass each other counterclockwise (left-handed screw).slinear7Plcker coordinates for lines in a 3-dimensional space.ulinearGiven a pair of points represented by homogeneous coordinates generate Plcker coordinates for the line through them, directed from the second towards the first.vlinearGiven a pair of 3D points, generate Plcker coordinates for the line through them, directed from the second towards the first.wlinearOThese elements form a basis for the Plcker space, or the Grassmanian manifold Gr(2,V4). w ::  (s a) a x ::  (s a) a y ::  (s a) a z ::  (s a) a { ::  (s a) a | ::  (s a) a xlinearOThese elements form a basis for the Plcker space, or the Grassmanian manifold Gr(2,V4). w ::  (s a) a x ::  (s a) a y ::  (s a) a z ::  (s a) a { ::  (s a) a | ::  (s a) a ylinearOThese elements form a basis for the Plcker space, or the Grassmanian manifold Gr(2,V4). w ::  (s a) a x ::  (s a) a y ::  (s a) a z ::  (s a) a { ::  (s a) a | ::  (s a) a zlinearOThese elements form a basis for the Plcker space, or the Grassmanian manifold Gr(2,V4). w ::  (s a) a x ::  (s a) a y ::  (s a) a z ::  (s a) a { ::  (s a) a | ::  (s a) a {linearOThese elements form a basis for the Plcker space, or the Grassmanian manifold Gr(2,V4). w ::  (s a) a x ::  (s a) a y ::  (s a) a z ::  (s a) a { ::  (s a) a | ::  (s a) a |linearOThese elements form a basis for the Plcker space, or the Grassmanian manifold Gr(2,V4). w ::  (s a) a x ::  (s a) a y ::  (s a) a z ::  (s a) a { ::  (s a) a | ::  (s a) a }linearZThese elements form an alternate basis for the Plcker space, or the Grassmanian manifold Gr(2,V4). } ::  a =>  (s a) a ~ ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a ~linearZThese elements form an alternate basis for the Plcker space, or the Grassmanian manifold Gr(2,V4). } ::  a =>  (s a) a ~ ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a linearZThese elements form an alternate basis for the Plcker space, or the Grassmanian manifold Gr(2,V4). } ::  a =>  (s a) a ~ ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a linearZThese elements form an alternate basis for the Plcker space, or the Grassmanian manifold Gr(2,V4). } ::  a =>  (s a) a ~ ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a linearZThese elements form an alternate basis for the Plcker space, or the Grassmanian manifold Gr(2,V4). } ::  a =>  (s a) a ~ ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a linearZThese elements form an alternate basis for the Plcker space, or the Grassmanian manifold Gr(2,V4). } ::  a =>  (s a) a ~ ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s a) a  ::  a =>  (s 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.%opqrstuvwxyz{|}~%stuvopqrwxy}|~z{5(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portableSafe-8HUVlinearCompute 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 d(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 TrustworthyHSVX?*linear*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 representationlinear*A 3x2 matrix with row-major representationlinear*A 2x4 matrix with row-major representationlinear*A 2x3 matrix with row-major representationlinear*A 2x2 matrix with row-major representationlinearThis 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 * clinear3x3 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.-  -  76677777(C) 2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portableSafe^ linearBuild a look at view matrix linear7Build a matrix for a symmetric perspective-view frustum linear#Build an inverse perspective matrixlinear+Build a perspective matrix per the classic  glFrustum arguments.linearTBuild a matrix for a symmetric perspective-view frustum with a far plane at infinitelinearBuild 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:  l r b t n f !* ~ l b (-n) 1 = ~ (-1) (-1) (-1) 1  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 1.0linearGBuild 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 planelinearLeftlinearRightlinearBottomlinearToplinearNearlinearFarlinearLeftlinearRightlinearBottomlinearToplinearNearlinearFarlinearFOV (y direction, in radians)linear Aspect Ratiolinear Near planelinearFOV (y direction, in radians)linear Aspect Ratiolinear Near planelinearLeftlinearRightlinearBottomlinearToplinearNearlinearFarlinearLeftlinearRightlinearBottomlinearToplinearNearlinearFar         BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafe=>?@Ab!linear.A coassociative counital coalgebra over a ringlinear)An associative unital algebra over a ring   BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafe=>?@Aea/linearILinear functionals from elements of an (infinite) free module to a scalar/012/01220 BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable Trustworthy124567=>?@AHMSVXr =linearJA handy wrapper to help distinguish points from vectors at the type level?linearwAn 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@Alinear9Get the difference between two points as a vector offset.BlinearAdd a vector offset to a point.Clinear&Subtract a vector offset from a point.DlinearDCompute the quadrance of the difference (the square of the distance)Elinear.Distance between two points in an affine spaceKlinearVector spaces have origins.LlinearFAn isomorphism between points and vectors, given a reference point.=>?CBA@DEFGHIJKL?CBA@DE=>FGHIJKLA6B6C6(C) 2012-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimental non-portableSafeu%&./0134256789:;<=>?@AQRSTUVWXY23456789:;<=>?@AB{|}~ "!#$%&'()*+,-./01234567     /012 !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyzz{|}~                           ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J 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 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{|}~   $linear-1.20.9-2NLGh2yhzqjHRUiWebmTMlLinear.V Linear.BinaryLinear.ConjugateLinear.EpsilonLinear.Instances Linear.Vector Linear.Metric Linear.V1 Linear.V2 Linear.V3 Linear.V4 Linear.V0Linear.QuaternionLinear.Plucker Linear.TraceLinear.Plucker.Coincides Linear.MatrixLinear.ProjectionLinear.AlgebraLinear.Covector Linear.AffineLinear'reflection-2.1.4-D3IaixAKGmk6dzEKDGsgtnData.Reflectionint putLinear getLinearTrivialConjugate Conjugate conjugate$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$fGAdditiveRec1Metricdot quadranceqddistancenormsignorm normalizeproject$fMetricVector$fMetricHashMap $fMetricMap$fMetricIntMap$fMetricZipList $fMetricMaybe $fMetric[]$fMetricIdentityVtoVectorFiniteSizetoVfromVDim 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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