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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Linear-Affine.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">linear-1.20.3: Linear Algebra</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>License</th><td>BSD-style (see the file LICENSE)</td></tr><tr><th>Maintainer</th><td>Edward Kmett <ekmett@gmail.com></td></tr><tr><th>Stability</th><td>provisional</td></tr><tr><th>Portability</th><td>portable</td></tr><tr><th>Safe Haskell</th><td>Trustworthy</td></tr><tr><th>Language</th><td>Haskell98</td></tr></table><p class="caption">Linear.Affine</p></div><div id="description"><p class="caption">Description</p><div class="doc"><p>Operations on affine spaces.</p></div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><span class="keyword">class</span> <a href="Linear-Vector.html#t:Additive">Additive</a> (<a href="Linear-Affine.html#t:Diff">Diff</a> p) => <a href="#t:Affine">Affine</a> p <span class="keyword">where</span><ul class="subs"><li><span class="keyword">type</span> <a href="#t:Diff">Diff</a> p :: * -> *</li><li><a href="#v:.-45-.">(.-.)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => p a -> p a -> <a href="Linear-Affine.html#t:Diff">Diff</a> p a</li><li><a href="#v:.-43--94-">(.+^)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => p a -> <a href="Linear-Affine.html#t:Diff">Diff</a> p a -> p a</li><li><a href="#v:.-45--94-">(.-^)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => p a -> <a href="Linear-Affine.html#t:Diff">Diff</a> p a -> p a</li></ul></li><li class="src short"><a href="#v:qdA">qdA</a> :: (<a href="Linear-Affine.html#t:Affine">Affine</a> p, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Foldable.html#t:Foldable">Foldable</a> (<a href="Linear-Affine.html#t:Diff">Diff</a> p), <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => p a -> p a -> a</li><li class="src short"><a href="#v:distanceA">distanceA</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Foldable.html#t:Foldable">Foldable</a> (<a href="Linear-Affine.html#t:Diff">Diff</a> p), <a href="Linear-Affine.html#t:Affine">Affine</a> p) => p a -> p a -> a</li><li class="src short"><span class="keyword">newtype</span> <a href="#t:Point">Point</a> f a = <a href="#v:P">P</a> (f a)</li><li class="src short"><a href="#v:lensP">lensP</a> :: <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Type.html#t:Lens-39-">Lens'</a> (<a href="Linear-Affine.html#t:Point">Point</a> g a) (g a)</li><li class="src short"><a href="#v:_Point">_Point</a> :: <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Type.html#t:Iso-39-">Iso'</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a) (f a)</li><li class="src short"><a href="#v:origin">origin</a> :: (<a href="Linear-Vector.html#t:Additive">Additive</a> f, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Linear-Affine.html#t:Point">Point</a> f a</li><li class="src short"><a href="#v:relative">relative</a> :: (<a href="Linear-Vector.html#t:Additive">Additive</a> f, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Linear-Affine.html#t:Point">Point</a> f a -> <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Type.html#t:Iso-39-">Iso'</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a) (f a)</li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">class</span> <a href="Linear-Vector.html#t:Additive">Additive</a> (<a href="Linear-Affine.html#t:Diff">Diff</a> p) => <a name="t:Affine" class="def">Affine</a> p <span class="keyword">where</span> <a href="src/Linear-Affine.html#Affine" class="link">Source</a></p><div class="doc"><p>An affine space is roughly a vector space in which we have
forgotten or at least pretend to have forgotten the origin.</p><pre>a .+^ (b .-. a) = b@
(a .+^ u) .+^ v = a .+^ (u ^+^ v)@
(a .-. b) ^+^ v = (a .+^ v) .-. q@</pre></div><div class="subs minimal"><p class="caption">Minimal complete definition</p><p class="src"><a href="Linear-Affine.html#v:.-45-.">(.-.)</a>, <a href="Linear-Affine.html#v:.-43--94-">(.+^)</a></p></div><div class="subs associated-types"><p class="caption">Associated Types</p><p class="src"><span class="keyword">type</span> <a name="t:Diff" class="def">Diff</a> p :: * -> * <a href="src/Linear-Affine.html#Diff" class="link">Source</a></p></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a name="v:.-45-." class="def">(.-.)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => p a -> p a -> <a href="Linear-Affine.html#t:Diff">Diff</a> p a <span class="fixity">infixl 6</span><span class="rightedge"></span> <a href="src/Linear-Affine.html#.-." class="link">Source</a></p><div class="doc"><p>Get the difference between two points as a vector offset.</p></div><p class="src"><a name="v:.-43--94-" class="def">(.+^)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => p a -> <a href="Linear-Affine.html#t:Diff">Diff</a> p a -> p a <span class="fixity">infixl 6</span><span class="rightedge"></span> <a href="src/Linear-Affine.html#.%2B%5E" class="link">Source</a></p><div class="doc"><p>Add a vector offset to a point.</p></div><p class="src"><a name="v:.-45--94-" class="def">(.-^)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => p a -> <a href="Linear-Affine.html#t:Diff">Diff</a> p a -> p a <span class="fixity">infixl 6</span><span class="rightedge"></span> <a href="src/Linear-Affine.html#.-%5E" class="link">Source</a></p><div class="doc"><p>Subtract a vector offset from a point.</p></div></div><div class="subs instances"><p id="control.i:Affine" class="caption collapser" onclick="toggleSection('i:Affine')">Instances</p><div id="section.i:Affine" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> []</span> <a href="src/Linear-Affine.html#line-114" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor-Identity.html#t:Identity">Identity</a></span> <a href="src/Linear-Affine.html#line-119" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Complex.html#t:Complex">Complex</a></span> <a href="src/Linear-Affine.html#line-115" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:ZipList">ZipList</a></span> <a href="src/Linear-Affine.html#line-116" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Maybe.html#t:Maybe">Maybe</a></span> <a href="src/Linear-Affine.html#line-117" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/containers-0.5.6.2/Data-IntMap-Strict.html#t:IntMap">IntMap</a></span> <a href="src/Linear-Affine.html#line-118" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> <a href="file:///usr/share/doc/libghc-vector-doc/html/Data-Vector.html#t:Vector">Vector</a></span> <a href="src/Linear-Affine.html#line-120" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> <a href="Linear-V0.html#t:V0">V0</a></span> <a href="src/Linear-Affine.html#line-121" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> <a href="Linear-V1.html#t:V1">V1</a></span> <a href="src/Linear-Affine.html#line-122" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> <a href="Linear-V2.html#t:V2">V2</a></span> <a href="src/Linear-Affine.html#line-123" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> <a href="Linear-V3.html#t:V3">V3</a></span> <a href="src/Linear-Affine.html#line-124" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> <a href="Linear-V4.html#t:V4">V4</a></span> <a href="src/Linear-Affine.html#line-125" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> <a href="Linear-Plucker.html#t:Plucker">Plucker</a></span> <a href="src/Linear-Affine.html#line-126" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> <a href="Linear-Quaternion.html#t:Quaternion">Quaternion</a></span> <a href="src/Linear-Affine.html#line-127" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Affine.html#t:Affine">Affine</a> ((->) b)</span> <a href="src/Linear-Affine.html#line-128" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ord.html#t:Ord">Ord</a> k => <a href="Linear-Affine.html#t:Affine">Affine</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/containers-0.5.6.2/Data-Map-Lazy.html#t:Map">Map</a> k)</span> <a href="src/Linear-Affine.html#line-129" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left">(<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/libghc-hashable-doc/html/Data-Hashable.html#t:Hashable">Hashable</a> k) => <a href="Linear-Affine.html#t:Affine">Affine</a> (<a href="file:///usr/share/doc/libghc-unordered-containers-doc/html/Data-HashMap-Strict.html#t:HashMap">HashMap</a> k)</span> <a href="src/Linear-Affine.html#line-130" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Vector.html#t:Additive">Additive</a> f => <a href="Linear-Affine.html#t:Affine">Affine</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-239" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-V.html#t:Dim">Dim</a> * n => <a href="Linear-Affine.html#t:Affine">Affine</a> (<a href="Linear-V.html#t:V">V</a> * n)</span> <a href="src/Linear-Affine.html#line-131" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:qdA" class="def">qdA</a> :: (<a href="Linear-Affine.html#t:Affine">Affine</a> p, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Foldable.html#t:Foldable">Foldable</a> (<a href="Linear-Affine.html#t:Diff">Diff</a> p), <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => p a -> p a -> a <a href="src/Linear-Affine.html#qdA" class="link">Source</a></p><div class="doc"><p>Compute the quadrance of the difference (the square of the distance)</p></div></div><div class="top"><p class="src"><a name="v:distanceA" class="def">distanceA</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Foldable.html#t:Foldable">Foldable</a> (<a href="Linear-Affine.html#t:Diff">Diff</a> p), <a href="Linear-Affine.html#t:Affine">Affine</a> p) => p a -> p a -> a <a href="src/Linear-Affine.html#distanceA" class="link">Source</a></p><div class="doc"><p>Distance between two points in an affine space</p></div></div><div class="top"><p class="src"><span class="keyword">newtype</span> <a name="t:Point" class="def">Point</a> f a <a href="src/Linear-Affine.html#Point" class="link">Source</a></p><div class="doc"><p>A handy wrapper to help distinguish points from vectors at the
type level</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:P" class="def">P</a> (f a)</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:Point" class="caption collapser" onclick="toggleSection('i:Point')">Instances</p><div id="section.i:Point" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-vector-doc/html/Data-Vector-Unboxed.html#t:Unbox">Unbox</a> (f a) => <a href="file:///usr/share/doc/libghc-vector-doc/html/Data-Vector-Generic.html#t:Vector">Vector</a> <a href="file:///usr/share/doc/libghc-vector-doc/html/Data-Vector-Unboxed.html#t:Vector">Vector</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-280" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-vector-doc/html/Data-Vector-Unboxed.html#t:Unbox">Unbox</a> (f a) => <a href="file:///usr/share/doc/libghc-vector-doc/html/Data-Vector-Generic-Mutable-Base.html#t:MVector">MVector</a> <a href="file:///usr/share/doc/libghc-vector-doc/html/Data-Vector-Unboxed.html#t:MVector">MVector</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-262" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Monad.html#t:Monad">Monad</a> f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Monad.html#t:Monad">Monad</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-136" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-136" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a> f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-136" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Foldable.html#t:Foldable">Foldable</a> f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Foldable.html#t:Foldable">Foldable</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-136" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Traversable.html#t:Traversable">Traversable</a> f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Traversable.html#t:Traversable">Traversable</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-138" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/GHC-Generics.html#t:Generic1">Generic1</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-145" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-distributive-doc/html/Data-Distributive.html#t:Distributive">Distributive</a> f => <a href="file:///usr/share/doc/libghc-distributive-doc/html/Data-Distributive.html#t:Distributive">Distributive</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-196" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-adjunctions-doc/html/Data-Functor-Rep.html#t:Representable">Representable</a> f => <a href="file:///usr/share/doc/libghc-adjunctions-doc/html/Data-Functor-Rep.html#t:Representable">Representable</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-199" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-bytes-doc/html/Data-Bytes-Serial.html#t:Serial1">Serial1</a> f => <a href="file:///usr/share/doc/libghc-bytes-doc/html/Data-Bytes-Serial.html#t:Serial1">Serial1</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-155" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-semigroupoids-doc/html/Data-Functor-Apply.html#t:Apply">Apply</a> f => <a href="file:///usr/share/doc/libghc-semigroupoids-doc/html/Data-Functor-Apply.html#t:Apply">Apply</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-138" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-semigroupoids-doc/html/Data-Functor-Bind.html#t:Bind">Bind</a> f => <a href="file:///usr/share/doc/libghc-semigroupoids-doc/html/Data-Functor-Bind.html#t:Bind">Bind</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-193" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/transformers-0.4.2.0/Data-Functor-Classes.html#t:Eq1">Eq1</a> f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/transformers-0.4.2.0/Data-Functor-Classes.html#t:Eq1">Eq1</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-137" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/transformers-0.4.2.0/Data-Functor-Classes.html#t:Ord1">Ord1</a> f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/transformers-0.4.2.0/Data-Functor-Classes.html#t:Ord1">Ord1</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-137" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/transformers-0.4.2.0/Data-Functor-Classes.html#t:Read1">Read1</a> f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/transformers-0.4.2.0/Data-Functor-Classes.html#t:Read1">Read1</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-137" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/transformers-0.4.2.0/Data-Functor-Classes.html#t:Show1">Show1</a> f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/transformers-0.4.2.0/Data-Functor-Classes.html#t:Show1">Show1</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-137" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Vector.html#t:Additive">Additive</a> f => <a href="Linear-Vector.html#t:Additive">Additive</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-138" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Metric.html#t:Metric">Metric</a> f => <a href="Linear-Metric.html#t:Metric">Metric</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-138" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-V1.html#t:R1">R1</a> f => <a href="Linear-V1.html#t:R1">R1</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-217" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-V2.html#t:R2">R2</a> f => <a href="Linear-V2.html#t:R2">R2</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-221" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-V3.html#t:R3">R3</a> f => <a href="Linear-V3.html#t:R3">R3</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-227" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-V4.html#t:R4">R4</a> f => <a href="Linear-V4.html#t:R4">R4</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-233" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Vector.html#t:Additive">Additive</a> f => <a href="Linear-Affine.html#t:Affine">Affine</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-239" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Eq.html#t:Eq">Eq</a> (f a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-136" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> (f a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-139" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left">(<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Data.html#t:Data">Data</a> (f a), <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Typeable-Internal.html#t:Typeable">Typeable</a> (* -> *) f, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Typeable-Internal.html#t:Typeable">Typeable</a> * a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Data.html#t:Data">Data</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-148" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> (f a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-139" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ord.html#t:Ord">Ord</a> (f a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-136" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Read.html#t:Read">Read</a> (f a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Read.html#t:Read">Read</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-136" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Show.html#t:Show">Show</a> (f a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Show.html#t:Show">Show</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-136" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ix.html#t:Ix">Ix</a> (f a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ix.html#t:Ix">Ix</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-139" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/GHC-Generics.html#t:Generic">Generic</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-142" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Foreign-Storable.html#t:Storable">Storable</a> (f a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Foreign-Storable.html#t:Storable">Storable</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-139" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/binary-0.7.5.0/Data-Binary.html#t:Binary">Binary</a> (f a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/binary-0.7.5.0/Data-Binary.html#t:Binary">Binary</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-163" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-bytes-doc/html/Data-Bytes-Serial.html#t:Serial">Serial</a> (f a) => <a href="file:///usr/share/doc/libghc-bytes-doc/html/Data-Bytes-Serial.html#t:Serial">Serial</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-159" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-cereal-doc/html/Data-Serialize.html#t:Serialize">Serialize</a> (f a) => <a href="file:///usr/share/doc/libghc-cereal-doc/html/Data-Serialize.html#t:Serialize">Serialize</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-167" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/deepseq-1.4.1.1/Control-DeepSeq.html#t:NFData">NFData</a> (f a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/deepseq-1.4.1.1/Control-DeepSeq.html#t:NFData">NFData</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-152" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-hashable-doc/html/Data-Hashable.html#t:Hashable">Hashable</a> (f a) => <a href="file:///usr/share/doc/libghc-hashable-doc/html/Data-Hashable.html#t:Hashable">Hashable</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-140" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-vector-doc/html/Data-Vector-Unboxed.html#t:Unbox">Unbox</a> (f a) => <a href="file:///usr/share/doc/libghc-vector-doc/html/Data-Vector-Unboxed.html#t:Unbox">Unbox</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-260" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-At.html#t:Ixed">Ixed</a> (f a) => <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-At.html#t:Ixed">Ixed</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-209" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Wrapped.html#t:Wrapped">Wrapped</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-188" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Linear-Epsilon.html#t:Epsilon">Epsilon</a> (f a) => <a href="Linear-Epsilon.html#t:Epsilon">Epsilon</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-139" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left">(~) * t (<a href="Linear-Affine.html#t:Point">Point</a> g b) => <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Wrapped.html#t:Rewrapped">Rewrapped</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a) t</span> <a href="src/Linear-Affine.html#line-187" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Traversable.html#t:Traversable">Traversable</a> f => <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Each.html#t:Each">Each</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a) (<a href="Linear-Affine.html#t:Point">Point</a> f b) a b</span> <a href="src/Linear-Affine.html#line-213" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">data</span> <a href="file:///usr/share/doc/libghc-vector-doc/html/Data-Vector-Unboxed.html#t:MVector">MVector</a> s (<a href="Linear-Affine.html#t:Point">Point</a> f a) = <a name="v:MV_P" class="def">MV_P</a> !(<a href="file:///usr/share/doc/libghc-vector-doc/html/Data-Vector-Unboxed.html#t:MVector">MVector</a> s (f a))</span> <a href="src/Linear-Affine.html#line-259" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">type</span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/GHC-Generics.html#t:Rep1">Rep1</a> (<a href="Linear-Affine.html#t:Point">Point</a> f)</span> <a href="src/Linear-Affine.html#line-135" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">type</span> <a href="file:///usr/share/doc/libghc-adjunctions-doc/html/Data-Functor-Rep.html#t:Rep">Rep</a> (<a href="Linear-Affine.html#t:Point">Point</a> f) = <a href="file:///usr/share/doc/libghc-adjunctions-doc/html/Data-Functor-Rep.html#t:Rep">Rep</a> f</span> <a href="src/Linear-Affine.html#line-200" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">type</span> <a href="Linear-Affine.html#t:Diff">Diff</a> (<a href="Linear-Affine.html#t:Point">Point</a> f) = f</span> <a href="src/Linear-Affine.html#line-240" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">type</span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/GHC-Generics.html#t:Rep">Rep</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a)</span> <a href="src/Linear-Affine.html#line-135" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">data</span> <a href="file:///usr/share/doc/libghc-vector-doc/html/Data-Vector-Unboxed.html#t:Vector">Vector</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a) = <a name="v:V_P" class="def">V_P</a> !(<a href="file:///usr/share/doc/libghc-vector-doc/html/Data-Vector-Unboxed.html#t:Vector">Vector</a> (f a))</span> <a href="src/Linear-Affine.html#line-258" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">type</span> <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-At.html#t:Index">Index</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a) = <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-At.html#t:Index">Index</a> (f a)</span> <a href="src/Linear-Affine.html#line-206" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">type</span> <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-At.html#t:IxValue">IxValue</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a) = <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-At.html#t:IxValue">IxValue</a> (f a)</span> <a href="src/Linear-Affine.html#line-207" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">type</span> <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Wrapped.html#t:Unwrapped">Unwrapped</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a) = f a</span> <a href="src/Linear-Affine.html#line-189" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:lensP" class="def">lensP</a> :: <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Type.html#t:Lens-39-">Lens'</a> (<a href="Linear-Affine.html#t:Point">Point</a> g a) (g a) <a href="src/Linear-Affine.html#lensP" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:_Point" class="def">_Point</a> :: <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Type.html#t:Iso-39-">Iso'</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a) (f a) <a href="src/Linear-Affine.html#_Point" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:origin" class="def">origin</a> :: (<a href="Linear-Vector.html#t:Additive">Additive</a> f, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Linear-Affine.html#t:Point">Point</a> f a <a href="src/Linear-Affine.html#origin" class="link">Source</a></p><div class="doc"><p>Vector spaces have origins.</p></div></div><div class="top"><p class="src"><a name="v:relative" class="def">relative</a> :: (<a href="Linear-Vector.html#t:Additive">Additive</a> f, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Linear-Affine.html#t:Point">Point</a> f a -> <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Type.html#t:Iso-39-">Iso'</a> (<a href="Linear-Affine.html#t:Point">Point</a> f a) (f a) <a href="src/Linear-Affine.html#relative" class="link">Source</a></p><div class="doc"><p>An isomorphism between points and vectors, given a reference
point.</p></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.16.1</p></div></body></html>
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