C_      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTU V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                                                                                                                                            !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~           ! " # $ % & '!(!)!*!+!,!-!.!/!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+{+|+}+~+,,,,,--.////0001,,,22333333333333333333334444444444444444444444455555555555555555555555555555555666666666666666666666677777777777777777777 7 7 7 7 7777777777777777778 8!8"8#8$8%8&8'8(8)8*8+8,9-9.9/909192939495:6:7:8:9:::;:<:=:>:?:@:A:B:C:D:E:F:G:H;I;J;K;L;M;N;O;P;Q;R;S;T;U;V;W;X;Y;Z;[;\;];^;_;`;a;b;c;d;e;f;g;h;i;j;k;l;m;n;o;p;q;r;s;t;u;v;w;x;y;z;{;|;};~;;;;;;;;;;<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<==========================================================>> > > > > >>>>>>>>>>>>>>>>>>> >!>">#>$>%>&>'>(>)>*>+>,>->.>/>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?{?|?}?~????????????????????????@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA A A A A AAAAAAAAAABBBBBBBBB B!B"B#B$B%B&B'B(B)B*B+B,B-B.B/B0B1B2B3B4B5B6B7B8B9B:B;B<B=B>B?B@BABBBCBDBEBFBGBHBIBJBKBLBMBNBOBPBQBRBSBTBUBVCWCXCYCZC[C\C]C^C_C`CaCbCcCdCeCfCgChCiCjCkClCmCnCoCpCqCrCsCtCuCvCwCxCyCzC{C|C}C~CCCCCCCCCCCCCCCCCCCCCCCCCC/DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDHSafeST]q/An additive semigroup with idempotent addition.  a + a = aan additive abelian semigroup a + b = b + aTpartitionWith f c returns a list containing f a b for each a b such that a + b = c,  (a + b) + c = a + (b + c) sinnum 1 a = a sinnum (2 * n) a = sinnum n a + sinnum n a sinnum (2 * n + 1) a = sinnum n a + sinnum n a + asinnum1p n r = sinnum (1 + n) r    6Safe;<=>?STs1 ?An additive monoid zero + a = a = a + zeroJ?An associative algebra built with a free module over a semiringLdA pair of an additive abelian semigroup, and a multiplicative semigroup, with the distributive laws: a(b + c) = ab + ac -- left distribution (we are a LeftNearSemiring) (a + b)c = ac + bc -- right distribution (we are a [Right]NearSemiring)WCommon notation includes the laws for additive and multiplicative identity in semiring.If you want that, look at Rig instead.'Ideally we'd use the cyclic definition: ^class (LeftModule r r, RightModule r r, Additive r, Abelian r, Multiplicative r) => Semiring r[to enforce that every semiring r is an r-module over itself, but Haskell doesn't like that.MA multiplicative semigroupThe tensor algebraThe tensor algebra1the free commutative coalgebra over a set and Int?the free commutative coalgebra over a set and a given semigroup,the free commutative band coalgebra over Int#the free commutative band coalgebraThe tensor Hopf algebraThe tensor Hopf algebra0Every coalgebra gives rise to an algebra by vector space duality classically. Sadly, it requires vector space duality, which we cannot use constructively. The dual argument only relies in the fact that any constructive coalgebra can only inspect a finite number of coefficients, which we CAN exploit.?@ABCDEFGHIJKLMNOPQRSTMNOPRQLFGDEC?@ABSTJKHI?@ABDEFGHIJKMNOPE7G7N7O8Safe;<=>?STt67Safexb`factorWith f c` returns a non-empty list containing `f a b` for all `a, b` such that `a * b = c`.^Results of factorWith f 0 are undefined and may result in either an error or an infinite list.Safe;=>?~?HA bialgebra is both a unital algebra and counital coalgebra where the K and ) are compatible in some sense with the I and . That is to say that K and 8 are a coalgebra homomorphisms or (equivalently) that I and  are an algebra homomorphisms.HAn associative unital algebra over a semiring, built using a free module      8Safe;=>?A7;An multiplicative semigroup with idempotent multiplication.  a * a = a456789789654Safe;=>?O>A HopfAlgebra algebra on a semiring, where the module is free.When antipode . antipode = idM and antipode is an antihomomorphism then we are an InvolutiveBialgebra with inv = antipode as wellOPOPOP Safe;=>?LUVW[YXZWXYZ[UVUVWXYZ[Y7Z7[8 Safe;=>?STe&A commutative multiplicative semigroupbcdeedcb Safe;=>?STo  adjoint = id'adjoint (x + y) = adjoint x + adjoint yAn semigroup with involution 'adjoint a * adjoint b = adjoint (b * a)  ESafe"789789 Safea rectangular band is a nowhere commutative semigroup. That is to say, if ab = ba then a = b. From this it follows classically that aa = a and that such a band is isomorphic to the following structure SafeAb is an associate of a if there exists a unit u such that b = a*uTThis relationship is symmetric because if u is a unit, u^-1 exists and is a unit, so b*u^-1 = a*u*u^-1 = aSafe>  SafeSafe;=00FSafe>CDEFGFGDECSafe 27643958:; 23456789:;23456789:SafeO(z + x <= z + y = x <= y = x + z <= y + zOOSafe3XYXYXYSafenononoSafeNone1;=>?KOvSafe3A Ring without (n)egationSafet:NB: we're using the boolean semiring, not the boolean ringSafe;=>?SafeOSafe;="A Ring without an identity.SafebSafeSafe;=SafeS None*< !`Additive.(+)` default definitionGH default definitionIJ default definitionIK default definitionLM default definition `Group.(-)` default definition!LN default definition"LO default definition#'`Multiplicative.(*)` default definition$PQ default definition%RS default definition&TU default definition  !"#$%&  !"#$%&!Safe;<=>?'ILinear functionals from elements of an (infinite) free module to a scalar1SconvolveM antipodeM return = convolveM return antipodeM = comultM >=> uncurry joinM '()*+,-./01 '()-+,*/01.'())0"SafeKMLKLMKLM#Safe OQPOPQOPQ$Safe}STSTST%SafeVWVWVW&SafeYZYZYZ'Safep\]^\]^\]^(Safe1;=>?` the dual incidence algebra basis`abc`abc`a)Safe1;=>?klmnklmnklVSafew*Safev,A zero-product semiring has no zero divisors "a * b = 0 implies a == 0 || b == 0vv+Safe7Cz{|}z{{|}z{{WSafe7;=Euclidean (degree) function on r.Division algorithm. a  b) calculates quotient and remainder of a divided by b.>let (q, r) = divide a p in p*q + r == a && degree r < degree q8An integral domain is a commutative domain in which 1"`0.+(Integral) domain is the integral semiring.Extended euclidean algorithm.>euclid f g == xs ==> all (\(r, s, t) -> r == f * s + g * t) xselements divided bydivisorquotient and remainder77777.Safe-Safe,0Safe;=,SafeList of  (m_i, v_i)f with f = v_i (mod v_i) 2Safe;=bNone ?@ABCDEFGHIJKLMNOPQST  46789OPUVW[YXZbcde027643958:O !"#$%&'()*+,-./01  T?@ABSMNOPQe  789WXYZ[L0FGDECJKHI64dbcUVOP23456789:O !"#$%&'()-+,*/01.3None;=>?4None;=>?<The free Ring given a Rng obtained by adjoining Z, such that RngRing r = n*1 + r!This ring is commonly denoted r^.(The rng homomorphism from r to RngRing rigiven a rng homomorphism from a rng r into a ring s, liftRngHom yields a ring homomorphism from the ring `r^` into s.5None;=>?* *http://en.wikipedia.org/wiki/Opposite_ring6None;=>?[The endomorphism ring of an abelian group or the endomorphism semiring of an abelian monoid .http://en.wikipedia.org/wiki/Endomorphism_ring7None;=>?FT~Hlinear maps from elements of a free module to another free module over r >f $# x + y = (f $# x) + (f $# y) f $# (r .* x) = r .* (f $# x) Map r b a; represents a linear mapping from a free module with basis a over r to a free module with basis b over r.\Note well the reversed direction of the arrow, due to the contravariance of change of basis!]This way enables we can employ arbitrary pure functions as linear maps by lifting them using {, or build them by using the monad instance for Map r b. As a consequence Map is an instance of, well, almost everything.-extract a linear functional from a linear map(inefficiently) combine a linear combination of basis vectors to make a map. arrMap :: (Monoidal r, Semiring r) => (b -> [(r, a)]) -> Map r b a arrMap f = Map $ k b -> sum [ r * k a | (r, a) <- f b ]Dconvolution given an associative algebra and coassociative coalgebra  008None>?M ! ! !9NoneЪ,-.,-.,-.:None05 An element x is nilpotent if there exists n s.t.  pow1p x n is zero.565656;None 1;=>?FSTKMLHIJKLKLMJKLHIHIJKL<None 1;=>?FSTՃ/Cayley-Dickson quaternion isomorphism (one way) dual quaternion comultiplicationthe trivial diagonal algebraSTYZ\]^STYZ\]^=None 1;=>?FT&the hyperbolic trigonometric coalgebrathe trivial diagonal algebraOQPOPQ>None1;=>?FKOSTV              ?None 1;=>?FTY#dual number basis, D^2 = 0. D /= 0. STVWWXY[Z STVWYZ[WXWXYZ[@None 1;=>?FST݁/Cayley-Dickson quaternion isomorphism (one way)the trivial diagonal coalgebrathe quaternion algebraSTYZ\]^STYZ\]^ANone 1;=>?FTޯOQPOPQBNone 1;=>?FT!#dual number basis, D^2 = 0. D /= 0. STVW STVWCNone 1;=>?FST]2half of the Cayley-Dickson quaternion isomorphism STYZVWXYZ[\] STYZXYZVW[\]VWXYZ1Safe;=/SafeDSafe%*>?VConvenient synonym for .Fraction field k(D) of  domain D.7XYZ[\]^G_H`abcdefghijklmnopqrstuvwxyz{|}~IJK      !"#$%&'()*+,-./01234567L8MNO9:;<=>?@ABCDEFGHIJKLMNOPQRSTUVPQWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                                                                                                                              ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P QRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~RS      !"#$%&'()*+,-./012345678TU9:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abc d e f g h i j k l m n o!p!p!q!r!s!t!u!v!w!x!y!z!{!|!}!~!!!!!!!!!!!!!!!!!!!!""""####$$$%%%&&&''''((((((((((()))))))))))****+++++WWWWWWWWWWWWWWWWW,,22333333333333333333334444444444444444444444455555555 5 5 5 5 5555555555555555555 5!6"6"6#6$6%6&6'6(6)6*6+6,6-6.6/60616263646566777778797:7;7<7=7>7?7@7A7B7C7D7E7F7G7H7I7J7K7L7M7N7O7P7Q7R7S7T7U7V7W7X7Y7Z7[7\7]7^7_8`8`8a8b8c8d8e8f8g8h8i8j8k9l9l9m9n9o9p9q9r9s: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>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>{>|>}>~>>>>>>>>>>>>>>???????????????????????????????????????????????????????????????@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ A A A A A AAAAAAAAAAAAAAAAAAAA A!A"A#A$A%A&A'A(A)A*A+A,A-A.A/A0A1A2A3A4A5A6A7A8A9A:A;A<A=A>A?A@AAABACBDBDBEBBBFBGBHBIBJBKBLBMBBBNBOBPBQBRBSBTBUBVBWBXBYBZB[B\B]B^B_B`BaBbBcBdBeBfBgBhBiBjBkBlBmBnBoBpBqBrBsBtBuBvBwBxByBzB{B|B}C~C~CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC/DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDX7D$algebra-4.3.1-8c9ZfhrauCWH0rnRcYpoMkNumeric.AlgebraNumeric.Additive.ClassNumeric.Algebra.ClassNumeric.Additive.GroupNumeric.Algebra.FactorableNumeric.Algebra.UnitalNumeric.Algebra.IdempotentNumeric.Algebra.HopfNumeric.Algebra.DivisionNumeric.Algebra.CommutativeNumeric.Algebra.InvolutiveNumeric.Band.RectangularNumeric.Decidable.AssociatesNumeric.Decidable.UnitsNumeric.Decidable.ZeroNumeric.Dioid.ClassNumeric.Order.ClassNumeric.Order.AdditiveNumeric.Partial.SemigroupNumeric.Partial.MonoidNumeric.Partial.GroupNumeric.Coalgebra.CategoricalNumeric.Rig.ClassNumeric.Rig.CharacteristicNumeric.Quadrance.ClassNumeric.Rig.OrderedNumeric.Rng.ClassNumeric.Ring.ClassNumeric.Ring.LocalNumeric.Ring.DivisionNumeric.Order.LocallyFiniteNumeric.Module.RepresentableNumeric.Covector%Numeric.Coalgebra.Trigonometric.Class"Numeric.Coalgebra.Hyperbolic.Class#Numeric.Algebra.Distinguished.ClassNumeric.Algebra.Dual.ClassNumeric.Algebra.Complex.Class Numeric.Algebra.Quaternion.ClassNumeric.Coalgebra.IncidenceNumeric.Algebra.IncidenceNumeric.Semiring.ZeroProduct%Numeric.Algebra.Unital.UnitNormalFormNumeric.Domain.EuclideanNumeric.Domain.PIDNumeric.Domain.UFDNumeric.Domain.GCDNumeric.Domain.IntegralNumeric.Domain.ClassNumeric.Field.ClassNumeric.Rng.ZeroNumeric.Ring.RngNumeric.Ring.OppositeNumeric.Ring.Endomorphism Numeric.Map Numeric.Log Numeric.ExpNumeric.Decidable.NilpotentNumeric.Coalgebra.TrigonometricNumeric.Coalgebra.QuaternionNumeric.Coalgebra.HyperbolicNumeric.Coalgebra.GeometricNumeric.Coalgebra.DualNumeric.Algebra.QuaternionNumeric.Algebra.HyperbolicNumeric.Algebra.DualNumeric.Algebra.ComplexNumeric.Field.FractionNumeric.Band.ClassNumeric.Module.ClassAdditivesinnum1pMonoidalzerosinnumGroupnegatesubtracttimesUnitaloneRig fromNaturalRing fromIntegerNumeric.Semiring.InvolutiveNumeric.Domain.Internalbase GHC.NaturalNatural IdempotentAbelian Partitionable partitionWith+sumWith1sum1sinnum1pIdempotent$fAdditive(,,,,)$fAdditive(,,,)$fAdditive(,,) $fAdditive(,) $fAdditive()$fAdditiveWord64$fAdditiveWord32$fAdditiveWord16$fAdditiveWord8$fAdditiveWord$fAdditiveInt64$fAdditiveInt32$fAdditiveInt16$fAdditiveInt8 $fAdditiveInt$fAdditiveInteger$fAdditiveNatural$fAdditiveBool$fAdditive(->)$fPartitionable(,,,,)$fPartitionable(,,,)$fPartitionable(,,)$fPartitionable(,)$fPartitionable()$fPartitionableNatural$fPartitionableBool$fAbelian(,,,,)$fAbelian(,,,) $fAbelian(,,) $fAbelian(,)$fAbelianWord64$fAbelianWord32$fAbelianWord16$fAbelianWord8 $fAbelianWord$fAbelianInt64$fAbelianInt32$fAbelianInt16 $fAbelianInt8 $fAbelianInt$fAbelianNatural$fAbelianInteger $fAbelianBool $fAbelian() $fAbelian(->)$fIdempotent(,,,,)$fIdempotent(,,,)$fIdempotent(,,)$fIdempotent(,)$fIdempotent(->)$fIdempotentBool$fIdempotent()sumWithModule RightModule*. LeftModule.* CoalgebracomultAlgebramultSemiringMultiplicative*pow1p productWith1product1 pow1pIntegralsumsinnumIdempotent$fMultiplicative(,,,,)$fMultiplicative(,,,)$fMultiplicative(,,)$fMultiplicative(,)$fMultiplicative()$fMultiplicativeWord64$fMultiplicativeWord32$fMultiplicativeWord16$fMultiplicativeWord8$fMultiplicativeWord$fMultiplicativeInt64$fMultiplicativeInt32$fMultiplicativeInt16$fMultiplicativeInt8$fMultiplicativeInt$fMultiplicativeInteger$fMultiplicativeNatural$fMultiplicativeBool$fSemiring(,,,,)$fSemiring(,,,)$fSemiring(,,) $fSemiring(,) $fSemiring()$fSemiringWord64$fSemiringWord32$fSemiringWord16$fSemiringWord8$fSemiringWord$fSemiringInt64$fSemiringInt32$fSemiringInt16$fSemiringInt8 $fSemiringInt$fSemiringBool$fSemiringNatural$fSemiringInteger$fAlgebrar(,,,,)$fAlgebrar(,,,)$fAlgebrar(,,) $fAlgebrar(,)$fAlgebrarIntSet $fAlgebrarSet $fAlgebrar() $fAlgebrarSeq $fAlgebrar[] $fAlgebra()a$fSemiring(->)$fMultiplicative(->)$fCoalgebrarIntMap$fCoalgebrarMap$fCoalgebrarIntSet$fCoalgebrarSet$fCoalgebrarSeq$fCoalgebrar[]$fCoalgebrar(,,,,)$fCoalgebrar(,,,)$fCoalgebrar(,,)$fCoalgebrar(,)$fCoalgebrar()$fCoalgebrar(->)$fLeftModuler(,,,,)$fLeftModuler(,,,)$fLeftModuler(,,)$fLeftModuler(,)$fLeftModule()m$fLeftModuler(->)$fLeftModuler()$fLeftModuleIntegerWord64$fLeftModuleNaturalWord64$fLeftModuleIntegerWord32$fLeftModuleNaturalWord32$fLeftModuleIntegerWord16$fLeftModuleNaturalWord16$fLeftModuleIntegerWord8$fLeftModuleNaturalWord8$fLeftModuleIntegerWord$fLeftModuleNaturalWord$fLeftModuleIntegerInt64$fLeftModuleNaturalInt64$fLeftModuleIntegerInt32$fLeftModuleNaturalInt32$fLeftModuleIntegerInt16$fLeftModuleNaturalInt16$fLeftModuleIntegerInt8$fLeftModuleNaturalInt8$fLeftModuleIntegerInt$fLeftModuleNaturalInt$fLeftModuleIntegerInteger$fLeftModuleNaturalInteger$fLeftModuleNaturalNatural$fLeftModuleNaturalBool$fRightModuler(,,,,)$fRightModuler(,,,)$fRightModuler(,,)$fRightModuler(,)$fRightModule()m$fRightModuler(->)$fRightModuler()$fRightModuleIntegerWord64$fRightModuleNaturalWord64$fRightModuleIntegerWord32$fRightModuleNaturalWord32$fRightModuleIntegerWord16$fRightModuleNaturalWord16$fRightModuleIntegerWord8$fRightModuleNaturalWord8$fRightModuleIntegerWord$fRightModuleNaturalWord$fRightModuleIntegerInt64$fRightModuleNaturalInt64$fRightModuleIntegerInt32$fRightModuleNaturalInt32$fRightModuleIntegerInt16$fRightModuleNaturalInt16$fRightModuleIntegerInt8$fRightModuleNaturalInt8$fRightModuleIntegerInt$fRightModuleNaturalInt$fRightModuleIntegerInteger$fRightModuleNaturalInteger$fRightModuleNaturalNatural$fRightModuleNaturalBool $fModulerm$fMonoidal(,,,,)$fMonoidal(,,,)$fMonoidal(,,) $fMonoidal(,) $fMonoidal()$fMonoidal(->)$fMonoidalWord64$fMonoidalWord32$fMonoidalWord16$fMonoidalWord8$fMonoidalWord$fMonoidalInt64$fMonoidalInt32$fMonoidalInt16$fMonoidalInt8 $fMonoidalInt$fMonoidalInteger$fMonoidalNatural$fMonoidalBool- $fGroup(,,,,) $fGroup(,,,) $fGroup(,,) $fGroup(,) $fGroup() $fGroupWord64 $fGroupWord32 $fGroupWord16 $fGroupWord8 $fGroupWord $fGroupInt64 $fGroupInt32 $fGroupInt16 $fGroupInt8 $fGroupInt$fGroupInteger $fGroup(->) Factorable factorWith$fFactorable(,,,,)$fFactorable(,,,)$fFactorable(,,)$fFactorable(,)$fFactorable()$fFactorableBool BialgebraCounitalCoalgebracounit UnitalAlgebraunitpow productWithproduct$fUnital(,,,,) $fUnital(,,,) $fUnital(,,) $fUnital(,) $fUnital()$fUnitalWord64$fUnitalWord32$fUnitalWord16 $fUnitalWord8 $fUnitalWord$fUnitalNatural $fUnitalInt64 $fUnitalInt32 $fUnitalInt16 $fUnitalInt8 $fUnitalInt$fUnitalInteger $fUnitalBool$fUnitalAlgebrarSeq$fUnitalAlgebrar[]$fUnitalAlgebrar(,,,,)$fUnitalAlgebrar(,,,)$fUnitalAlgebrar(,,)$fUnitalAlgebrar(,)$fUnitalAlgebrar() $fUnital(->)$fCounitalCoalgebrarSeq$fCounitalCoalgebrar[]$fCounitalCoalgebrar(,,,,)$fCounitalCoalgebrar(,,,)$fCounitalCoalgebrar(,,)$fCounitalCoalgebrar(,)$fCounitalCoalgebrar()$fCounitalCoalgebrar(->)$fBialgebrarSeq$fBialgebrar[]$fBialgebrar(,,,,)$fBialgebrar(,,,)$fBialgebrar(,,)$fBialgebrar(,)$fBialgebrar()IdempotentBialgebraIdempotentCoalgebraIdempotentAlgebraBand pow1pBandpowBand $fBand(,,,,) $fBand(,,,) $fBand(,,) $fBand(,) $fBandBool$fBand()$fIdempotentAlgebrar(,,,,)$fIdempotentAlgebrar(,,,)$fIdempotentAlgebrar(,,)$fIdempotentAlgebrar(,)$fIdempotentAlgebrar()$fIdempotentAlgebrarIntSet$fIdempotentAlgebrarSet$fIdempotentCoalgebrar(,,,,)$fIdempotentCoalgebrar(,,,)$fIdempotentCoalgebrar(,,)$fIdempotentCoalgebrar(,)$fIdempotentCoalgebrar()$fIdempotentCoalgebrarIntSet$fIdempotentCoalgebrarSet$fIdempotentBialgebrarh HopfAlgebraantipode$fHopfAlgebrar(,,,,)$fHopfAlgebrar(,,,)$fHopfAlgebrar(,,)$fHopfAlgebrar(,)DivisionAlgebra recipriocalDivisionrecip/\\^$fDivision(,,,,)$fDivision(,,,)$fDivision(,,) $fDivision(,) $fDivision()$fDivision(->)CommutativeBialgebraCocommutativeCoalgebraCommutativeAlgebra Commutative$fCommutative(,,,,)$fCommutative(,,,)$fCommutative(,,)$fCommutative(,)$fCommutativeWord64$fCommutativeWord32$fCommutativeWord16$fCommutativeWord8$fCommutativeWord$fCommutativeNatural$fCommutativeInt64$fCommutativeInt32$fCommutativeInt16$fCommutativeInt8$fCommutativeInt$fCommutativeInteger$fCommutativeBool$fCommutative()$fCommutativeAlgebrarIntSet$fCommutativeAlgebrarSet$fCommutativeAlgebrar(,,,,)$fCommutativeAlgebrar(,,,)$fCommutativeAlgebrar(,,)$fCommutativeAlgebrar(,)$fCommutativeAlgebrar()$fCommutative(->)$fCocommutativeCoalgebrarIntMap$fCocommutativeCoalgebrarMap$fCocommutativeCoalgebrarIntSet$fCocommutativeCoalgebrarSet$fCocommutativeCoalgebrar(,,,,)$fCocommutativeCoalgebrar(,,,)$fCocommutativeCoalgebrar(,,)$fCocommutativeCoalgebrar(,)$fCocommutativeCoalgebrar()$fCocommutativeCoalgebrar(->)$fCommutativeBialgebrarhTriviallyInvolutiveBialgebraInvolutiveBialgebraTriviallyInvolutiveCoalgebraInvolutiveCoalgebracoinvTriviallyInvolutiveAlgebraInvolutiveAlgebrainvTriviallyInvolutiveInvolutiveSemiringInvolutiveMultiplicationadjoint $fInvolutiveMultiplication(,,,,)$fInvolutiveMultiplication(,,,)$fInvolutiveMultiplication(,,)$fInvolutiveMultiplication(,)$fInvolutiveMultiplication() $fInvolutiveMultiplicationWord64 $fInvolutiveMultiplicationWord32 $fInvolutiveMultiplicationWord16$fInvolutiveMultiplicationWord8!$fInvolutiveMultiplicationNatural$fInvolutiveMultiplicationWord$fInvolutiveMultiplicationBool$fInvolutiveMultiplicationInt64$fInvolutiveMultiplicationInt32$fInvolutiveMultiplicationInt16$fInvolutiveMultiplicationInt8!$fInvolutiveMultiplicationInteger$fInvolutiveMultiplicationInt$fInvolutiveSemiring(,,,,)$fInvolutiveSemiring(,,,)$fInvolutiveSemiring(,,)$fInvolutiveSemiring(,)$fInvolutiveSemiringWord64$fInvolutiveSemiringWord32$fInvolutiveSemiringWord16$fInvolutiveSemiringWord8$fInvolutiveSemiringWord$fInvolutiveSemiringNatural$fInvolutiveSemiringInt64$fInvolutiveSemiringInt32$fInvolutiveSemiringInt16$fInvolutiveSemiringInt8$fInvolutiveSemiringInt$fInvolutiveSemiringInteger$fInvolutiveSemiringBool$fInvolutiveSemiring()$fTriviallyInvolutive(,,,,)$fTriviallyInvolutive(,,,)$fTriviallyInvolutive(,,)$fTriviallyInvolutive(,)$fTriviallyInvolutive()$fTriviallyInvolutiveWord64$fTriviallyInvolutiveWord32$fTriviallyInvolutiveWord16$fTriviallyInvolutiveWord8$fTriviallyInvolutiveNatural$fTriviallyInvolutiveWord$fTriviallyInvolutiveInt64$fTriviallyInvolutiveInt32$fTriviallyInvolutiveInt16$fTriviallyInvolutiveInt8$fTriviallyInvolutiveInteger$fTriviallyInvolutiveInt$fTriviallyInvolutiveBool$fInvolutiveAlgebrar(,,,,)$fInvolutiveAlgebrar(,,,)$fInvolutiveAlgebrar(,,)$fInvolutiveAlgebrar(,)$fInvolutiveAlgebrar()$fInvolutiveMultiplication(->)#$fTriviallyInvolutiveAlgebrar(,,,,)"$fTriviallyInvolutiveAlgebrar(,,,)!$fTriviallyInvolutiveAlgebrar(,,) $fTriviallyInvolutiveAlgebrar(,)$fTriviallyInvolutiveAlgebrar()$fTriviallyInvolutive(->)$fInvolutiveCoalgebrar(,,,,)$fInvolutiveCoalgebrar(,,,)$fInvolutiveCoalgebrar(,,)$fInvolutiveCoalgebrar(,)$fInvolutiveCoalgebrar()%$fTriviallyInvolutiveCoalgebrar(,,,,)$$fTriviallyInvolutiveCoalgebrar(,,,)#$fTriviallyInvolutiveCoalgebrar(,,)"$fTriviallyInvolutiveCoalgebrar(,)!$fTriviallyInvolutiveCoalgebrar()$fInvolutiveBialgebrarh $fTriviallyInvolutiveBialgebrarhRect $fBandRect$fMultiplicativeRect$fSemigroupoidTYPERect$fEqRect $fOrdRect $fShowRect $fReadRectDecidableAssociates isAssociateisAssociateIntegralisAssociateWhole$fDecidableAssociates(,,,,)$fDecidableAssociates(,,,)$fDecidableAssociates(,,)$fDecidableAssociates(,)$fDecidableAssociates()$fDecidableAssociatesWord64$fDecidableAssociatesWord32$fDecidableAssociatesWord16$fDecidableAssociatesWord8$fDecidableAssociatesWord$fDecidableAssociatesNatural$fDecidableAssociatesInt64$fDecidableAssociatesInt32$fDecidableAssociatesInt16$fDecidableAssociatesInt8$fDecidableAssociatesInt$fDecidableAssociatesInteger$fDecidableAssociatesBoolDecidableUnits recipUnitisUnit^?recipUnitIntegralrecipUnitWhole$fDecidableUnits(,,,,)$fDecidableUnits(,,,)$fDecidableUnits(,,)$fDecidableUnits(,)$fDecidableUnits()$fDecidableUnitsWord64$fDecidableUnitsWord32$fDecidableUnitsWord16$fDecidableUnitsWord8$fDecidableUnitsWord$fDecidableUnitsNatural$fDecidableUnitsInt64$fDecidableUnitsInt32$fDecidableUnitsInt16$fDecidableUnitsInt8$fDecidableUnitsInt$fDecidableUnitsInteger$fDecidableUnitsBool DecidableZeroisZero$fDecidableZero(,,,,)$fDecidableZero(,,,)$fDecidableZero(,,)$fDecidableZero(,)$fDecidableZero()$fDecidableZeroWord64$fDecidableZeroWord32$fDecidableZeroWord16$fDecidableZeroWord8$fDecidableZeroWord$fDecidableZeroNatural$fDecidableZeroInt64$fDecidableZeroInt32$fDecidableZeroInt16$fDecidableZeroInt8$fDecidableZeroInt$fDecidableZeroInteger$fDecidableZeroBoolDioid$fDioidrOrder<~<>~>~~/~order comparableorderOrd $fOrder(,,,,) $fOrder(,,,) $fOrder(,,) $fOrder(,) $fOrder() $fOrderSet $fOrderWord64 $fOrderWord32 $fOrderWord16 $fOrderWord8 $fOrderWord$fOrderNatural $fOrderInt64 $fOrderInt32 $fOrderInt16 $fOrderInt8 $fOrderInt$fOrderInteger $fOrderBool AdditiveOrder$fAdditiveOrder(,,,,)$fAdditiveOrder(,,,)$fAdditiveOrder(,,)$fAdditiveOrder(,)$fAdditiveOrder()$fAdditiveOrderBool$fAdditiveOrderNatural$fAdditiveOrderIntegerPartialSemigrouppadd$fPartialSemigroupEither$fPartialSemigroup(,,,,)$fPartialSemigroup(,,,)$fPartialSemigroup(,,)$fPartialSemigroup(,)$fPartialSemigroup()$fPartialSemigroupBool$fPartialSemigroupMaybe$fPartialSemigroupWord64$fPartialSemigroupWord32$fPartialSemigroupWord16$fPartialSemigroupWord8$fPartialSemigroupWord$fPartialSemigroupInt64$fPartialSemigroupInt32$fPartialSemigroupInt16$fPartialSemigroupInt8$fPartialSemigroupNatural$fPartialSemigroupInteger$fPartialSemigroupInt PartialMonoidpzero$fPartialMonoid(,,,,)$fPartialMonoid(,,,)$fPartialMonoid(,,)$fPartialMonoid(,)$fPartialMonoidMaybe$fPartialMonoid()$fPartialMonoidWord64$fPartialMonoidWord32$fPartialMonoidWord16$fPartialMonoidWord8$fPartialMonoidWord$fPartialMonoidInt64$fPartialMonoidInt32$fPartialMonoidInt16$fPartialMonoidInt8$fPartialMonoidNatural$fPartialMonoidInteger$fPartialMonoidInt$fPartialMonoidBool PartialGrouppnegatepminus psubtract$fPartialGroup(,,,,)$fPartialGroup(,,,)$fPartialGroup(,,)$fPartialGroup(,)$fPartialGroup()$fPartialGroupNatural$fPartialGroupWord64$fPartialGroupWord32$fPartialGroupWord16$fPartialGroupWord8$fPartialGroupWord$fPartialGroupInt64$fPartialGroupInt32$fPartialGroupInt16$fPartialGroupInt8$fPartialGroupInteger$fPartialGroupIntMorphism$fCounitalCoalgebrarMorphism$fCoalgebrarMorphism $fEqMorphism $fOrdMorphism$fShowMorphism$fReadMorphism$fPartialSemigroupMorphism$fPartialMonoidMorphism$fPartialGroupMorphism$fDataMorphism $fRig(,,,,) $fRig(,,,) $fRig(,,)$fRig(,)$fRig() $fRigWord64 $fRigWord32 $fRigWord16 $fRigWord8 $fRigWord $fRigInt64 $fRigInt32 $fRigInt16 $fRigInt8$fRigInt $fRigBool $fRigNatural $fRigIntegerCharacteristiccharcharIntcharWord$fCharacteristic(,,,,)$fCharacteristic(,,,)$fCharacteristic(,,)$fCharacteristic(,)$fCharacteristic()$fCharacteristicWord64$fCharacteristicWord32$fCharacteristicWord16$fCharacteristicWord8$fCharacteristicWord$fCharacteristicInt64$fCharacteristicInt32$fCharacteristicInt16$fCharacteristicInt8$fCharacteristicInt$fCharacteristicNatural$fCharacteristicInteger$fCharacteristicBool Quadrance quadrance$fQuadrancerWord64$fQuadrancerWord32$fQuadrancerWord16$fQuadrancerWord8$fQuadrancerInt64$fQuadrancerInt32$fQuadrancerInt16$fQuadrancerInt8$fQuadrancerInteger$fQuadrancerNatural$fQuadrancerWord$fQuadrancerInt$fQuadrancerBool$fQuadrancer(,,,,)$fQuadrancer(,,,)$fQuadrancer(,,)$fQuadrancer(,)$fQuadrancer()$fQuadrance()a OrderedRig$fOrderedRig(,,,,)$fOrderedRig(,,,)$fOrderedRig(,,)$fOrderedRig(,)$fOrderedRig()$fOrderedRigBool$fOrderedRigNatural$fOrderedRigIntegerRng$fRngr fromIntegral $fRing(,,,,) $fRing(,,,) $fRing(,,) $fRing(,)$fRing() $fRingWord64 $fRingWord32 $fRingWord16 $fRingWord8 $fRingWord $fRingInt64 $fRingInt32 $fRingInt16 $fRingInt8 $fRingInt $fRingInteger LocalRing DivisionRing$fDivisionRingrLocallyFiniteOrderrange rangeSizemoebiusInversion$fLocallyFiniteOrder(,,,,)$fLocallyFiniteOrder(,,,)$fLocallyFiniteOrder(,,)$fLocallyFiniteOrder(,)$fLocallyFiniteOrder()$fLocallyFiniteOrderWord64$fLocallyFiniteOrderWord32$fLocallyFiniteOrderWord16$fLocallyFiniteOrderWord8$fLocallyFiniteOrderWord$fLocallyFiniteOrderInt64$fLocallyFiniteOrderInt32$fLocallyFiniteOrderInt16$fLocallyFiniteOrderInt8$fLocallyFiniteOrderInt$fLocallyFiniteOrderBool$fLocallyFiniteOrderSet$fLocallyFiniteOrderInteger$fLocallyFiniteOrderNaturaladdRep sinnum1pRepzeroRep sinnumRep negateRepminusRep subtractReptimesRepmulReponeRepfromNaturalRepfromIntegerRepCovector$*multMunitMcomultMcounitM convolveMinvMcoinvM antipodeM$fRightModulerCovector$fRightModuleCovectorCovector$fLeftModulerCovector$fLeftModuleCovectorCovector$fGroupCovector$fAbelianCovector$fMonoidalCovector$fBandCovector$fIdempotentCovector$fRingCovector $fRigCovector$fUnitalCovector$fSemiringCovector$fCommutativeCovector$fMultiplicativeCovector$fAdditiveCovector$fMonadPlusCovector$fAlternativeCovector$fPlusCovector $fAltCovector$fMonadCovector$fBindCovector$fApplicativeCovector$fApplyCovector$fFunctorCovector Trigonometriccossin$fTrigonometricCovector Hyperboliccoshsinh$fHyperbolicCovector Distinguishede$fDistinguishedCovector Infinitesimald$fInfinitesimalCovector Complicatedi$fComplicatedCovector Hamiltonianjk$fHamiltonianCovector Interval'zeta'moebius'$fCounitalCoalgebrarInterval'$fCoalgebrarInterval' $fEqInterval'$fOrdInterval'$fShowInterval'$fReadInterval'$fDataInterval'Intervalzetamoebius$fUnitalAlgebrarInterval$fAlgebrarInterval $fEqInterval $fOrdInterval$fShowInterval$fReadInterval$fDataIntervalZeroProductSemiring$fZeroProductSemiringBool$fZeroProductSemiringNatural$fZeroProductSemiringIntegerUnitNormalForm splitUnit normalize leadingUnit$fUnitNormalFormInteger EuclideandegreedividequotremPIDegcdUFD GCDDomaingcdreduceFractionlcmIntegralDomaindivides maybeQuotDomaineuclidprschineseRemainderField$fFielddZeroRng runZeroRng$fRightModuleIntegerZeroRng$fLeftModuleIntegerZeroRng$fRightModuleNaturalZeroRng$fLeftModuleNaturalZeroRng $fRngZeroRng$fCommutativeZeroRng$fSemiringZeroRng$fMultiplicativeZeroRng$fGroupZeroRng$fMonoidalZeroRng$fAbelianZeroRng$fIdempotentZeroRng$fAdditiveZeroRng $fEqZeroRng $fOrdZeroRng $fShowZeroRng $fReadZeroRngRngRing rngRingHom liftRngHom $fRingRngRing $fRigRngRing$fSemiringRngRing$fDivisionRngRing$fUnitalRngRing$fRightModuleRngRingRngRing$fLeftModuleRngRingRngRing$fCommutativeRngRing$fMultiplicativeRngRing$fGroupRngRing$fRightModuleIntegerRngRing$fLeftModuleIntegerRngRing$fMonoidalRngRing$fRightModuleNaturalRngRing$fLeftModuleNaturalRngRing$fAbelianRngRing$fAdditiveRngRing $fShowRngRing $fReadRngRingOpposite runOpposite$fRingOpposite $fRigOpposite$fSemiringOpposite$fDivisionOpposite$fUnitalOpposite$fBandOpposite$fIdempotentOpposite$fCommutativeOpposite$fMultiplicativeOpposite$fDecidableAssociatesOpposite$fDecidableUnitsOpposite$fDecidableZeroOpposite$fAbelianOpposite$fGroupOpposite$fRightModuleOppositeOpposite$fRightModulerOpposite$fLeftModulerOpposite$fLeftModuleOppositeOpposite$fMonoidalOpposite$fAdditiveOpposite$fTraversable1Opposite$fFoldable1Opposite$fTraversableOpposite$fFoldableOpposite$fFunctorOpposite $fOrdOpposite $fEqOpposite$fShowOpposite$fReadOppositeEndappEndtoEndfromEnd frobenius$fRightModulerEnd$fLeftModulerEnd$fRightModuleEndEnd$fLeftModuleEndEnd $fRingEnd$fRigEnd $fSemiringEnd$fCommutativeEnd $fUnitalEnd$fMultiplicativeEnd $fGroupEnd $fMonoidalEnd $fAbelianEnd $fAdditiveEnd $fMonoidEnd$fSemigroupEndMap$@ comultMapmultMap counitMapunitMap convolveMap antipodeMapcoinvMapinvMap $fRingMap$fRigMap$fCommutativeMap $fGroupMap $fAbelianMap $fMonoidalMap$fMonadPlusMap$fAlternativeMap $fPlusMap$fAltMap$fRightModulerMap$fRightModuleMapMap$fLeftModulerMap$fLeftModuleMapMap $fSemiringMap $fUnitalMap$fMultiplicativeMap $fAdditiveMap$fArrowChoiceMap$fArrowPlusMap$fArrowZeroMap$fMonadReaderbMap$fArrowApplyMap $fArrowMap $fMonadMap $fBindMap$fApplicativeMap $fApplyMap $fFunctorMap$fSemigroupoidTYPEMap$fCategoryTYPEMapLogrunLog$fPartitionableLog$fIdempotentLog $fAbelianLog $fGroupLog$fRightModuleIntegerLog$fLeftModuleIntegerLog $fMonoidalLog$fRightModuleNaturalLog$fLeftModuleNaturalLog $fAdditiveLogExprunExp$fFactorableExp $fBandExp$fCommutativeExp $fDivisionExp $fUnitalExp$fMultiplicativeExpDecidableNilpotent isNilpotent$fDecidableNilpotent(,,,,)$fDecidableNilpotent(,,,)$fDecidableNilpotent(,,)$fDecidableNilpotent(,)$fDecidableNilpotentWord64$fDecidableNilpotentWord32$fDecidableNilpotentWord16$fDecidableNilpotentWord8$fDecidableNilpotentInt64$fDecidableNilpotentInt32$fDecidableNilpotentInt16$fDecidableNilpotentInt8$fDecidableNilpotentInt$fDecidableNilpotentInteger$fDecidableNilpotentNatural$fDecidableNilpotentBool$fDecidableNilpotent()Trig TrigBasisCosSin$fCounitalCoalgebrakTrigBasis$fHopfAlgebrakTrigBasis$fInvolutiveCoalgebrakTrigBasis$fInvolutiveAlgebrakTrigBasis$fBialgebrakTrigBasis$fCoalgebrakTrigBasis$fUnitalAlgebrakTrigBasis$fAlgebrakTrigBasis$fTrigonometric(->)$fComplicated(->)$fDistinguished(->)$fTrigonometricTrigBasis$fComplicatedTrigBasis$fDistinguishedTrigBasis$fInvolutiveSemiringTrig$fInvolutiveMultiplicationTrig$fRightModuleTrigTrig$fLeftModuleTrigTrig $fRingTrig $fRigTrig $fUnitalTrig$fSemiringTrig$fCommutativeTrig$fMultiplicativeTrig$fPartitionableTrig$fIdempotentTrig $fAbelianTrig $fGroupTrig$fMonoidalTrig$fRightModulerTrig$fLeftModulerTrig$fAdditiveTrig$fTraversable1Trig$fFoldable1Trig$fTraversableTrig$fFoldableTrig$fMonadReaderTrigBasisTrig $fMonadTrig $fBindTrig$fApplicativeTrig $fApplyTrig $fFunctorTrig$fDistributiveTrig$fRepresentableTrig$fTrigonometricTrig$fComplicatedTrig$fDistinguishedTrig $fEqTrigBasis$fOrdTrigBasis$fShowTrigBasis$fReadTrigBasis$fEnumTrigBasis $fIxTrigBasis$fBoundedTrigBasis$fDataTrigBasis$fEqTrig $fShowTrig $fReadTrig $fDataTrig Quaternion'QuaternionBasis'E'I'J'K' complicate' scalarPart' vectorPart'$fHopfAlgebrarQuaternionBasis'&$fInvolutiveCoalgebrarQuaternionBasis'$$fInvolutiveAlgebrarQuaternionBasis'$fBialgebrarQuaternionBasis'$$fCounitalCoalgebrarQuaternionBasis'$fCoalgebrarQuaternionBasis' $fUnitalAlgebrarQuaternionBasis'$fAlgebrarQuaternionBasis'$fHamiltonian(->)$fHamiltonianQuaternionBasis'$fComplicatedQuaternionBasis'$fDistinguishedQuaternionBasis'$fDivisionQuaternion'$fQuadrancerQuaternion'%$fInvolutiveMultiplicationQuaternion'#$fRightModuleQuaternion'Quaternion'"$fLeftModuleQuaternion'Quaternion'$fRingQuaternion'$fRigQuaternion'$fUnitalQuaternion'$fSemiringQuaternion'$fMultiplicativeQuaternion'$fPartitionableQuaternion'$fIdempotentQuaternion'$fAbelianQuaternion'$fGroupQuaternion'$fMonoidalQuaternion'$fRightModulerQuaternion'$fLeftModulerQuaternion'$fAdditiveQuaternion'$fTraversable1Quaternion'$fFoldable1Quaternion'$fTraversableQuaternion'$fFoldableQuaternion'($fMonadReaderQuaternionBasis'Quaternion'$fMonadQuaternion'$fBindQuaternion'$fApplicativeQuaternion'$fApplyQuaternion'$fFunctorQuaternion'$fDistributiveQuaternion'$fRepresentableQuaternion'$fHamiltonianQuaternion'$fComplicatedQuaternion'$fDistinguishedQuaternion'$fEqQuaternionBasis'$fOrdQuaternionBasis'$fEnumQuaternionBasis'$fReadQuaternionBasis'$fShowQuaternionBasis'$fBoundedQuaternionBasis'$fIxQuaternionBasis'$fDataQuaternionBasis'$fEqQuaternion'$fShowQuaternion'$fReadQuaternion'$fDataQuaternion'Hyper HyperBasisCoshSinh$fHopfAlgebrakHyperBasis $fInvolutiveCoalgebrakHyperBasis$fInvolutiveAlgebrakHyperBasis$fBialgebrakHyperBasis$fCounitalCoalgebrakHyperBasis$fCoalgebrakHyperBasis$fUnitalAlgebrakHyperBasis$fAlgebrakHyperBasis$fHyperbolic(->)$fHyperbolicHyperBasis$fInvolutiveSemiringHyper$fInvolutiveMultiplicationHyper$fRightModuleHyperHyper$fLeftModuleHyperHyper $fRingHyper $fRigHyper $fUnitalHyper$fSemiringHyper$fCommutativeHyper$fMultiplicativeHyper$fPartitionableHyper$fIdempotentHyper$fAbelianHyper $fGroupHyper$fMonoidalHyper$fRightModulerHyper$fLeftModulerHyper$fAdditiveHyper$fTraversable1Hyper$fFoldable1Hyper$fTraversableHyper$fFoldableHyper$fMonadReaderHyperBasisHyper $fMonadHyper $fBindHyper$fApplicativeHyper $fApplyHyper$fFunctorHyper$fDistributiveHyper$fRepresentableHyper$fHyperbolicHyper$fEqHyperBasis$fOrdHyperBasis$fShowHyperBasis$fReadHyperBasis$fEnumHyperBasis$fIxHyperBasis$fBoundedHyperBasis$fDataHyperBasis $fEqHyper $fShowHyper $fReadHyper $fDataHyper Comultivector Eigenmetricmetric Eigenbasis euclidean antiEuclideanv BasisCobladerunBasisCobladegrade filterGradereversecliffordConjugategradeInversion geometricouter contractL contractRdothestenes liftProduct $fCounitalCoalgebrarBasisCoblade$fCoalgebrarBasisCoblade$fEigenmetricrEuclidean$fEigenbasisEuclidean$fEqBasisCoblade$fOrdBasisCoblade$fNumBasisCoblade$fBitsBasisCoblade$fEnumBasisCoblade$fIxBasisCoblade$fBoundedBasisCoblade$fShowBasisCoblade$fReadBasisCoblade$fRealBasisCoblade$fIntegralBasisCoblade$fAdditiveBasisCoblade$fAbelianBasisCoblade$fLeftModuleBasisCoblade$fRightModuleBasisCoblade$fMonoidalBasisCoblade$fMultiplicativeBasisCoblade$fUnitalBasisCoblade$fCommutativeBasisCoblade$fSemiringBasisCoblade$fRigBasisCoblade$fDecidableZeroBasisCoblade!$fDecidableAssociatesBasisCoblade$fDecidableUnitsBasisCoblade $fEqEuclidean$fOrdEuclidean$fShowEuclidean$fReadEuclidean$fNumEuclidean $fIxEuclidean$fEnumEuclidean$fRealEuclidean$fIntegralEuclidean$fDataEuclidean$fAdditiveEuclidean$fLeftModuleEuclidean$fRightModuleEuclidean$fMonoidalEuclidean$fAbelianEuclidean$fLeftModuleEuclidean0$fRightModuleEuclidean0$fGroupEuclidean$fMultiplicativeEuclidean$fTriviallyInvolutiveEuclidean#$fInvolutiveMultiplicationEuclidean$fInvolutiveSemiringEuclidean$fUnitalEuclidean$fCommutativeEuclidean$fSemiringEuclidean$fRigEuclidean$fRingEuclideanDual' DualBasis'ED$fHopfAlgebrakDualBasis' $fInvolutiveCoalgebrakDualBasis'$fInvolutiveAlgebrakDualBasis'$fBialgebrakDualBasis'$fCounitalCoalgebrakDualBasis'$fCoalgebrakDualBasis'$fUnitalAlgebrakDualBasis'$fAlgebrakDualBasis'$fInfinitesimal(->)$fInfinitesimalDualBasis'$fDistinguishedDualBasis'$fDivisionDual'$fQuadrancerDual'$fInvolutiveSemiringDual'$fInvolutiveMultiplicationDual'$fRightModuleDual'Dual'$fLeftModuleDual'Dual' $fRingDual' $fRigDual' $fUnitalDual'$fSemiringDual'$fCommutativeDual'$fMultiplicativeDual'$fPartitionableDual'$fIdempotentDual'$fAbelianDual' $fGroupDual'$fMonoidalDual'$fRightModulerDual'$fLeftModulerDual'$fAdditiveDual'$fTraversable1Dual'$fFoldable1Dual'$fTraversableDual'$fFoldableDual'$fMonadReaderDualBasis'Dual' $fMonadDual' $fBindDual'$fApplicativeDual' $fApplyDual'$fFunctorDual'$fDistributiveDual'$fRepresentableDual'$fInfinitesimalDual'$fDistinguishedDual'$fEqDualBasis'$fOrdDualBasis'$fShowDualBasis'$fReadDualBasis'$fEnumDualBasis'$fIxDualBasis'$fBoundedDualBasis'$fDataDualBasis' $fEqDual' $fShowDual' $fReadDual' $fDataDual' QuaternionQuaternionBasisIJK complicate scalarPart vectorPart$fHopfAlgebrarQuaternionBasis%$fInvolutiveCoalgebrarQuaternionBasis#$fInvolutiveAlgebrarQuaternionBasis$fBialgebrarQuaternionBasis#$fCounitalCoalgebrarQuaternionBasis$fCoalgebrarQuaternionBasis$fUnitalAlgebrarQuaternionBasis$fAlgebrarQuaternionBasis$fHamiltonianQuaternionBasis$fComplicatedQuaternionBasis$fDistinguishedQuaternionBasis$fDivisionQuaternion$fQuadrancerQuaternion$$fInvolutiveMultiplicationQuaternion!$fRightModuleQuaternionQuaternion $fLeftModuleQuaternionQuaternion$fRingQuaternion$fRigQuaternion$fUnitalQuaternion$fSemiringQuaternion$fMultiplicativeQuaternion$fPartitionableQuaternion$fIdempotentQuaternion$fAbelianQuaternion$fGroupQuaternion$fMonoidalQuaternion$fRightModulerQuaternion$fLeftModulerQuaternion$fAdditiveQuaternion$fTraversable1Quaternion$fFoldable1Quaternion$fTraversableQuaternion$fFoldableQuaternion&$fMonadReaderQuaternionBasisQuaternion$fMonadQuaternion$fBindQuaternion$fApplicativeQuaternion$fApplyQuaternion$fFunctorQuaternion$fDistributiveQuaternion$fRepresentableQuaternion$fHamiltonianQuaternion$fComplicatedQuaternion$fDistinguishedQuaternion$fEqQuaternionBasis$fOrdQuaternionBasis$fEnumQuaternionBasis$fReadQuaternionBasis$fShowQuaternionBasis$fBoundedQuaternionBasis$fIxQuaternionBasis$fDataQuaternionBasis$fEqQuaternion$fShowQuaternion$fReadQuaternion$fDataQuaternionHyper' HyperBasis'Cosh'Sinh'$fHopfAlgebrakHyperBasis'!$fInvolutiveCoalgebrakHyperBasis'$fInvolutiveAlgebrakHyperBasis'$fBialgebrakHyperBasis'$fCounitalCoalgebrakHyperBasis'$fCoalgebrakHyperBasis'$fUnitalAlgebrakHyperBasis'$fAlgebrakHyperBasis'$fHyperbolicHyperBasis'$fDivisionHyper'$fQuadrancerHyper'$fInvolutiveSemiringHyper' $fInvolutiveMultiplicationHyper'$fRightModuleHyper'Hyper'$fLeftModuleHyper'Hyper' $fRingHyper' $fRigHyper'$fUnitalHyper'$fSemiringHyper'$fCommutativeHyper'$fMultiplicativeHyper'$fPartitionableHyper'$fIdempotentHyper'$fAbelianHyper' $fGroupHyper'$fMonoidalHyper'$fRightModulerHyper'$fLeftModulerHyper'$fAdditiveHyper'$fTraversable1Hyper'$fFoldable1Hyper'$fTraversableHyper'$fFoldableHyper'$fMonadReaderHyperBasis'Hyper' $fMonadHyper' $fBindHyper'$fApplicativeHyper' $fApplyHyper'$fFunctorHyper'$fDistributiveHyper'$fRepresentableHyper'$fHyperbolicHyper'$fEqHyperBasis'$fOrdHyperBasis'$fShowHyperBasis'$fReadHyperBasis'$fEnumHyperBasis'$fIxHyperBasis'$fBoundedHyperBasis'$fDataHyperBasis' $fEqHyper' $fShowHyper' $fReadHyper' $fDataHyper'Dual DualBasis$fHopfAlgebrakDualBasis$fInvolutiveCoalgebrakDualBasis$fInvolutiveAlgebrakDualBasis$fBialgebrakDualBasis$fCounitalCoalgebrakDualBasis$fCoalgebrakDualBasis$fUnitalAlgebrakDualBasis$fAlgebrakDualBasis$fInfinitesimalDualBasis$fDistinguishedDualBasis$fDivisionDual$fQuadrancerDual$fInvolutiveSemiringDual$fInvolutiveMultiplicationDual$fRightModuleDualDual$fLeftModuleDualDual $fRingDual $fRigDual $fUnitalDual$fSemiringDual$fCommutativeDual$fMultiplicativeDual$fPartitionableDual$fIdempotentDual $fAbelianDual $fGroupDual$fMonoidalDual$fRightModulerDual$fLeftModulerDual$fAdditiveDual$fTraversable1Dual$fFoldable1Dual$fTraversableDual$fFoldableDual$fMonadReaderDualBasisDual $fMonadDual $fBindDual$fApplicativeDual $fApplyDual $fFunctorDual$fDistributiveDual$fRepresentableDual$fInfinitesimalDual$fDistinguishedDual $fEqDualBasis$fOrdDualBasis$fShowDualBasis$fReadDualBasis$fEnumDualBasis $fIxDualBasis$fBoundedDualBasis$fDataDualBasis$fEqDual $fShowDual $fReadDual $fDataDualComplex ComplexBasisrealPartimagPart uncomplicate$fHopfAlgebrakComplexBasis"$fInvolutiveCoalgebrakComplexBasis $fInvolutiveAlgebrakComplexBasis$fBialgebrakComplexBasis $fCounitalCoalgebrakComplexBasis$fCoalgebrakComplexBasis$fUnitalAlgebrakComplexBasis$fAlgebrakComplexBasis$fComplicatedComplexBasis$fDistinguishedComplexBasis$fDivisionComplex$fQuadrancerComplex$fInvolutiveSemiringComplex!$fInvolutiveMultiplicationComplex$fRightModuleComplexComplex$fLeftModuleComplexComplex $fRingComplex $fRigComplex$fUnitalComplex$fSemiringComplex$fCommutativeComplex$fMultiplicativeComplex$fPartitionableComplex$fIdempotentComplex$fAbelianComplex$fGroupComplex$fMonoidalComplex$fRightModulerComplex$fLeftModulerComplex$fAdditiveComplex$fTraversable1Complex$fFoldable1Complex$fTraversableComplex$fFoldableComplex $fMonadReaderComplexBasisComplex$fMonadComplex $fBindComplex$fApplicativeComplex$fApplyComplex$fFunctorComplex$fDistributiveComplex$fRepresentableComplex$fComplicatedComplex$fDistinguishedComplex$fEqComplexBasis$fOrdComplexBasis$fShowComplexBasis$fReadComplexBasis$fEnumComplexBasis$fIxComplexBasis$fBoundedComplexBasis$fDataComplexBasis $fEqComplex $fShowComplex $fReadComplex $fDataComplexgcd'RatioFraction% numerator denominator$fEuclideanFraction $fPIDFraction $fUFDFraction$fGCDDomainFraction$fIntegralDomainFraction$fUnitNormalFormFraction$fCharacteristicFraction $fRigFraction$fMultiplicativeFraction$fUnitalFraction$fAdditiveFraction$fRightModuleNaturalFraction$fLeftModuleNaturalFraction$fRightModuleIntegerFraction$fLeftModuleIntegerFraction$fMonoidalFraction$fGroupFraction$fSemiringFraction$fAbelianFraction$fRingFraction$fDecidableAssociatesFraction$fDecidableUnitsFraction$fDecidableZeroFraction$fCommutativeFraction$fDivisionFraction $fOrdFraction $fEqFraction$fZeroProductSemiringFraction$fShowFractionProxy Control.Arrowarr$#