{"comments":null,"declarations":[{"children":[{"comments":null,"info":{"declType":"typeClassMember","type":{"annotation":[],"contents":[{"annotation":[],"contents":[{"annotation":[],"contents":[["Prim"],"Function"],"tag":"TypeConstructor"},{"annotation":[],"contents":"a","tag":"TypeVar"}],"tag":"TypeApp"},{"annotation":[],"contents":"a","tag":"TypeVar"}],"tag":"TypeApp"}},"sourceSpan":{"end":[30,18],"name":"../../../support/bower_components/purescript-prelude/src/Data/DivisionRing.purs","start":[30,3]},"title":"recip"},{"comments":null,"info":{"declType":"instance","dependencies":[],"type":{"annotation":[],"contents":[{"annotation":[],"contents":[["Data","DivisionRing"],"DivisionRing"],"tag":"TypeConstructor"},{"annotation":[],"contents":[["Prim"],"Number"],"tag":"TypeConstructor"}],"tag":"TypeApp"}},"sourceSpan":{"end":[55,20],"name":"../../../support/bower_components/purescript-prelude/src/Data/DivisionRing.purs","start":[54,1]},"title":"divisionringNumber"}],"comments":"The `DivisionRing` class is for non-zero rings in which every non-zero\nelement has a multiplicative inverse. Division rings are sometimes also\ncalled *skew fields*.\n\nInstances must satisfy the following laws in addition to the `Ring` laws:\n\n- Non-zero ring: `one /= zero`\n- Non-zero multiplicative inverse: `recip a * a = a * recip a = one` for\n  all non-zero `a`\n\nThe result of `recip zero` is left undefined; individual instances may\nchoose how to handle this case.\n\nIf a type has both `DivisionRing` and `CommutativeRing` instances, then\nit is a field and should have a `Field` instance.\n","info":{"arguments":[["a",null]],"declType":"typeClass","fundeps":[],"superclasses":[{"constraintAnn":[],"constraintArgs":[{"annotation":[],"contents":"a","tag":"TypeVar"}],"constraintClass":[["Data","Ring"],"Ring"],"constraintData":null,"constraintKindArgs":[]}]},"kind":null,"sourceSpan":{"end":[30,18],"name":"../../../support/bower_components/purescript-prelude/src/Data/DivisionRing.purs","start":[29,1]},"title":"DivisionRing"},{"children":[],"comments":"Left division, defined as `leftDiv a b = recip b * a`. Left and right\ndivision are distinct in this module because a `DivisionRing` is not\nnecessarily commutative.\n\nIf the type `a` is also a `EuclideanRing`, then this function is\nequivalent to `div` from the `EuclideanRing` class. When working\nabstractly, `div` should generally be preferred, unless you know that you\nneed your code to work with noncommutative rings.\n","info":{"declType":"value","type":{"annotation":[],"contents":{"identifier":"a","kind":null,"skolem":null,"type":{"annotation":[],"contents":[{"constraintAnn":[],"constraintArgs":[{"annotation":[],"contents":"a","tag":"TypeVar"}],"constraintClass":[["Data","DivisionRing"],"DivisionRing"],"constraintData":null,"constraintKindArgs":[]},{"annotation":[],"contents":[{"annotation":[],"contents":[{"annotation":[],"contents":[["Prim"],"Function"],"tag":"TypeConstructor"},{"annotation":[],"contents":"a","tag":"TypeVar"}],"tag":"TypeApp"},{"annotation":[],"contents":[{"annotation":[],"contents":[{"annotation":[],"contents":[["Prim"],"Function"],"tag":"TypeConstructor"},{"annotation":[],"contents":"a","tag":"TypeVar"}],"tag":"TypeApp"},{"annotation":[],"contents":"a","tag":"TypeVar"}],"tag":"TypeApp"}],"tag":"TypeApp"}],"tag":"ConstrainedType"},"visibility":"TypeVarInvisible"},"tag":"ForAll"}},"kind":null,"sourceSpan":{"end":[40,51],"name":"../../../support/bower_components/purescript-prelude/src/Data/DivisionRing.purs","start":[40,1]},"title":"leftDiv"},{"children":[],"comments":"Right division, defined as `rightDiv a b = a * recip b`. Left and right\ndivision are distinct in this module because a `DivisionRing` is not\nnecessarily commutative.\n\nIf the type `a` is also a `EuclideanRing`, then this function is\nequivalent to `div` from the `EuclideanRing` class. When working\nabstractly, `div` should generally be preferred, unless you know that you\nneed your code to work with noncommutative rings.\n","info":{"declType":"value","type":{"annotation":[],"contents":{"identifier":"a","kind":null,"skolem":null,"type":{"annotation":[],"contents":[{"constraintAnn":[],"constraintArgs":[{"annotation":[],"contents":"a","tag":"TypeVar"}],"constraintClass":[["Data","DivisionRing"],"DivisionRing"],"constraintData":null,"constraintKindArgs":[]},{"annotation":[],"contents":[{"annotation":[],"contents":[{"annotation":[],"contents":[["Prim"],"Function"],"tag":"TypeConstructor"},{"annotation":[],"contents":"a","tag":"TypeVar"}],"tag":"TypeApp"},{"annotation":[],"contents":[{"annotation":[],"contents":[{"annotation":[],"contents":[["Prim"],"Function"],"tag":"TypeConstructor"},{"annotation":[],"contents":"a","tag":"TypeVar"}],"tag":"TypeApp"},{"annotation":[],"contents":"a","tag":"TypeVar"}],"tag":"TypeApp"}],"tag":"TypeApp"}],"tag":"ConstrainedType"},"visibility":"TypeVarInvisible"},"tag":"ForAll"}},"kind":null,"sourceSpan":{"end":[51,52],"name":"../../../support/bower_components/purescript-prelude/src/Data/DivisionRing.purs","start":[51,1]},"title":"rightDiv"}],"name":"Data.DivisionRing","reExports":[]}