docs.json

{"reExports":[],"name":"Data.DivisionRing","comments":null,"declarations":[{"children":[{"comments":null,"title":"recip","info":{"declType":"typeClassMember","type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeVar","contents":"a"}]},{"annotation":[],"tag":"TypeVar","contents":"a"}]}},"sourceSpan":{"start":[30,3],"name":"../../../support/bower_components/purescript-prelude/src/Data/DivisionRing.purs","end":[30,18]}},{"comments":null,"title":"divisionringNumber","info":{"declType":"instance","dependencies":[],"type":{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Data","DivisionRing"],"DivisionRing"]},{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Number"]}]}},"sourceSpan":{"start":[54,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/DivisionRing.purs","end":[55,20]}}],"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","title":"DivisionRing","info":{"fundeps":[],"arguments":[["a",null]],"declType":"typeClass","superclasses":[{"constraintAnn":[],"constraintClass":[["Data","Ring"],"Ring"],"constraintArgs":[{"annotation":[],"tag":"TypeVar","contents":"a"}],"constraintData":null}]},"sourceSpan":{"start":[29,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/DivisionRing.purs","end":[30,18]}},{"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","title":"leftDiv","info":{"declType":"value","type":{"annotation":[],"tag":"ForAll","contents":["a",{"annotation":[],"tag":"ConstrainedType","contents":[{"constraintAnn":[],"constraintClass":[["Data","DivisionRing"],"DivisionRing"],"constraintArgs":[{"annotation":[],"tag":"TypeVar","contents":"a"}],"constraintData":null},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeVar","contents":"a"}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeVar","contents":"a"}]},{"annotation":[],"tag":"TypeVar","contents":"a"}]}]}]},null]}},"sourceSpan":{"start":[40,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/DivisionRing.purs","end":[40,51]}},{"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","title":"rightDiv","info":{"declType":"value","type":{"annotation":[],"tag":"ForAll","contents":["a",{"annotation":[],"tag":"ConstrainedType","contents":[{"constraintAnn":[],"constraintClass":[["Data","DivisionRing"],"DivisionRing"],"constraintArgs":[{"annotation":[],"tag":"TypeVar","contents":"a"}],"constraintData":null},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeVar","contents":"a"}]},{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeApp","contents":[{"annotation":[],"tag":"TypeConstructor","contents":[["Prim"],"Function"]},{"annotation":[],"tag":"TypeVar","contents":"a"}]},{"annotation":[],"tag":"TypeVar","contents":"a"}]}]}]},null]}},"sourceSpan":{"start":[51,1],"name":"../../../support/bower_components/purescript-prelude/src/Data/DivisionRing.purs","end":[51,52]}}]}