Metadata revisions for manifolds-0.1.3.1

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No. Time User SHA256
-r3 2016-04-15T12:11:45Z leftaroundabout 0777f4c989c4d561037e183c7c26c36c8d4709b5dea687b5a4529ef97573b94d
  • Changed the library component's library dependency on 'constrained-categories' from

    >=0.2 && <0.3
    to
    >=0.2 && <0.2.5

-r2 2015-10-27T11:02:38Z leftaroundabout ebda72ec413d603c603961f55cdc450137db991c3c956f4993618df787fc3868
  • Changed the library component's library dependency on 'hmatrix' from

    >=0.16 && <0.18
    to
    >=0.16 && <0.17

-r1 2015-08-25T16:06:00Z leftaroundabout 078a790a2e462108e5d1ed6314f264d40b3fd1b063f56595e3874fcb5137eeea
  • Changed description from

    Manifolds, a generalisation of the notion of \"smooth curves\" or sufaces,
    are topological spaces /locally homeomorphic to a vector space/. This gives
    rise to what is actually the most natural / mathematically elegant way of dealing
    with them: calculations can be carried out locally, in connection with Riemannian
    products etc., in a vector space, the tangent space / tangent bundle.
    
    However, this does not trivially translate to non-local operations. Common
    ways to carry those out include using a single affine map to cover (almost) all of the manifold
    (in general not possible homeomorphically, which leads to both topological and geometrical
    problems), to embed the manifold into a larger-dimensional vector space (which tends
    to distract from the manifold's own properties and is often not friendly to computations)
    or approximating the manifold by some kind of finite simplicial mesh (which intrinsically
    introduces non-differentiability issues and leads to the question of what precision
    is required).
    
    This library tries to mitigate these problems by using Haskell's
    functional nature to keep the representation close to the mathematical ideal of
    local linearity with homeomorphic coordinate transforms, and, where it is
    necessary to recede to the less elegant alternatives, exploiting lazy evaluation
    etc. to optimise the compromises that have to be made.
    to
    Manifolds, a generalisation of the notion of &#x201c;smooth curves&#x201d; or surfaces,
    are topological spaces /locally homeomorphic to a vector space/. This structure gives
    rise to what I'd consider the most natural / mathematically elegant way of dealing
    with them: calculations are carried out locally, in connection with Riemannian
    products etc., in a vector space: the tangent space / tangent bundle.
    
    However, this does not trivially translate to non-local operations. Common
    ways to carry those out include using a single affine map to cover (almost) all of the manifold
    (in general not possible homeomorphically, which leads to both topological and geometrical
    problems), to embed the manifold into a larger-dimensional vector space (which tends
    to distract from the manifold's own properties and is often not friendly to computations)
    or approximating the manifold by some kind of finite simplicial mesh (which intrinsically
    introduces non-differentiability issues and leads to the question of what precision
    is required).
    
    This library tries to mitigate these problems by using Haskell's
    functional nature to keep the representation close to the mathematical ideal of
    local linearity with homeomorphic coordinate transforms, and, where it is
    necessary to recede to the less elegant alternatives, exploiting lazy evaluation
    etc. to optimise the compromises that have to be made.

-r0 2015-08-07T23:55:22Z leftaroundabout 76352c6dca6d4dd5ef7d4770e9a53ae74f8a49cb5228aeed245c99fae91d30b9