Changes between Version 3 and Version 9 of Ticket #24622


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Timestamp:
02/07/18 19:50:07 (2 years ago)
Author:
egourgoulhon
Comment:

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  • Ticket #24622

    • Property Commit changed from 06f8fd34981fb8b201134439a55ecf79f962a5c9 to 46b8f66385cd1c34e5310d627a0e44983f87cc4a

  • Ticket #24622 – Description

    v3 v9  
    1 This ticket implements pseudo-Riemannian manifolds, i.e. real differentiable manifolds equipped with a metric tensor. Important subcases are of course Riemannian manifolds and Lorentzian manifolds. Taking into account that generic metric tensors are already implemented in Sage (see [http://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/metric.html here]), this ticket introduces
     1This ticket implements pseudo-Riemannian manifolds, i.e. real differentiable manifolds equipped with a metric tensor. Important subcases are of course Riemannian manifolds and Lorentzian manifolds. Taking into account that pseudo-Riemannian metric tensors are already implemented in Sage (see [http://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/metric.html here]), this ticket introduces
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    3 - the parent class `PseudoRiemannianManifold`, as a subclass of the existing class `DifferentiableManifold`
    4 - new methods `gradient` and `laplacian` for scalar fields
    5 - new methods `divergence`, `laplacian` for tensor fields
    6 - new methods `curl`, `dot_product`, `cross_product` and `norm` for vector fields
     3- the parent class `PseudoRiemannianManifold`, as a subclass of the existing class `DifferentiableManifold`, with the specific methods `metric` and `volume_form`
     4- new methods `gradient`, `laplacian` and `dalembertian` for scalar fields
     5- new methods `divergence`, `laplacian` and `dalembertian` for tensor fields
     6- new methods `curl`, `dot`, `cross` and `norm` for vector fields
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    88For a greater generality, all these methods have an optional argument `metric`; if it is omitted, the metric of the underlying pseudo-Riemannian manifold is assumed. The follow-up ticket #24623 implements Euclidean spaces.