- Lie derivative
- Exterior product
- Tensor product
- Hodge operator
- Covariant derivativeFeatures List
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Automatic formulation and solution of typical 2D/3D dimensional problems
(see atlas 2D/3D Wizard):
- calculation of metric, connection, Laplace operator for any 2D and 3D coordinate system
- calculation of curvature, torsion, tangent, principal normal and binormal vectors for plane and space curves in any coordinate system
- calculation of metric, second fundamental form, mean curvature vectors, Laplace operator, connection, curvature, Riemann and Ricci tensors, Gauss curvature for any surface in any 3D coordinate system
- Ability to do differential geometry calculations in any dimension (some sort of calculations can be done even with symbolic dimension)
- Easy definition of and operation with typical differential geometry quantities:
- Calculation of typical differential geometry operators:
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Easy definition of and operation with N-dimensional manifold as a whole
- definition of charts and mappings (an atlas on a manifold)
- predefined operators ( restriction of a tensor field and differential of a mapping) for transformation of differential geometry quantities from one chart into another
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Automatic calculation of
mapping invariants:
- for embedding of a curve: the curve normalized moving frame and the curve curvatures
- for embedding or immersion: first and second fundamental forms and mean curvature vector field
- for submersions: A and T tensor fields, mean curvature vector of corresponding fibers, integrability obstruction of corresponding horizontal distribution and riemannian obstruction (if the submersion is not a riemannian one)
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Automatic calculation of
mapping projectors:
- for embedding or immersion: normal and tangent projectors
- for submersions: horizontal and vertical projectors
- Technical documentation:
