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: atlas™ - modern differential geometry for Maple™ : Features
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- Automatic
formulation and solution of typical
2-D/3-D dimensional problems (see
atlas 2-D/3-D Wizard):
- calculation
of metric, connection, Laplace
operator for any 2-D and 3-D
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 3-D 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:
- domains
(manifold charts), mappings,
submersions, immersions etc.
- constants,
functions, tensors, forms,
vectors, coframes, frames,
metrics, connections, curvatures,
torsions etc.
- Calculation
of typical differential geometry
operators:
- exterior
derivative, Lie derivative,
interior product, exterior
product, tensor product, natural
vectors, Hodge operator, covariant
derivative, dual operator,
gradient operator, divergence
operator etc.
- Easy definition
of and operation with N-dimensional
manifold as a whole:
- definition
of charts and mappings (an
atlas on a manifold)
- predefined
operators for transformation
of differential geometry quantities
from one chart into another
- 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)
- Automatic
calculation of mapping projectors:
- for embedding
or immersion: normal and tangent
projectors
- for submersions:
horizontal and vertical projectors
- Technical
documentation: reference manual
(also available in PDF and HTML
formats), example and template
worksheets.
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• Maple 8 or higher,
tested against Maple 8, Maple 9, Maple
10, Maple 11
• 2 MB free disk space
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DigiArea Group Ltd
DigiArea Group Ltd was founded by Alexander A.
Shklyaev. DigiArea Group develops and markets
Maple and Mathematica packages, online and 3-D
scientific games. For further information about
DigiArea Group and its products, please contact
info@digi-area.com
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 Purchase
Now! |
| atlas™ - modern
differential geometry for Maple™ and other third party products
are available for immediate purchase in the Maplesoft
webstore. |
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