[GiNaC-list] A differential geometry-specific extension

Diego Conti diego.conti at unimib.it
Fri Dec 21 12:08:19 CET 2007

I have been working on an extension to GiNaC for differential geometry, 
and I have released a first version, available from 

Current features include:
- Vector spaces: determine a basis from a list of generators, and 
similar computations. 
- Manifolds and differential forms: exterior derivative; wedge product. 
- Lie groups: the general linear group; subgroups determined by the 
choice of a subalgebra; abstract Lie groups defined in abbreviated form, 
e.g. writing (0,0,12) for the Heisenberg group, characterized by the 
existence of a basis of left-invariant one-forms e1,e2,e3 such that 
de3=e1 ^ e2 and e1,e2 are closed. 
- Riemannian metrics and G-structures, defined on a Lie group or a 
coordinate patch of a generic manifold, and represented by an 
orthonormal basis of 1-forms (adapted frame); spinors, Clifford 
- Connections: the Levi-Civita connection; curvature; covariant 
derivatives; define connections on generic manifolds and impose 
conditions on the Christoffel symbols, e.g. to obtain curvature conditions. 

I thought maybe someone in this list would be interested.
Diego Conti

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