SamplePublisher`GrassmannCalculus`
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Details and Options
Examples
(1)
Basic Examples
(1)
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<<GrassmannCalculus`
The is initially set to , which contains the following coordinate systems.
ActiveGrassmannAtlas
PublicGrassmannAtlas
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Keys
 | ActiveGrassmannAtlas |
Out[2]=
{Grassmann Line,Grassmann Plane,Grassmann 3-Space,Euclidean Line,Euclidean Plane,Euclidean 3-Space,Grassmann Polar,Polar,Elliptic Plane,Grassmann Elliptic Plane,Cylindrical,Grassmann Cylindrical,Spherical,Grassmann Spherical,Minkowski Space,Minkowski Grassmann Space}
A particular Grassmann Association in the atlas, say "Spherical", can be displayed as follows:
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| ActiveGrassmannAtlas |
Out[3]=
GrassmannAssociationTitleSpherical,CoordinatesOriginQFalse,GrassmannCoordinates{r,θ,φ},GrassmannParameters{},CoordinateDomainr≥0&&0≤θ≤π&&-π<φ≤π,ParameterDomainTrue,BasisTypeVector,Basis{,,},VectorBasis{,,},FormBasis{dr,dθ,dφ},OrthonormalBasis,,,MetricsMetric{{1,0,0},{0,,0},{0,0,}},InverseMetric{1,0,0},0,,0,0,0,,ScaleFactors{1,r,rSin[θ]},VolumeFactorSin[θ],VectorToFormdr,dθ,dφ,FormToVectordr,dθ,dφ,VectorToOrthonormal,r,rSin[θ],OrthonormalToVector,,Csc[θ],FormToOrthonormaldr,dθ,dφCsc[θ],OrthonormalToFormdr,dθr,dφrSin[θ],SymbolsScalarSymbols{a,b,c,d,r,θ,φ},UserScalarSymbols{a,b,c,d},VectorSymbolsdr,dθ,dφ,p,q,s,u,α,β,ψ,ω,,,,,,,BasisSymbolsdr,dθ,dφ,,,,,,,UserVectorSymbols{p,q,s,u},UserFormSymbols{α,β,ψ,ω}
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