SamplePublisher`GrassmannCalculus`
GrassmannKeyList  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
The following shows the key structure for the standard data in a Grassmann Association.
In[2]:=
 | GrassmannKeyList |
Out[2]=
{GrassmannAssociationTitle,{Coordinates,{OriginQ,GrassmannCoordinates,GrassmannParameters,CoordinateDomain,ParameterDomain,BasisType,Basis,VectorBasis,FormBasis,OrthonormalBasis}},{Metrics,{Metric,InverseMetric,ScaleFactors,VolumeFactor,VectorToForm,FormToVector,VectorToOrthonormal,OrthonormalToVector,FormToOrthonormal,OrthonormalToForm}},{Symbols,{ScalarSymbols,UserScalarSymbols,VectorSymbols,BasisSymbols,UserVectorSymbols,UserFormSymbols}}}
The following command retrieves the GrassmannCoordinates from an Association.
In[3]:=
CurrentGrassmannAssociation〚"Coordinates","GrassmannCoordinates"〛
Out[3]=
{x,y}
But since this is the active Grassmann Association, most of the values can also be obtained by:
In[4]:=
 | GrassmannCoordinates |
Out[4]=
{x,y}
The following is the top level key list for the , which is an Association of Grassmann Associations. The entire list is fairly long. But all the subsidiary Grassmann Associations have the same structure as above.
PublicGrassmannAtlas
In[5]:=
Keys
| PublicGrassmannAtlas |
Out[5]=
{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}
The following extracts the transition rules from the vector basis to the form basis for Minkowski space.
In[6]:=
| PublicGrassmannAtlas |
Out[6]=
{-dt,dx,dy,dz}
e
t
e
x
e
y
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z
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