SamplePublisher`GrassmannCalculus`
GrassmannCoreDialogInput  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
The following brings up the Dialog Input window, which you can practice with.
In[2]:=
 | GrassmannCoreDialogInput |
The following brought up the Dialog Input window and the fields were filled with the output shown to establish a 2-dimensional Bipolar system of coordinates. For convenience some additional scalar, vector and form symbols were declared.
In[3]:=
bipolarCoreData=
[]
 | GrassmannCoreDialogInput |
Out[3]=
Bipolar,False,{u,v},{a},-π<u≤π&&v∈Reals&&(u≠0||v≠0),a>0,Vector,,0,0,,{b,c,d},{p,q,r,s},{α,β,ψ,ω}
2
a
2
(Cos[u]-Cosh[v])
2
a
2
(Cos[u]-Cosh[v])
The following statement generates the Grassmann Association for the Bipolar coordinate system.
In[4]:=
bipolarAssociation=
[]@@bipolarCoreData
 | BuildSpacePreferencesAssociation |
Out[4]=
GrassmannAssociationTitleBipolar,CoordinatesOriginQFalse,GrassmannCoordinates{u,v},GrassmannParameters{a},CoordinateDomain-π<u≤π&&v∈Reals&&(u≠0||v≠0),ParameterDomaina>0,BasisTypeVector,Basis{,},VectorBasis{,},FormBasis{du,dv},OrthonormalBasis,,MetricsMetric,0,0,,InverseMetric,0,0,,ScaleFactors,,VolumeFactor,VectorToFormdu,dv,FormToVectordu,dv,VectorToOrthonormal,,OrthonormalToVector(-Cos[u]+Cosh[v]),(-Cos[u]+Cosh[v]),FormToOrthonormaldu(-Cos[u]+Cosh[v]),dv(-Cos[u]+Cosh[v]),OrthonormalToForm,,SymbolsScalarSymbols{a,b,c,d,u,v},UserScalarSymbols{b,c,d},VectorSymbolsdu,dv,p,q,r,s,α,β,ψ,ω,,,,,BasisSymbolsdu,dv,,,,,UserVectorSymbols{p,q,r,s},UserFormSymbols{α,β,ψ,ω}
e
u
e
v
e
u
e
v
e
u
e
v
2
a
2
(Cos[u]-Cosh[v])
2
a
2
(Cos[u]-Cosh[v])
2
(Cos[u]-Cosh[v])
2
a
2
(Cos[u]-Cosh[v])
2
a
a
-Cos[u]+Cosh[v]
a
-Cos[u]+Cosh[v]
2
a
2
(Cos[u]-Cosh[v])
e
u
2
a
2
(Cos[u]-Cosh[v])
e
v
2
a
2
(Cos[u]-Cosh[v])
e
u
2
(Cos[u]-Cosh[v])
2
a
e
v
2
(Cos[u]-Cosh[v])
2
a
e
u
a
e
u
-Cos[u]+Cosh[v]
e
v
a
e
v
-Cos[u]+Cosh[v]
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u
e
u
a
e
v
e
v
a
e
u
a
e
v
a
e
u
adu
-Cos[u]+Cosh[v]
e
v
adv
-Cos[u]+Cosh[v]
e
u
e
v
e
u
e
v
e
u
e
v
e
u
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v
This contains additional generated information, comprising the standard data, including transition rules between the various bases. This can now be set as the active Grassmann Association by:
In[5]:=
| SetActiveSpacePreferences |
The Bipolar system would now be reflected on the Grassmann Calculus Palette. Using the All button on the palette will bring up a window displaying the standard data and Paste buttons for copying the items into a notebook. You can also view items on the palette and then paste items into the notebook from the P button on the palette.
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