GrassmannCalculus`
SpecialScalars  |
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Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | SetActiveSpacePreferences |
 | PublicGrassmannAtlas |
The are:
SpecialScalars
In[3]:=
 | SpecialScalars |
Out[3]=
★g,★n,,★λ,★0,,★c,_,
_,_,_
★σ
★t
(-1)
The meaning of some of these special scalars are:
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| ★c |
★c is a symbolic scalar factor used to convert congruence to equality. Its FullForm is CongruenceFactor.
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| ★n |
★n is a symbolic scalar symbol used to represent the dimension of a space. Its FullForm is DimensionSymbol.
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| ★λ |
★λ is a symbol used in the expression of the Generalized Grassmann product. Its FullForm is GeneralizedProductOrder.
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| ★0 |
★0 is a symbol which represents the grade of 0 or the grade of an expression which evaluates to zero. Its FullForm is GradeOfZero.
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| ★g |
★g is an alias for MetricDeterminant. MetricDeterminant is a symbol representing the determinant of the metric tensor. It has no set value, but may be interpreted as the determinant of the metric tensor by some GrassmannAlgebra functions.
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| ★σ |
★σ is a symbol used in its overscripted form to represent the sign of a generalized product in a hypercomplex expression. Its FullForm is HypercomplexSign.
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| ★t |
★t is a symbol whose subscripted versions represent scalar parameters for use in various output expressions, for example the output of ExteriorQuotient and SignedOctonionProduct. Its FullForm is ScalarParameter.
〈expr〉
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| SetCoordinateVectorSpace |
Using , to find the common factor, on the following expression returns the common factor with a sign.
CongruenceSimplify
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(⋀)⋁(⋀)//★
e
x
e
y
e
z
e
y
Out[12]=
-
e
y
With symbolic vector symbols it returns the common factor with a sign and an extra scalar factor. But if we use rules to substitute in terms of basis vectors, the AngleBracket can be evaluated.
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(p⋀q)⋁(r⋀q)//★%/.Thread[{p,q,r}{,,}]%//
e
x
e
y
e
z
| SimplifyScalars |
Out[13]=
-q〈p⋀q⋀r〉
Out[13]=
-〈⋀⋀〉
e
x
e
y
e
z
e
y
Out[13]=
-
e
y
In[14]:=
(p⋀q)⋁(r⋀q)//★%/.Thread[{p,q,r}{+,,-}]%//
e
x
e
z
e
y
e
x
e
z
| SimplifyScalars |
Out[14]=
-q〈p⋀q⋀r〉
Out[14]=
-〈(+)⋀⋀(-)〉
e
x
e
z
e
y
e
x
e
z
e
y
Out[14]=
2
e
y
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