SamplePublisher`GrassmannCalculus`DifferentialGeometry`
ToScalarContractors  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | SetCoordinateVectorSpace |
Here is a higher order Contractor expanded into scalar Contractors and evaluated with without using a metric.
In[3]:=
〈
dx⋀dy⋀dz,e
y
〉
%// | ToScalarContractors |
Out[3]=
〈dx⋀dy⋀dz,〉
e
y
Out[3]=
-(dx⋀dz)
Non-basis vectors or forms cannot be further evaluated beyond scalar contractors.
In[4]:=
p↦α⋀β%//
%//
| ConvertToContractor |
| ToScalarContractors |
Out[4]=
p↦α⋀β
Out[4]=
〈α⋀β,p〉
Out[4]=
β〈α,p〉-α〈β,p〉
In[5]:=
〈
α⋀β⋀ψ,p⋀q〉
%// | ToScalarContractors |
Out[5]=
〈α⋀β⋀ψ,p⋀q〉
Out[5]=
ψ(-〈α,q〉〈β,p〉+〈α,p〉〈β,q〉)-β(-〈α,q〉〈ψ,p〉+〈α,p〉〈ψ,q〉)+α(-〈β,q〉〈ψ,p〉+〈β,p〉〈ψ,q〉)
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