SamplePublisher`GrassmannCalculus`
RightContractor (↤)  |
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Details and Options
Examples
(2)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | SetActiveSpacePreferences |
 | PublicGrassmannAtlas |
RightContractor
In[3]:=
{RightContractor[α,p],α↤p}
Out[3]=
{α↤p,α↤p}
According to the sign rule, the following left and right contractions are equivalent.
In[4]:=
{p↦α,α↤p},{↦dx,dx↤},{⋀↦dx⋀dy,dx⋀dy↤⋀},{⋀↦dx⋀dy⋀dz,dx⋀dy⋀dz↤⋀},↦,↤//Column%//
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| EvaluateContractors |
Out[4]=
{p↦α,α↤p} |
{ e x e x |
{ e x e y e x e y |
{ e x e y e x e y |
v 2 f 3 f 3 v 2 |
Out[4]=
{〈α,p〉,〈α,p〉} |
{1,1} |
{1,1} |
{dz,dz} |
f 3 v 2 f 3 v 2 |
The following left and right contractors have opposite signs.
In[5]:=
{p↦α⋀β,α⋀β↤p},{↦dx⋀dy,dx⋀dy↤},↦,↤//Column%//
e
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| EvaluateContractors |
Out[5]=
{p↦α⋀β,α⋀β↤p} |
{ e x e x |
v 1 f 2 f 2 v 1 |
Out[5]=
{β〈α,p〉-α〈β,p〉,-β〈α,p〉+α〈β,p〉} |
{dy,-dy} |
f 2 v 1 f 2 v 1 |
The sign change can be deduced from the following. For the left contraction we have to move the forms that match the vector, , to the left and then is the result. For the right contraction we have to move to the other side and that generates the sign factor.
fmatch
fextra
fmatch
In[6]:=
↦⋀,⋀↤
vmatch
k
fmatch
k
fextra
m-k
fextra
m-k
fmatch
k
vmatch
k
Force on a Moving Charge in Magnetic Field
(1)
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