SamplePublisher`GrassmannCalculus`
Contractor  |
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Details and Options
Examples
(5)
Basic Examples
(1)
See below for a general overview of the contraction routines
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | SetActiveSpacePreferences |
 | PublicGrassmannAtlas |
A Contractor can be entered as a plain expression or from the palette. evaluates scalar contractors.
ContractorRules
In[3]:=
[dx,],
[]
 | Contractor |
e
x
dx,e
x
%/. | ContractorRules |
Out[3]=
{〈dx,〉,〈dx,〉}
e
x
e
x
Out[3]=
{1,1}
General exterior elements can be entered.
In[4]:=
〈
1+dx+dx⋀dy+dx⋀dy⋀dz,ae
x
e
x
e
y
e
z
〉
%// | EvaluateContractors |
Out[4]=
〈1+dx+dx⋀dy+dx⋀dy⋀dz,a+b⋀⋀〉
e
x
e
x
e
y
e
z
Out[4]=
a+b+ady+ady⋀dz
A is equivalent to a . A may give a change of sign.
LeftContractor
Contractor
RightContractor
In[5]:=
{↦dx⋀dy,dx⋀dy↤}%//
〈
dx⋀dy,e
x
〉
,e
x
e
x
| EvaluateContractors |
Out[5]=
{〈dx⋀dy,〉,↦dx⋀dy,dx⋀dy↤}
e
x
e
x
e
x
Out[5]=
{dy,dy,-dy}
General Overview of Contraction Routines
(4)
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