SamplePublisher`GrassmannCalculus`
LeftContractor (↦)  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | SetActiveSpacePreferences |
 | PublicGrassmannAtlas |
LeftContractor
In[3]:=
{LeftContractor[p,α],p↦α}
Out[3]=
{p↦α,p↦α}
A is equivalent to and can be converted to a . The command does convert it.
LeftContractor
Contractor
EvaluateContractors
In[4]:=
p↦α%//
| ConvertToContractor |
Out[4]=
p↦α
Out[4]=
〈α,p〉
A scalar contraction.
In[5]:=
x+y+z↦adx+bdy+cdz%//
e
x
e
y
e
z
| EvaluateContractors |
Out[5]=
x+y+z↦adx+bdy+cdz
e
x
e
y
e
z
Out[5]=
ax+by+cz
The following shows a step by step evaluation.
In[6]:=
x+y+z↦adx+bdy+cdz%//
[LeftContractor,All]%//
%/.
[]
e
x
e
y
e
z
| GrassmannBreakout |
| ConvertToContractor |
| ContractorRules |
Out[6]=
x+y+z↦adx+bdy+cdz
e
x
e
y
e
z
Out[6]=
ax(↦dx)+bx(↦dy)+cx(↦dz)+ay(↦dx)+by(↦dy)+cy(↦dz)+az(↦dx)+bz(↦dy)+cz(↦dz)
e
x
e
x
e
x
e
y
e
y
e
y
e
z
e
z
e
z
Out[6]=
ax〈dx,〉+ay〈dx,〉+az〈dx,〉+bx〈dy,〉+by〈dy,〉+bz〈dy,〉+cx〈dz,〉+cy〈dz,〉+cz〈dz,〉
e
x
e
y
e
z
e
x
e
y
e
z
e
x
e
y
e
z
Out[6]=
ax+by+cz
If the vector doesn't fit into the form the result is zero.
In[7]:=
vector
2
form
1
| EvaluateContractors |
Out[7]=
vector
2
form
1
Out[7]=
0
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