SamplePublisher`GrassmannCalculus`DifferentialGeometry`
ExpandContractors  |
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Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | SetCoordinateVectorSpace |
| ★★S |
In[3]:=
〈
adx+bdy,ce
x
e
z
〉
%// | ExpandContractors |
Out[3]=
〈adx+bdy,c+d〉
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z
Out[3]=
ac〈dx,〉+ad〈dx,〉+bc〈dy,〉+bd〈dy,〉
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e
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In[4]:=
〈
adw+bdx⋀dz,ce
x
e
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z
〉
%// | ExpandContractors |
Out[4]=
〈adw+bdx⋀dz,c+⋀(d)〉
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z
Out[4]=
ac〈dw,〉+ad〈dw,⋀〉+bc〈dx⋀dz,〉+bd〈dx⋀dz,⋀〉
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Contraction of a k-vector on a scalar will always be zero.
In[5]:=
〈
a,e
x
〉
%// | ExpandContractors |
Out[5]=
〈a,〉
e
x
Out[5]=
0
Contraction of two scalars is their product.
In[6]:=
〈
2,3〉
%// | ExpandContractors |
Out[6]=
〈2,3〉
Out[6]=
6
The following composes an inner Contractor of a 3-form and 3-factor and then expands it, and evaluates.
In[7]:=
form3=
["Form"];
[3,a];vector3=
["Vector"];
[3,b];
//Timingstep1//
 | SwitchBasis |
| ComposeMElement |
| SwitchBasis |
| ComposeMElement |
〈
form3,vector3〉
step1=%// | ExpandContractors |
| EvaluateContractorsMF |
Out[7]=
〈dw⋀dx⋀dy+dw⋀dx⋀dz+dw⋀dy⋀dz+dx⋀dy⋀dz,⋀⋀+⋀⋀+⋀⋀+⋀⋀〉
a
1
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Out[7]=
{0.187201,〈dw⋀dx⋀dy,⋀⋀〉+〈dw⋀dx⋀dz,⋀⋀〉+〈dw⋀dy⋀dz,⋀⋀〉+〈dx⋀dy⋀dz,⋀⋀〉+〈dw⋀dx⋀dy,⋀⋀〉+〈dw⋀dx⋀dz,⋀⋀〉+〈dw⋀dy⋀dz,⋀⋀〉+〈dx⋀dy⋀dz,⋀⋀〉+〈dw⋀dx⋀dy,⋀⋀〉+〈dw⋀dx⋀dz,⋀⋀〉+〈dw⋀dy⋀dz,⋀⋀〉+〈dx⋀dy⋀dz,⋀⋀〉+〈dw⋀dx⋀dy,⋀⋀〉+〈dw⋀dx⋀dz,⋀⋀〉+〈dw⋀dy⋀dz,⋀⋀〉+〈dx⋀dy⋀dz,⋀⋀〉}
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1
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1
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Out[7]=
a
1
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1
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2
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3
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4
b
4
""