SamplePublisher`GrassmannCalculus`
ExteriorLinearTransform  |
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Examples
(2)
Basic Examples
(2)
In[1]:=
 | SetBookVectorSpace |
Out[1]=
{,,,,}
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In[1]:=
genFactors=
[{3,5},3]//MatrixForm
 | RandomGrassmannMatrix |
Out[1]//MatrixForm=
94 | -558 | 367 | 14 | -72 |
22 | -129 | 83 | 3 | -15 |
2 | -16 | 15 | 1 | -6 |
In[2]:=
wedgeProduct=Wedge@@(genFactors.Basis)
Out[2]=
(94-558+367+14-72)⋀(22-129+83+3-15)⋀(2-16+15+-6)
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In[3]:=
genTransform=
[{3,3},3]//MatrixForm
| RandomGrassmannMatrix |
Out[3]//MatrixForm=
-64 | -58 | -10 |
-262 | -248 | -43 |
8 | 6 | 1 |
In[4]:=
Det[genTransform]
Out[4]=
-4
In[5]:=
tProduct=
[genTransform][wedgeProduct]tProduct=%//
//ExpandAll
 | ExteriorLinearTransform |
| FastExteriorExpand |
Out[5]=
-(-7312+43354-6(4742+180-923))⋀(-30170+178876-117383-4455+22842)⋀(886-5254+3449+131-672)
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Out[5]=
-44⋀⋀-2⋀⋀+48⋀⋀-4⋀⋀-36⋀⋀-6⋀⋀+25⋀⋀+60⋀⋀+30⋀⋀-15⋀⋀
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In[6]:=
wedgeProduct//
//ExpandAll
 | FastExteriorExpand |
Out[6]=
-44⋀⋀-2⋀⋀+48⋀⋀-4⋀⋀-36⋀⋀-6⋀⋀+25⋀⋀+60⋀⋀+30⋀⋀-15⋀⋀
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Why do they not differ by the determinant?
""