SamplePublisher`GrassmannCalculus`
RandomGrassmannBoundElement  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
A random point is prepended to the m-element.
In[2]:=
 | SetBookPointAssociation |
In[3]:=
| RandomGrassmannBoundElement |
| RandomGrassmannBoundElement |
| RandomGrassmannBoundElement |
Out[3]=
(★-+3-5+)⋀(-4-3+3+3)
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Out[3]=
(★+-3-9+5)⋀(6+33-58+20)⋀(2+10-18+6)
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Out[3]=
(★+3-10+7-10)⋀(-2+4+3-17)⋀(-2+2+2-15)⋀(-+6)
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The following generates m-elements in the subspace. The point is also in the subspace.
{,}
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In[4]:=
| RandomGrassmannBoundElement |
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| RandomGrassmannBoundElement |
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| RandomGrassmannBoundElement |
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Out[4]=
(★+2-3)⋀(-+3)
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Out[4]=
(★+5+2)⋀(3)⋀(2+6)
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Out[4]=
(★+-7)⋀(2-6)⋀(-18+63)⋀(-6+21)
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If you wish not to confine the point to the subspace use:
In[5]:=
 | RandomGrassmannPoint |
| RandomGrassmannVectorElement |
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Out[5]=
(★+3+2+8)⋀(9-16)⋀(3-6)
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The following generates a random 2-element in a subspace defined by two random vectors and then checks that a parametrized point is in the subspace.
In[6]:=
vector1=
[1]vector2=
[1]step1=
[2,{vector1,vector2}]origin=First[step1]step2=step1//
[Wedge,Automatic]
[step2⋀(origin+avector1+bvector2)]
| RandomGrassmannVectorElement |
 | RandomGrassmannVectorElement |
| RandomGrassmannBoundElement |
| GrassmannBreakout |
| ZeroQ |
Out[6]=
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Out[6]=
6+9-3+3
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Out[6]=
(★-9(-2-9)+2(6+9-3+3))⋀(-4(-2-9)+3(6+9-3+3))⋀(-6(-2-9)+6(6+9-3+3))
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Out[6]=
★-9(-2-9)+2(6+9-3+3)
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Out[6]=
-54★⋀⋀-54★⋀⋀-342★⋀⋀-108★⋀⋀-486★⋀⋀+198★⋀⋀
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Out[6]=
True
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""