SamplePublisher`GrassmannCalculus`
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
The following is an Association that gives random Grassmann points, lines and planes in various spaces.
In[2]:=
sa=Association"Generic point in 2-space"
[2,{x,y},"Vector"];★+
.
,"Point in 2-space"
[2,{x,y},"Vector"];
[],"Line in 2-space"
[2,{x,y},"Vector"];
[]⋀
[],"Generic point in 4-space"
[4,{w,x,y,z},"Vector"];★+
.
,"Point in 4-space"
[4,{w,x,y,z},"Vector"];
[],"Line in 4-space"
[4,{w,x,y,z},"Vector"];
[]⋀
[],"Plane in 4-space"
[4,{w,x,y,z},"Vector"];
[]⋀
[]⋀
[];
 | SetCoordinateBoundVectorSpace |
| FreeBasis |
| GrassmannCoordinates |
| SetCoordinateBoundVectorSpace |
| RandomGrassmannPoint |
| SetCoordinateBoundVectorSpace |
| RandomGrassmannPoint |
| RandomGrassmannVector |
| SetCoordinateBoundVectorSpace |
| FreeBasis |
| GrassmannCoordinates |
| SetCoordinateBoundVectorSpace |
| RandomGrassmannPoint |
| SetCoordinateBoundVectorSpace |
| RandomGrassmannPoint |
| RandomGrassmannVector |
| SetCoordinateBoundVectorSpace |
| RandomGrassmannPoint |
| RandomGrassmannVector |
| RandomGrassmannVector |
The following command generates the Keys palette to go with this Association, which has the symbol .
sa
In[3]:=
 | AssociationKeysPalette |
To use an item from the palette, first click the paste button at the top, here, and then use the Association Keys drop down menu to select an item in the Association.
sa[]
In[4]:=
sa["Generic point in 2-space"]sa["Point in 2-space"]sa["Line in 2-space"]sa["Generic point in 4-space"]sa["Point in 4-space"]sa["Line in 4-space"]sa["Plane in 4-space"]
Out[4]=
★+x+y
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Out[4]=
★++6
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Out[4]=
(★+2)⋀(3+4)
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Out[4]=
★+w+x+y+z
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Out[4]=
★-+3++8
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Out[4]=
(★+3+10+2+5)⋀(-3-10-3+2)
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Out[4]=
(★+5+8+-4)⋀(8-7+-3)⋀(2+3+4+2)
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Here we use the key items to Wedge a generic point with a line, then use GroebnerBasis to show there are only 3 independent relations to give 3 equations that represent a line in 4-space. The particular result will depend on the random line that was generated.
In[5]:=
step1=sa["Line in 4-space"]⋀sa["Generic point in 4-space"]step2=step1//
step3=Coefficientstep2,
[3]gb=GroebnerBasisstep3,
Thread[gb0]
 | FastExteriorExpand |
 | GradeBasis |
 | GrassmannCoordinates |
Usually an Association will be defined within a routine and contain static items calculated within the routine and use a plain for the Rule.
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