SamplePublisher`GrassmannCalculus`
AngleBracket  |
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Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
The AngleBracket of a scalar times the n-Basis element is automatically evaluated to the scalar.
In[2]:=
 | AngleBracket |
e
x
e
y
Out[2]=
15
An AngleBracket often arises from a regressive product that returns a zero grade scalar. For example, an intersection of a line and a point position in Grassmann 2-space to give the equation for a line.
In[3]:=
q⋀r⋁p0%//★
Out[3]=
q⋀r⋁p0
Out[3]=
〈p⋀q⋀r〉0
Using specific values for q and r and a position element for p gives the explicit equation for the line.
In[4]:=
(★+a+b)⋀(★)⋁(★+x+y)%//★//Collect#,
&0
e
x
e
y
e
x
e
y
 | GrassmannCoordinates |
Out[4]=
(★+a+b)⋀★⋁(★+x+y)
e
x
e
y
e
x
e
y
Out[4]=
bx-ay0
 |
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""