GrassmannCalculus`
RegressiveProduct (⋁)  |
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Details and Options
Examples
(4)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Setting some Book preferences:
In[2]:=
★A;
;
 | ★ℬ |
5
These inputs are equivalent:
In[3]:=
{
RegressiveProduct
[x,y],Vee[x,y],x⋁y}Out[3]=
{x⋁y,x⋁y,x⋁y}
Because the regressive product is associative these inputs are also equivalent:
In[4]:=
{RegressiveProduct[x,y⋁z],Vee[Vee[x,y],z],Vee[x⋁Vee[y]⋁z]}
Out[4]=
{x⋁y⋁z,x⋁y⋁z,x⋁y⋁z}
The regressive product is listable.
In[5]:=
a⋁{x,y,z}
Out[5]=
{a⋁x,a⋁y,a⋁z}
A principal use of the regressive product is to find intersections of spaces. These two 3-planes in 5-space intersect in a line but it is only know up to a congruence factor.
In[6]:=
(⋀⋀)⋁(⋀⋀)%//
e
1
e
4
e
5
e
2
e
3
e
4
 | ToCommonFactor |
Out[6]=
e
1
e
4
e
5
e
2
e
3
e
4
Out[6]=
★c
e
4
A more intuitive example might be the intersection of a horizontal and vertical line in the GrassmannPlane. The use of sets and is appropriate in Projective or metric spaces.
CongruenceSimplify
★c1
In[7]:=
SetActiveAssociation
"Grassmann Plane"
| PublicGrassmannAtlas |
In[8]:=
((★+3)⋀)⋁((★+5)⋀)%//★
e
y
e
x
e
x
e
y
Out[8]=
(★+3)⋀⋁(★+5)⋀
e
y
e
x
e
x
e
y
Out[8]=
★+5+3
e
x
e
y
Axioms of the Regressive Product
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The Unit n-element
(1)
Fill and Fold
(1)
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