GrassmannCalculus`
ExteriorProduct (⋀)  |
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Details and Options
Examples
(8)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Setting some Book preferences:
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★A;
;
 | ★ |
5
These inputs are equivalent:
In[3]:=
{ExteriorProduct[x,y],Wedge[x,y],x⋀y}
Out[3]=
{x⋀y,x⋀y,x⋀y}
Because the exterior product is associative these inputs are also equivalent:
In[4]:=
{ExteriorProduct[x,y⋀z],Wedge[Wedge[x,y],z],Wedge[x⋀Wedge[y]⋀z]}
Out[4]=
{x⋀y⋀z,x⋀y⋀z,x⋀y⋀z}
The exterior product is listable.
In[5]:=
{a,b,c}⋀{x,y,z}
Out[5]=
{a⋀x,b⋀y,c⋀z}
The following shows relative timings for various linear expansions of an exterior product. If the product contains only basis vectors and scalars is the fastest.
GrassmannBreakout
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| ★ℬ |
5
In[7]:=
product1=(+2+3+4)⋀(-+3-+)⋀(-5+2+)⋀(+5-3+7);
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In[8]:=
product1//
[Wedge,Automatic]//Timingproduct1//
//Timingproduct1//
//Timing
 | GrassmannBreakout |
| ExpandAndSimplifyExteriorProducts |
| ★ |
Out[8]=
{0.0468003,216⋀⋀⋀-144⋀⋀⋀+64⋀⋀⋀+184⋀⋀⋀-400⋀⋀⋀}
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Out[8]=
{0.764405,216⋀⋀⋀-144⋀⋀⋀+64⋀⋀⋀+184⋀⋀⋀-400⋀⋀⋀}
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Out[8]=
{3.75962,216⋀⋀⋀-144⋀⋀⋀+64⋀⋀⋀+184⋀⋀⋀-400⋀⋀⋀}
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Exterior Products and Linear Dependence
(1)
Why Aren't Repeats of Even Grade Elements Zero?
(1)
Examples of Exterior Products, Simplifications and Expansions
(1)
Simple Properties of Exterior Product
(1)
Axioms of the Exterior Product
(1)
Additional Rule for Exchanging Factors
(1)
Determinants
(1)
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