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Builtin Symbolic Tensors
Derive and Verify Vector Identities
Simplify expressions involving combinations of cross products and dot products in any dimension.
Famous threedimensional identities.
In[1]:=
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TensorExpand[(v\[Cross]w).v == 0]
Out[1]=
In[2]:=
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TensorExpand[a\[Cross](b\[Cross]c) == b (a.c)  c (a.b)]
Out[2]=
In[3]:=
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TensorExpand[(a\[Cross]b).(c\[Cross]d) == a.c b.d  a.d b.c]
Out[3]=
Less famous threedimensional identities.
In[4]:=
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TensorExpand[ a (b\[Cross]c).d  b (a\[Cross]c).d + c (a\[Cross]b).d  d (a\[Cross]b).c == 0]
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In[5]:=
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TensorExpand[(a\[Cross]b)\[Cross](c\[Cross]d)]
Out[5]=
Two fourdimensional identities.
In[6]:=
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TensorExpand[a\[Cross]b\[Cross]c == b\[Cross]c\[Cross]a]
Out[6]=
In[7]:=
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TensorExpand[(a\[Cross]b\[Cross]c).(d\[Cross]e\[Cross]f)]
Out[7]=