I would like to expand a tensor expression of 3-d vectors. However, the code runs really slow, the problem is asked here: Why is TensorExpand so slow for vector operations?
However, I found that by assuming the 3-d vectors as real numbers, the code could be faster. For example, to expand $(a-b)\times c.d$:
$Assumptions = (a | b | c | d) \[Element] Reals; TensorExpand[( a - b)\[Cross]c.d]
Instead of using
$Assumptions = (a | b | c | d) \Vectors
Reals. It was really faster, except that the result was not perfect:
$$ a\times c.d+b (-1)\times c.d$$
I got a -1 here, which should be b.
Can we have some operations that could put the "b" in the correct place?