Bug introduced in 10.0.0 and fixed in 10.3.1

If I use TensorReduce on the result of TensorWedge:

$Assumptions = {a ∈ Vectors[dim], b ∈ Vectors[dim]};
TensorWedge[a, b]

I actually get

a \wedge b
1/2 a \wedge b
1/4 a \wedge b
  • $\begingroup$ A funny bug, this one: Assuming[a ∈ Vectors[n] && b ∈ Vectors[n], Nest[TensorReduce, TensorWedge[a, b], 4]]. $\endgroup$ Nov 23, 2015 at 17:46
  • $\begingroup$ Seems to be a new bug in version 10 (I tested 10.2). This does not happen in version 9. $\endgroup$ Nov 23, 2015 at 18:34
  • 1
    $\begingroup$ This is strange... we're looking into it. Thanks! $\endgroup$
    – Stefan R
    Nov 25, 2015 at 17:44

1 Answer 1


There was a missing multinomial factor in the transformation rules that TensorReduce has for TensorWedge. This will be fixed in an upcoming version of Mathematica. Thank you for finding it!


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