torsion

Torsion describes a condition wherein an independent set of n unison vectors
(<uvector.htm>) fails to define a periodicity block of dimension n, because of
the existence of torsion elements, meaning intervals which are not products of
the proposed set of unison vectors, but some power of which are.

Torsion may be tested by forming the n by n+1 matrix whose rows correspond to
the unison vectors, and calculating the
gcd(<http://mathworld.wolfram.com/GreatestCommonDivisor.html>) of the minors
(<http://mathworld.wolfram.com/Minor.html>)
of the matrix. If the rows are linearly independent but the gcd is not one, we
have torsion.

The term comes from mathematical usage, see
<http://mathworld.wolfram.com/TorsionGroup.html>.