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You can conjugate the braid so there are no unused strands anynore. In order to prevent the simplification, you can use two expressions of the same braid.

In your example:

cb1 = B([1,2,1]) cb2 = B([-2,-1,-2])

mybraid = B([1])

myconjbraid = cb1mybraidcb2

myconjbraid produces the same link as mybraid, but since it has no unused strands, it will contain also the trivial components.