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Factorization

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Description

Summary

Writing a state as a tensor product where its leading or trailing qubits are in a
definite basis state.

Remarks

|001> + |011> is |0> (x) (|0> + |1>) (x) |1>: the first
and last qubits agree across the whole superposition, so they factor out and only the
middle carries it.
**Which positions agree is not computed here.** It is
FactorOutCommon(AngouriMath.Functions.Algebra.MonoidAlgebra.IBasisOps{`0}), the same call that takes the common
monomial out of a polynomial -- the meet of the support. What is specific to states is
only how the answer is written down, and that division is the whole point of the spine.
**What this does not do.** Only a common *prefix or suffix* is factored, because a ket
says which qubit it describes by its position in the product and there is no notation
here for "the state of qubits 1 and 3". Nor does it find general separability:
(|0> + |1>) (x) (|0> + |1>) has no qubit in a definite state at all,
so the meet is empty and nothing is factored, yet it is a product state. Detecting that
is a rank-one test on the amplitudes across a bipartition -- a different algorithm,
belonging to this file rather than to the spine, and not written yet.

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