DSL for specifying new tensors

When specifying a new tensor type, a few functions need to be provided:

AngularMomentumAlgebra.system(::Type{TensorType}) which returns the AngularMomentumAlgebra.System the tensor acts on,
Base.iszero which indicates whether a reduced matrix element of the tensor vanishes without actually computing it,
couplings which generates all sets of quantum numbers the tensor couples to from a given set of quantum numbers,
rme which computes the actual reduced matrix element.

AngularMomentumAlgebra.@tensor — Macro

@tensor(exprs, TensorType)

Macro to generate Base.iszero, rme and couplings for TensorType, given a set of selection rules and an expression for the reduced matrix element.

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AngularMomentumAlgebra.strip′ — Function

strip′(s::Symbol)

Strip s of a trailing ′, error if it is not present.

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AngularMomentumAlgebra.identify_quantum_numbers — Function

identify_quantum_numbers(selection_rules)

Given the block of selection rules, identify the quantum numbers pertaining to the tensor under consideration. It is assumed that the left-hand side consists of a primed quantum number only, which is specified to be equal to an expression or belonging to a set/interval.

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AngularMomentumAlgebra.recursepm — Function

recursepm(e::Expr)

Recursively expand the expression e for instances of ± and ∓, generating + and - minus branches.

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recursepm(lhs, rhs)

Recursively expand lhs and rhs for instances of ± and ∓ and join all resulting cases into a short-circuiting || test.

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AngularMomentumAlgebra.parse_selection_rule — Function

parse_selection_rule(rule)

Parse a selection rule in the DSL of @tensor; if the selection rule is an equality, its left- and right-hand sides are recursively expanded for possible cases of ± and ∓ with recursepm.

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AngularMomentumAlgebra.generate_iszero — Function

generate_iszero(TensorType, selection_rules, selection_rules_linenum)

Generate a function for testing if the matrix element of TensorType vanishes, given a set a quantum number deduced from selection_rules, given at line number selection_rules_linenum.

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AngularMomentumAlgebra.generate_rme — Function

generate_rme(TensorType, selection_rules, doc, rme, rme_linenum)

Generate a function for computing the reduced matrix element of TensorType, given a set a quantum number deduced from selection_rules, along with the docstring and the definition rme, given at line number rme_linenum.

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AngularMomentumAlgebra.generate_couplings — Function

generate_copulings(TensorType, selection_rules, selection_rules_linenum)

Generate a function that given the quantum numbers γj generates lists of all permissible γj′ for which the reduced matrix element ⟨γj′||::TensorType||γj⟩ does not vanish. This is deduced from the selection_rules, given at line number selection_rules_linenum.

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