A Quantum Algebra Supplement - Unit Tests

(* Combine product of Integrations *)
Test[
    QAIntegrate[Subscript[x, 1], V, 3, x] QAIntegrate[Subscript[y, 2], V, 3, y],
    QAIntegrate[Subscript[x, 1] Subscript[y, 2], V, 3, x, y],
    TestID->"Integrate-20181213-P3R4W5"
]

(* Apply DiracDelta in Integrate about 2 integration ranges *)
Test[
    QAIntegrate[
        Subscript[x, 1] Subscript[y, 2] * 
        DiracDelta[Subscript[x, 1] - Subscript[y, 1], Subscript[x, 2] - Subscript[y, 2], Subscript[x, 3] - Subscript[y, 3]], 
        V, 3, x, y],
    QAIntegrate[Subscript[x, 1] Subscript[x, 2], V, 3, x],
    TestID->"Integrate-20181213-N8K6H2"
]

(* Integrate about Exponential resolved to DiracDelta *)
Test[
    QAIntegrate[
        Power[E, I (Subscript[k, 1] (Subscript[x, 1] - Subscript[y, 1]) + Subscript[k, 2] (Subscript[x, 2] - Subscript[y, 2]))], 
        Infinity, 2, k],
    DiracDelta[Subscript[x, 1] - Subscript[y, 1], Subscript[x, 2] - Subscript[y, 2]] 4 Pi^2,
    TestID->"Integrate-20181216-P1R1T9"
]

(* Test of Name Ordering Rule, op1 ** op2 are in reverse order *)
Test[
    (op1 = Operator[q, "H", { Subscript[k, 1], Subscript[k, 2] }, {}];
    op2 = Operator[p, "H", { Subscript[l, 1], Subscript[l, 2] }, {}];
    (op1 ** op2) /. { DefineNameOrderingRule[False, 2] }),
    op2 ** op1,
    TestID->"NameOrdering-20181226-X4S4F9"
]

(* Derivation of an Operator Product *)
Test[
    QAD[Operator[a, { Subscript[x, 1] }, {}] ** Operator[b, { Subscript[x, 1] }, { s }], Subscript[x, 1]],

    QAD[Operator[a, { Subscript[x, 1] }, {}], Subscript[x, 1]] ** Operator[b, { Subscript[x, 1] }, { s }] + 
        Operator[a, { Subscript[x, 1] }, {}] ** QAD[Operator[b, { Subscript[x, 1] }, { s }], Subscript[x, 1]],

    TestID->"Derivation-20181217-L0J8L0"
]