Function foeTest

src/compute-engine/rubi/rubi-utils.ts:3283–3307

FunctionOfExponentialTest: walk u, registering exponential bases/exponents. * Returns true iff u is a function of a single common F^v.

(u: Expression, x: string, st: FoeState)

      // (a Cos)^m (b Csc)^n == (a Sin[θ+π/2])^m (-b Sec[θ+π/2])^n
      if (g.head === 'cos' && h.head === 'csc')
        return ce.function('Multiply', [
          buildMono(ce, g.coef, 'sin', argP, g.exp),
          buildMono(ce, h.coef.neg(), 'sec', argP, h.exp),
        ]);
      // (a Cos)^m (b Sec)^n == (a Sin[θ+π/2])^m (b Csc[θ+π/2])^n
      if (g.head === 'cos' && h.head === 'sec')
        return ce.function('Multiply', [
          buildMono(ce, g.coef, 'sin', argP, g.exp),
          buildMono(ce, h.coef, 'csc', argP, h.exp),
        ]);
    }
    if (g.kind === 'mono' && h.kind === 'binom' && h.head === 'cos') {
      const binomM = buildBinom(ce, h.a, h.b.neg(), 'sin', argM, h.exp); // a − b Sin[θ−π/2]
      const binomP = buildBinom(ce, h.a, h.b, 'sin', argP, h.exp); //       a + b Sin[θ+π/2]
      // (g Sin)^p (a+b Cos)^m == (g Cos[θ−π/2])^p (a−b Sin[θ−π/2])^m
      if (g.head === 'sin')
        return ce.function('Multiply', [
          buildMono(ce, g.coef, 'cos', argM, g.exp),
          binomM,
        ]);
      // (g Csc)^p (a+b Cos)^m == (g Sec[θ−π/2])^p (a−b Sin[θ−π/2])^m
      if (g.head === 'csc')
        return ce.function('Multiply', [
          buildMono(ce, g.coef, 'sec', argM, g.exp),
          binomM,
        ]);
      // (g Cot)^p (a+b Cos)^m == (-g Tan[θ−π/2])^p (a−b Sin[θ−π/2])^m
      if (g.head === 'cot')