manualintegrate.py 文件源码

def trig_rule(integral):
    integrand, symbol = integral
    if isinstance(integrand, sympy.sin) or isinstance(integrand, sympy.cos):
        arg = integrand.args[0]

        if not isinstance(arg, sympy.Symbol):
            return  # perhaps a substitution can deal with it

        if isinstance(integrand, sympy.sin):
            func = 'sin'
        else:
            func = 'cos'

        return TrigRule(func, arg, integrand, symbol)

    if integrand == sympy.sec(symbol)**2:
        return TrigRule('sec**2', symbol, integrand, symbol)
    elif integrand == sympy.csc(symbol)**2:
        return TrigRule('csc**2', symbol, integrand, symbol)

    if isinstance(integrand, sympy.tan):
        rewritten = sympy.sin(*integrand.args) / sympy.cos(*integrand.args)
    elif isinstance(integrand, sympy.cot):
        rewritten = sympy.cos(*integrand.args) / sympy.sin(*integrand.args)
    elif isinstance(integrand, sympy.sec):
        arg = integrand.args[0]
        rewritten = ((sympy.sec(arg)**2 + sympy.tan(arg) * sympy.sec(arg)) /
                     (sympy.sec(arg) + sympy.tan(arg)))
    elif isinstance(integrand, sympy.csc):
        arg = integrand.args[0]
        rewritten = ((sympy.csc(arg)**2 + sympy.cot(arg) * sympy.csc(arg)) /
                     (sympy.csc(arg) + sympy.cot(arg)))
    else:
        return

    return RewriteRule(
        rewritten,
        integral_steps(rewritten, symbol),
        integrand, symbol
    )