def rubi_integrate(expr, var, showsteps=False):
"""
Rule based algorithm for integration. Integrates the expression by applying
transformation rules to the expression.
Returns `Integrate` if an expression cannot be integrated.
Parameters
==========
expr : integrand expression
var : variable of integration
Returns Integral object if unable to integrate.
"""
rubi = LoadRubiReplacer().load()
expr = expr.replace(sym_exp, rubi_exp)
expr = process_trig(expr)
expr = rubi_powsimp(expr)
if isinstance(expr, (int, Integer)) or isinstance(expr, (float, Float)):
return S(expr) * var
if isinstance(expr, Add):
results = 0
for ex in expr.args:
results += rubi.replace(Integral(ex, var))
return process_final_integral(results)
results = util_rubi_integrate(Integral(expr, var))
return process_final_integral(results)
def rubi_integrate(expr, var, showsteps=False):
'''
Rule based algorithm for integration. Integrates the expression by applying
transformation rules to the expression.
Returns `Integrate` if an expression cannot be integrated.
Parameters
==========
expr : integrand expression
var : variable of integration
Returns Integral object if unable to integrate.
'''
expr = expr.replace(sym_exp, exp)
rules_applied[:] = []
expr = process_trig(expr)
expr = rubi_powsimp(expr)
if isinstance(expr, (int, Integer)) or isinstance(expr, (float, Float)):
return S(expr) * var
if isinstance(expr, Add):
results = 0
for ex in expr.args:
rules_applied[:] = []
results += rubi.replace(Integral(ex, var))
rules_applied[:] = []
return process_final_integral(results)
results = rubi.replace(Integral(expr, var), max_count=10)
return process_final_integral(results)
def rubi_integrate(expr, var, showsteps=False):
'''
Rule based algorithm for integration. Integrates the expression by applying
transformation rules to the expression.
Returns `Integrate` if an expression cannot be integrated.
Parameters
==========
expr : integrand expression
var : variable of integration
Returns Integral object if unable to integrate.
'''
expr = expr.replace(sym_exp, exp)
rules_applied[:] = []
expr = process_trig(expr)
expr = rubi_powsimp(expr)
if isinstance(expr, (int, Integer)) or isinstance(expr, (float, Float)):
return S(expr)*var
if isinstance(expr, Add):
results = 0
for ex in expr.args:
rules_applied[:] = []
results += rubi.replace(Integral(ex, var))
rules_applied[:] = []
return process_final_integral(results)
results = rubi.replace(Integral(expr, var), max_count = 10)
return process_final_integral(results)
def util_rubi_integrate(expr, showsteps=False, max_loop=10):
rubi = LoadRubiReplacer().load()
expr = process_trig(expr)
expr = expr.replace(sym_exp, rubi_exp)
for i in range(max_loop):
results = expr.replace(lambda x: isinstance(x, Integral),
lambda x: rubi.replace(x, max_count=10))
if expr == results:
return results
return results
def util_rubi_integrate(expr, var, showsteps=False):
expr = process_trig(expr)
expr = expr.replace(sym_exp, exp)
if isinstance(expr, (int, Integer)) or isinstance(expr, (float, Float)):
return S(expr) * var
if isinstance(expr, Add):
return rubi_integrate(expr, var)
if len(rules_applied) > 10:
if _has_cycle() or len(rules_applied) > 20:
return Integrate(expr, var)
results = rubi.replace(Integral(expr, var), max_count=10)
rules_applied[:] = []
return results
def util_rubi_integrate(expr, var, showsteps=False):
expr = process_trig(expr)
expr = expr.replace(sym_exp, exp)
if isinstance(expr, (int, Integer)) or isinstance(expr, (float, Float)):
return S(expr)*var
if isinstance(expr, Add):
return rubi_integrate(expr, var)
if len(rules_applied) > 10:
if _has_cycle() or len(rules_applied) > 20:
return Integrate(expr, var)
results = rubi.replace(Integral(expr, var), max_count = 10)
rules_applied[:] = []
return results