def fricas_integrator(expression, v, a=None, b=None, noPole=True):
"""
Integration using FriCAS
EXAMPLES::
sage: from sage.symbolic.integration.external import fricas_integrator # optional - fricas
sage: fricas_integrator(sin(x), x) # optional - fricas
-cos(x)
sage: fricas_integrator(cos(x), x) # optional - fricas
sin(x)
sage: fricas_integrator(1/(x^2-2), x, 0, 1) # optional - fricas
1/4*sqrt(2)*(log(3*sqrt(2) - 4) - log(sqrt(2)))
sage: fricas_integrator(1/(x^2+6), x, -oo, oo) # optional - fricas
1/6*sqrt(6)*pi
"""
if not isinstance(expression, Expression):
expression = SR(expression)
if a is None:
result = expression._fricas_().integrate(v)
else:
import sage.rings.infinity
if a == sage.rings.infinity.PlusInfinity():
a = "%plusInfinity"
elif a == sage.rings.infinity.MinusInfinity():
a = "%minusInfinity"
if b == sage.rings.infinity.PlusInfinity():
b = "%plusInfinity"
elif b == sage.rings.infinity.MinusInfinity():
b = "%minusInfinity"
if noPole:
result = expression._fricas_().integrate(
"{}={}..{}".format(v, a, b), '"noPole"')
else:
result = expression._fricas_().integrate("{}={}..{}".format(
v, a, b))
locals = {str(v): v for v in expression.variables()}
if str(result) == "potentialPole":
raise ValueError("The integrand has a potential pole"
" in the integration interval")
return result.sage()
def fricas_integrator(expression, v, a=None, b=None, noPole=True):
"""
Integration using FriCAS
EXAMPLES::
sage: from sage.symbolic.integration.external import fricas_integrator # optional - fricas
sage: fricas_integrator(sin(x), x) # optional - fricas
-cos(x)
sage: fricas_integrator(cos(x), x) # optional - fricas
sin(x)
sage: fricas_integrator(1/(x^2-2), x, 0, 1) # optional - fricas
1/4*sqrt(2)*(log(3*sqrt(2) - 4) - log(sqrt(2)))
sage: fricas_integrator(1/(x^2+6), x, -oo, oo) # optional - fricas
1/6*sqrt(6)*pi
"""
if not isinstance(expression, Expression):
expression = SR(expression)
if a is None:
result = expression._fricas_().integrate(v)
else:
import sage.rings.infinity
if a == sage.rings.infinity.PlusInfinity():
a = "%plusInfinity"
elif a == sage.rings.infinity.MinusInfinity():
a = "%minusInfinity"
if b == sage.rings.infinity.PlusInfinity():
b = "%plusInfinity"
elif b == sage.rings.infinity.MinusInfinity():
b = "%minusInfinity"
if noPole:
result = expression._fricas_().integrate("{}={}..{}".format(v, a, b), '"noPole"')
else:
result = expression._fricas_().integrate("{}={}..{}".format(v, a, b))
locals = {str(v): v for v in expression.variables()}
if str(result) == "potentialPole":
raise ValueError("The integrand has a potential pole"
" in the integration interval")
return result.sage()
def fricas_integrator(expression, v, a=None, b=None):
"""
Integration using FriCAS
EXAMPLES::
sage: from sage.symbolic.integration.external import fricas_integrator # optional - fricas
sage: fricas_integrator(sin(x), x) # optional - fricas
-cos(x)
sage: fricas_integrator(cos(x), x) # optional - fricas
sin(x)
sage: fricas_integrator(1/(x^2-2), x, 0, 1) # optional - fricas
1/4*(log(3*sqrt(2) - 4) - log(sqrt(2)))*sqrt(2)
sage: fricas_integrator(1/(x^2+6), x, -oo, oo) # optional - fricas
1/6*pi*sqrt(6)
"""
if not isinstance(expression, Expression):
expression = SR(expression)
if a is None:
result = expression._fricas_().integrate(v)
else:
import sage.rings.infinity
if a == sage.rings.infinity.PlusInfinity():
a = "%plusInfinity"
elif a == sage.rings.infinity.MinusInfinity():
a = "%minusInfinity"
if b == sage.rings.infinity.PlusInfinity():
b = "%plusInfinity"
elif b == sage.rings.infinity.MinusInfinity():
b = "%minusInfinity"
result = expression._fricas_().integrate("{}={}..{}".format(v, a, b))
locals = {str(v): v for v in expression.variables()}
if str(result) == "potentialPole":
raise ValueError("The integrand has a potential pole"
" in the integration interval")
parsed_result = result.unparsed_input_form()
import sage.misc.sage_eval
try:
return sage.misc.sage_eval.sage_eval(parsed_result, locals=locals)
except:
raise ValueError("Unable to parse: {}".format(parsed_result))
def fricas_integrator(expression, v, a=None, b=None):
"""
Integration using FriCAS
EXAMPLES::
sage: from sage.symbolic.integration.external import fricas_integrator # optional - fricas
sage: fricas_integrator(sin(x), x) # optional - fricas
-cos(x)
sage: fricas_integrator(cos(x), x) # optional - fricas
sin(x)
sage: fricas_integrator(1/(x^2-2), x, 0, 1) # optional - fricas
1/4*(log(3*sqrt(2) - 4) - log(sqrt(2)))*sqrt(2)
sage: fricas_integrator(1/(x^2+6), x, -oo, oo) # optional - fricas
1/6*pi*sqrt(6)
"""
if not isinstance(expression, Expression):
expression = SR(expression)
if a is None:
result = expression._fricas_().integrate(v)
else:
import sage.rings.infinity
if a == sage.rings.infinity.PlusInfinity():
a = "%plusInfinity"
elif a == sage.rings.infinity.MinusInfinity():
a = "%minusInfinity"
if b == sage.rings.infinity.PlusInfinity():
b = "%plusInfinity"
elif b == sage.rings.infinity.MinusInfinity():
b = "%minusInfinity"
result = expression._fricas_().integrate("{}={}..{}".format(v, a, b))
locals = {str(v): v for v in expression.variables()}
if str(result) == "potentialPole":
raise ValueError("The integrand has a potential pole"
" in the integration interval")
parsed_result = result.unparsed_input_form()
import sage.misc.sage_eval
try:
return sage.misc.sage_eval.sage_eval(parsed_result, locals=locals)
except:
raise ValueError("Unable to parse: {}".format(parsed_result))
