I found number of integrals where sagemath says ValueError: power::eval(): division by zero: when using giac algorithm.
But when I try the same integrate command in giac directly, it actually gives no output. Not able to integrate it. giac just says Done.
So I wonder why then sagemath gives division by zero? It also gives very large output below that, which I do not know where it came from, since giac does not show any output.
Using giac 1.7 and sagemath 9.3 on Linux
Here is the command inside giac
10>> integrate((e*x+d)^(9/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x)
Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.
The choice was done assuming [a,c,d,exp(1),exp(2)]=[60,-94,37,-33,49]
Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.
The choice was done assuming [a,c,d,exp(1),exp(2)]=[-3,-98,-46,47,-64]
Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.
The choice was done assuming [a,c,d,exp(1),exp(2)]=[-22,22,-65,22,-81]
Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.
The choice was done assuming [a,c,d,exp(1),exp(2)]=[1,6,75,-85,-12]
Evaluation time: 10.44
Done
// Time 10.44
And inside sagemath
var('e x d a c')
sage: integrate((e*x+d)^(9/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm="giac")
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
/usr/lib/python3.9/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression._div_ (build/cythonized/sage/symbolic/expression.cpp:25839)()
3894 else:
-> 3895 x = left._gobj / _right._gobj
3896 return new_Expression_from_GEx(left._parent, x)
ValueError: power::eval(): division by zero
During handling of the above exception, another exception occurred:
ZeroDivisionError Traceback (most recent call last)
/usr/lib/python3.9/site-packages/sage/interfaces/giac.py in _sage_(self, locals)
1131 try:
-> 1132 return symbolic_expression_from_string(result, lsymbols,
1133 accept_sequence=True)
/usr/lib/python3.9/site-packages/sage/calculus/calculus.py in symbolic_expression_from_string(s, syms, accept_sequence)
2407 if isinstance(v,Function)})
-> 2408 return parse_func(s)
2409
/usr/lib/python3.9/site-packages/sage/misc/parser.pyx in sage.misc.parser.Parser.parse_sequence (build/cythonized/sage/misc/parser.c:5837)()
549
--> 550 cpdef parse_sequence(self, s):
551 """
/usr/lib/python3.9/site-packages/sage/misc/parser.pyx in sage.misc.parser.Parser.parse_sequence (build/cythonized/sage/misc/parser.c:5702)()
565 cdef Tokenizer tokens = Tokenizer(s)
--> 566 all = self.p_sequence(tokens)
567 if tokens.next() != EOS:
/usr/lib/python3.9/site-packages/sage/misc/parser.pyx in sage.misc.parser.Parser.p_sequence (build/cythonized/sage/misc/parser.c:6450)()
631 elif token == '(':
--> 632 obj = self.p_tuple(tokens)
633 elif token == EOS:
/usr/lib/python3.9/site-packages/sage/misc/parser.pyx in sage.misc.parser.Parser.p_tuple (build/cythonized/sage/misc/parser.c:7237)()
699 tokens.reset(start)
--> 700 return self.p_eqn(tokens)
701
/usr/lib/python3.9/site-packages/sage/misc/parser.pyx in sage.misc.parser.Parser.p_eqn (build/cythonized/sage/misc/parser.c:7394)()
728 """
--> 729 lhs = self.p_expr(tokens)
730 cdef int op = tokens.next()
/usr/lib/python3.9/site-packages/sage/misc/parser.pyx in sage.misc.parser.Parser.p_expr (build/cythonized/sage/misc/parser.c:7746)()
768 cdef int op
--> 769 operand1 = self.p_term(tokens)
770 op = tokens.next()
/usr/lib/python3.9/site-packages/sage/misc/parser.pyx in sage.misc.parser.Parser.p_term (build/cythonized/sage/misc/parser.c:8150)()
812 else:
--> 813 operand1 = operand1 / operand2
814 op = tokens.next()
/usr/lib/python3.9/site-packages/sage/structure/element.pyx in sage.structure.element.Element.__truediv__ (build/cythonized/sage/structure/element.c:13162)()
1734 if HAVE_SAME_PARENT(cl):
-> 1735 return (<Element>left)._div_(right)
1736 if BOTH_ARE_ELEMENT(cl):
/usr/lib/python3.9/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression._div_ (build/cythonized/sage/symbolic/expression.cpp:25919)()
3900 if 'division by zero' in str(msg):
-> 3901 raise ZeroDivisionError("symbolic division by zero")
3902 else:
ZeroDivisionError: symbolic division by zero
During handling of the above exception, another exception occurred:
NotImplementedError Traceback (most recent call last)
<ipython-input-6-754567723580> in <module>
----> 1 integrate((e*x+d)**(Integer(9)/Integer(2))/(a*d*e+(a*e**Integer(2)+c*d**Integer(2))*x+c*d*e*x**Integer(2)),x, algorithm="giac")
/usr/lib/python3.9/site-packages/sage/misc/functional.py in integral(x, *args, **kwds)
757 """
758 if hasattr(x, 'integral'):
--> 759 return x.integral(*args, **kwds)
760 else:
761 from sage.symbolic.ring import SR
/usr/lib/python3.9/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression.integral (build/cythonized/sage/symbolic/expression.cpp:66867)()
12645 R = SR
12646 return R(integral(f, v, a, b, **kwds))
> 12647 return integral(self, *args, **kwds)
12648
12649 integrate = integral
/usr/lib/python3.9/site-packages/sage/symbolic/integration/integral.py in integrate(expression, v, a, b, algorithm, hold)
988 if not integrator:
989 raise ValueError("Unknown algorithm: %s" % algorithm)
--> 990 return integrator(expression, v, a, b)
991 if a is None:
992 return indefinite_integral(expression, v, hold=hold)
/usr/lib/python3.9/site-packages/sage/symbolic/integration/external.py in giac_integrator(expression, v, a, b)
446 return expression.integrate(v, a, b, hold=True)
447 else:
--> 448 return result._sage_()
/usr/lib/python3.9/site-packages/sage/interfaces/giac.py in _sage_(self, locals)
1134
1135 except Exception:
-> 1136 raise NotImplementedError("Unable to parse Giac output: %s" % result)
1137 else:
1138 return [entry.sage() for entry in self]
NotImplementedError: Unable to parse Giac output: ((-4*a^8*c^2*d^2*exp(2)^8+2*a^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^8+44*a^7*c^3*d^4*exp(1)^2*exp(2)^6-12*a^7*c^3*d^4*exp(2)^7-22*a^7*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-
... pages and pages of output like the above follows....
p(1))*d^9*c^6-4*sqrt(d+x*exp(1))*d^7*exp(1)^2*c^5*a-2*sqrt(d+x*exp(1))*d^7*c^5*a*exp(2)+4*sqrt(d+x*exp(1))*d^5*exp(1)^2*c^4*a^2*exp(2)+2*sqrt(d+x*exp(1))*d^5*c^4*a^2*exp(2)^2-2*sqrt(d+x*exp(1))*d^3*c^3*a^3*exp(2)^3)/d^7/c^7
sage:
My question is: Where did all this output come from? The ones starting after Unable to parse Giac output:.
I know because giac has warning messages, this could have confused sagemath in parsing the return value. There is a question on this already.
But my question here is different. Since giac did not give any output from the integrate command, I was wondering then where did this very long output came from then?
