Not all failed one is due to RootSum. Here is one that fails in sagemage
but works in sympy and does not generate RootSum but Piecewise
var('A B a alpha b beta m n x ')
integrate(x^(1/2)/(b*x+a),x, algorithm="sympy")
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call last)
Cell In [7], line 1
----> 1 integrate(x**(Integer(1)/Integer(2))/(b*x+a),x, algorithm="sympy")
File ~/TMP/sage-9.8/src/sage/misc/functional.py:773, in integral(x, *args,
**kwds)
648 """
649 Return an indefinite or definite integral of an object ``x``.
650
(...)
770
771 """
772 if hasattr(x, 'integral'):
--> 773 return x.integral(*args, **kwds)
774 else:
775 from sage.symbolic.ring import SR
File ~/TMP/sage-9.8/src/sage/symbolic/expression.pyx:13211, in
sage.symbolic.expression.Expression.integral()
13209 R = SR
13210 return R(integral(f, v, a, b, **kwds))
> 13211 return integral(self, *args, **kwds)
13212
13213 integrate = integral
File ~/TMP/sage-9.8/src/sage/symbolic/integration/integral.py:1063, in
integrate(expression, v, a, b, algorithm, hold)
1061 if not integrator:
1062 raise ValueError("Unknown algorithm: %s" % algorithm)
-> 1063 return integrator(expression, v, a, b)
1064 if a is None:
1065 return indefinite_integral(expression, v, hold=hold)
File ~/TMP/sage-9.8/src/sage/symbolic/integration/external.py:69, in
sympy_integrator(expression, v, a, b)
67 else:
68 result = sympy.integrate(ex, (v, a._sympy_(), b._sympy_()))
---> 69 return result._sage_()
File ~/TMP/sage-9.8/src/sage/interfaces/sympy.py:603, in
_sympysage_piecewise(self)
588 """
589 EXAMPLES::
590
(...)
600 -y*z + cases(((log(x) != 0, x^y/log(x)), (1, y)))
601 """
602 from sage.functions.other import cases
--> 603 return cases([(p.cond._sage_(),p.expr._sage_()) for p in self.args])
File ~/TMP/sage-9.8/src/sage/interfaces/sympy.py:603, in <listcomp>(.0)
588 """
589 EXAMPLES::
590
(...)
600 -y*z + cases(((log(x) != 0, x^y/log(x)), (1, y)))
601 """
602 from sage.functions.other import cases
--> 603 return cases([(p.cond._sage_(),p.expr._sage_()) for p in self.args])
File
~/TMP/sage-9.8/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sympy/core/basic.py:1959,
in Basic._sage_(self)
1957 sympy_init() # may monkey-patch _sage_ method into self's class or
superclasses
1958 if old_method == self._sage_:
-> 1959 raise NotImplementedError('conversion to SageMath is not
implemented')
1960 else:
1961 # call the freshly monkey-patched method
1962 return self._sage_()
NotImplementedError: conversion to SageMath is not implemented
sage:
Here is same integral in sympy
>>> A,B,a,alpha,b,beta,m,n,x= symbols('A B a alpha b beta m n x ')
>>> integrate(S("x**(1/2)/(b*x+a)"),x)
Piecewise((zoo*sqrt(x), Eq(a, 0) & Eq(b, 0)), (2*x**(3/2)/(3*a), Eq(b, 0)),
(2*sqrt(x)/b, Eq(a, 0)), (-a*log(sqrt(x) - sqrt(-a/b))/(b**2*sqrt(-a/b)) +
a*log(sqrt(x) + sqrt(-a/b))/(b**2*sqrt(-a/b)) + 2*sqrt(x)/b, True))
>>>
Or without using S
>>> integrate(x**Rational(1/2)/(b*x+a),x)
Piecewise((zoo*sqrt(x), Eq(a, 0) & Eq(b, 0)), (2*x**(3/2)/(3*a), Eq(b, 0)),
(2*sqrt(x)/b, Eq(a, 0)), (-a*log(sqrt(x) - sqrt(-a/b))/(b**2*sqrt(-a/b)) +
a*log(sqrt(x) + sqrt(-a/b))/(b**2*sqrt(-a/b)) + 2*sqrt(x)/b, True))
I did not have the time to check each integral to find why it fails but
will post list of all failed ones from this one file next.
--Nasser
On Wednesday, April 26, 2023 at 1:26:55 PM UTC-5 Dima Pasechnik wrote:
> Thanks for showing this. As far as I know, the problem is that Sage does
> not support RootSum expressions - although they are very useful for
> integration in particular.
>
>
> On Wed, 26 Apr 2023, 19:22 'Nasser M. Abbasi' via sage-devel, <
> [email protected]> wrote:
>
>> I use sagemath to run the independent CAS integrations tests for Fricas,
>> Giac and Maxima, since it is much easier to use the same script to all CAS
>> systems instead of learning how to use each separate CAS. The result is put
>> on this page <https://12000.org/my_notes/CAS_integration_tests/index.htm>
>> .
>>
>> I found that sympy now can be used from sagemath.
>>
>> So I said, great. Instead of having separate script for sympy in python
>> will use the same sagemath script and just change the name of the algorithm
>> to 'sympy'. Makes life easier.
>>
>> But when I tried this on one test file, I found many integrals now fail,
>> where they work using sympy directly in Python.
>>
>> I am not sure if this is because sympy is not yet fully yet supported in
>> sagemath or if this is just a bug and overlooked support.
>>
>> For example, on this one file, sympy used to score 84.66% passing score
>> when used directly, but now in sagemath it scores 65.64%.
>>
>> This translates to about 30 more integrals failing in this file of 163
>> integrals.
>>
>> Below will give one example. All seem to give the same exception
>>
>> NotImplementedError('conversion to SageMath is not implemented')
>>
>> Here is one example in sagemath 9.8
>>
>> var('A B a alpha b beta m n x ')
>> integrate(x/((b*x^2+a)^m),x, algorithm='sympy')
>>
>>
>> ---------------------------------------------------------------------------
>> NotImplementedError Traceback (most recent call
>> last)
>> Cell In [2], line 1
>> ----> 1 integrate(x/(b*x**Integer(3)+a)**Integer(2),x, algorithm='sympy')
>>
>> File ~/TMP/sage-9.8/src/sage/misc/functional.py:773, in integral(x,
>> *args, **kwds)
>> 648 """
>> 649 Return an indefinite or definite integral of an object ``x``.
>> 650
>> (...)
>> 770
>> 771 """
>> 772 if hasattr(x, 'integral'):
>> --> 773 return x.integral(*args, **kwds)
>> 774 else:
>> 775 from sage.symbolic.ring import SR
>>
>> File ~/TMP/sage-9.8/src/sage/symbolic/expression.pyx:13211, in
>> sage.symbolic.expression.Expression.integral()
>> 13209 R = SR
>> 13210 return R(integral(f, v, a, b, **kwds))
>> > 13211 return integral(self, *args, **kwds)
>> 13212
>> 13213 integrate = integral
>>
>> File ~/TMP/sage-9.8/src/sage/symbolic/integration/integral.py:1063, in
>> integrate(expression, v, a, b, algorithm, hold)
>> 1061 if not integrator:
>> 1062 raise ValueError("Unknown algorithm: %s" % algorithm)
>> -> 1063 return integrator(expression, v, a, b)
>> 1064 if a is None:
>> 1065 return indefinite_integral(expression, v, hold=hold)
>>
>> File ~/TMP/sage-9.8/src/sage/symbolic/integration/external.py:69, in
>> sympy_integrator(expression, v, a, b)
>> 67 else:
>> 68 result = sympy.integrate(ex, (v, a._sympy_(), b._sympy_()))
>> ---> 69 return result._sage_()
>>
>> File ~/TMP/sage-9.8/src/sage/interfaces/sympy.py:216, in
>> _sympysage_add(self)
>> 214 s = 0
>> 215 for x in self.args:
>> --> 216 s += x._sage_()
>> 217 return s
>>
>> File
>> ~/TMP/sage-9.8/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sympy/core/basic.py:1959,
>>
>> in Basic._sage_(self)
>> 1957 sympy_init() # may monkey-patch _sage_ method into self's class
>> or superclasses
>> 1958 if old_method == self._sage_:
>> -> 1959 raise NotImplementedError('conversion to SageMath is not
>> implemented')
>> 1960 else:
>> 1961 # call the freshly monkey-patched method
>> 1962 return self._sage_()
>>
>>
>> Here is same integral in sympy itself. You see it works.
>>
>> >python
>> Python 3.10.9 (main, Dec 19 2022, 17:35:49) [GCC 12.2.0] on linux
>> >>> from sympy import *
>> >>> A,B,a,alpha,b,beta,m,n,x= symbols('A B a alpha b beta m n x ')
>> >>> integrate(x/(b*x**3+a)**2,x)
>>
>> x**2/(3*a**2 + 3*a*b*x**3) + RootSum(729*_t**3*a**4*b**2 + 1, Lambda(_t,
>> _t*log(81*_t**2*a**3*b + x)))
>>
>>
>> The sympy version is 1.11.1 in both cases, all on Linux.
>>
>> age: ver = installed_packages()
>> sage: ver['sympy']
>> '1.11.1'
>>
>> Will give the list of failed integrals in this one file in a follow up
>> post.
>>
>> --Nasser
>>
>>
>>
>>
>> --
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>> .
>>
>
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