looks like Piecewise () is another non-implemented conversion - although
it's probably easy to fix.
On Wed, 26 Apr 2023, 19:55 'Nasser M. Abbasi' via sage-devel, <
sage-devel@googlegroups.com> wrote:
> 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, <
>> sage-...@googlegroups.com> 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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