Here is list of integrals that fail in sagemath from this one file. It
seems Piecewise and RootSum are the cause of these failures.
sagemath version
var('A B a alpha b beta m n x ')
integrate(x/((b*x^2+a)^m),x, algorithm="sympy")
integrate(1/(b*x^3+a),x, algorithm="sympy")
integrate(x/(b*x^3+a),x, algorithm="sympy")
integrate(x^3/(b*x^3+a),x, algorithm="sympy")
integrate(x^4/(b*x^3+a),x, algorithm="sympy")
integrate(1/(b*x^3+a)^2,x, algorithm="sympy")
integrate(x/(b*x^3+a)^2,x, algorithm="sympy")
integrate(x^3/(b*x^3+a)^2,x, algorithm="sympy")
integrate(1/x^2/(b*x^3+a),x, algorithm="sympy")
integrate(1/x^3/(b*x^3+a),x, algorithm="sympy")
integrate(1/x^2/(b*x^3+a)^2,x, algorithm="sympy")
integrate(1/x^3/(b*x^3+a)^2,x, algorithm="sympy")
integrate(1/(b*x^4+a),x, algorithm="sympy")
integrate(x^2/(b*x^4+a),x, algorithm="sympy")
integrate(1/(b*x^4+a)^2,x, algorithm="sympy")
integrate(x^2/(b*x^4+a)^2,x, algorithm="sympy")
integrate(1/x^2/(b*x^4+a),x, algorithm="sympy")
integrate(1/(b*x+a)/x^(1/2),x, algorithm="sympy")
integrate(x^(1/2)/(b*x+a),x, algorithm="sympy")
integrate(x^(3/2)/(b*x+a),x, algorithm="sympy")
integrate(x^(5/2)/(b*x+a),x, algorithm="sympy")
integrate(1/(b*x+a)^2/x^(1/2),x, algorithm="sympy")
integrate(x^(1/2)/(b*x+a)^2,x, algorithm="sympy")
integrate(x^(3/2)/(b*x+a)^2,x, algorithm="sympy")
integrate(x^(5/2)/(b*x+a)^2,x, algorithm="sympy")
integrate(1/(b*x+a)^3/x^(1/2),x, algorithm="sympy")
integrate(x^(1/2)/(b*x+a)^3,x, algorithm="sympy")
integrate(x^(3/2)/(b*x+a)^3,x, algorithm="sympy")
integrate(x^(5/2)/(b*x+a)^3,x, algorithm="sympy")
integrate(1/x^(1/2)/(b*x^2+a),x, algorithm="sympy")
integrate(x^(1/2)/(b*x^2+a),x, algorithm="sympy")
integrate(x^(3/2)/(b*x^2+a),x, algorithm="sympy")
integrate(x^(5/2)/(b*x^2+a),x, algorithm="sympy")
integrate(1/x^(1/2)/(b*x^2+a)^2,x, algorithm="sympy")
integrate(x^(1/2)/(b*x^2+a)^2,x, algorithm="sympy")
integrate(x^(3/2)/(b*x^2+a)^2,x, algorithm="sympy")
integrate(x^(5/2)/(b*x^2+a)^2,x, algorithm="sympy")
integrate(1/x^(1/2)/(b*x^2+a)^3,x, algorithm="sympy")
integrate(x^(1/2)/(b*x^2+a)^3,x, algorithm="sympy")
sympy version
>python
from sympy import *
A,B,a,alpha,b,beta,m,n,x= symbols('A B a alpha b beta m n x ')
integrate(S("x/((b*x**2+a)**m)"),x)
integrate(S("1/(b*x**3+a)"),x)
integrate(S("x/(b*x**3+a)"),x)
integrate(S("x**3/(b*x**3+a)"),x)
integrate(S("x**4/(b*x**3+a)"),x)
integrate(S("1/(b*x**3+a)**2"),x)
integrate(S("x/(b*x**3+a)**2"),x)
integrate(S("x**3/(b*x**3+a)**2"),x)
integrate(S("1/x**2/(b*x**3+a)"),x)
integrate(S("1/x**3/(b*x**3+a)"),x)
integrate(S("1/x**2/(b*x**3+a)**2"),x)
integrate(S("1/x**3/(b*x**3+a)**2"),x)
integrate(S("1/(b*x**4+a)"),x)
integrate(S("x**2/(b*x**4+a)"),x)
integrate(S("1/(b*x**4+a)**2"),x)
integrate(S("x**2/(b*x**4+a)**2"),x)
integrate(S("1/x**2/(b*x**4+a)"),x)
integrate(S("1/(b*x+a)/x**(1/2)"),x)
integrate(S("x**(1/2)/(b*x+a)"),x)
integrate(S("x**(3/2)/(b*x+a)"),x)
integrate(S("x**(5/2)/(b*x+a)"),x)
integrate(S("1/(b*x+a)**2/x**(1/2)"),x)
integrate(S("x**(1/2)/(b*x+a)**2"),x)
integrate(S("x**(3/2)/(b*x+a)**2"),x)
integrate(S("x**(5/2)/(b*x+a)**2"),x)
integrate(S("1/(b*x+a)**3/x**(1/2)"),x)
integrate(S("x**(1/2)/(b*x+a)**3"),x)
integrate(S("x**(3/2)/(b*x+a)**3"),x)
integrate(S("x**(5/2)/(b*x+a)**3"),x)
integrate(S("1/x**(1/2)/(b*x**2+a)"),x)
integrate(S("x**(1/2)/(b*x**2+a)"),x)
integrate(S("x**(3/2)/(b*x**2+a)"),x)
integrate(S("x**(5/2)/(b*x**2+a)"),x)
integrate(S("1/x**(1/2)/(b*x**2+a)**2"),x)
integrate(S("x**(1/2)/(b*x**2+a)**2"),x)
integrate(S("x**(3/2)/(b*x**2+a)**2"),x)
integrate(S("x**(5/2)/(b*x**2+a)**2"),x)
integrate(S("1/x**(1/2)/(b*x**2+a)**3"),x)
integrate(S("x**(1/2)/(b*x**2+a)**3"),x)
All using sagemath 9.8 and sympy 1.11.1 on Linux
--Nasser
On Wednesday, April 26, 2023 at 1:22:08 PM UTC-5 Nasser M. Abbasi 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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