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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