If I recall correctly, this is what I did for the FriCAS interface. It
would be nice to factor out any common functionality, if possible.
On Wednesday, 26 April 2023 at 21:06:30 UTC+2 Oscar Benjamin wrote:
> One thing Sage could do with SymPy's RootSum is to call doit which
> will expand using radical formulae if possible:
>
> 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)))
>
> In [37]: x, a, b, _t = symbols('x, a, b, _t')
>
> In [38]: expr = x**2/(3*a**2 + 3*a*b*x**3) +
> RootSum(Poly(729*_t**3*a**4*b**2 + 1, _t), Lambda(_t,
> _t*log(81*_t**2*a**3*b + x)))
>
> In [39]: print(expr)
> 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)))
>
> In [40]: print(expr.doit())
> x**2/(3*a**2 + 3*a*b*x**3) +
> (-1/(a**4*b**2))**(1/3)*log(a**3*b*(-1/(a**4*b**2))**(2/3) + x)/9 +
> (-(-1/(a**4*b**2))**(1/3)/18 -
>
> sqrt(3)*I*(-1/(a**4*b**2))**(1/3)/18)*log(81*a**3*b*(-(-1/(a**4*b**2))**(1/3)/18
> - sqrt(3)*I*(-1/(a**4*b**2))**(1/3)/18)**2 + x) +
> (-(-1/(a**4*b**2))**(1/3)/18 +
>
> sqrt(3)*I*(-1/(a**4*b**2))**(1/3)/18)*log(81*a**3*b*(-(-1/(a**4*b**2))**(1/3)/18
> + sqrt(3)*I*(-1/(a**4*b**2))**(1/3)/18)**2 + x)
>
> A more precise instruction would be:
>
> expr.replace(lambda e: isinstance(e, RootSum), lambda e:
> e.doit(deep=False))
>
> --
> Oscar
>
> On Wed, 26 Apr 2023 at 19:26, Dima Pasechnik <dim...@gmail.com> 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.
> >>
> >> 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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