complex_root_of uses inexact index

[jdemeyer]

When numerically evaluating complex_root_of(a, k), the index k is passed as floating-point number:

sage: complex_root_of(x^8-1, 7).n(2)
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-1-4eba84b7c14c> in <module>()
----> 1 complex_root_of(x**Integer(8)-Integer(1), Integer(7)).n(Integer(2))

/home/patchbot/sage-patchbot/src/sage/structure/element.pyx in sage.structure.element.Element.n (build/cythonized/sage/structure/element.c:8131)()
    863             0.666666666666667
    864         """
--> 865         return self.numerical_approx(prec, digits, algorithm)
    866 
    867     N = deprecated_function_alias(13055, n)

/home/patchbot/sage-patchbot/src/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression.numerical_approx (build/cythonized/sage/symbolic/expression.cpp:36209)()
   5818         kwds = {'parent': R, 'algorithm': algorithm}
   5819         try:
-> 5820             x = x._convert(kwds)
   5821         except TypeError: # numerical approximation for real number failed
   5822             pass          # try again with complex

/home/patchbot/sage-patchbot/src/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression._convert (build/cythonized/sage/symbolic/expression.cpp:10663)()
   1257         sig_on()
   1258         try:
-> 1259             res = self._gobj.evalf(0, kwds)
   1260         finally:
   1261             sig_off()

/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/functions/other.pyc in _evalf_(self, poly, index, parent, algorithm)
   2918         except AttributeError:
   2919             prec = 53
-> 2920         sobj = CRootOf(Poly(poly._sympy_()), int(index))
   2921         return sobj.n(ceil(prec*3/10))._sage_()
   2922 

/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sympy/polys/rootoftools.pyc in __new__(cls, f, x, index, radicals, expand)
    130         if index < -degree or index >= degree:
    131             raise IndexError("root index out of [%d, %d] range, got %d" %
--> 132                              (-degree, degree - 1, index))
    133         elif index < 0:
    134             index += degree

IndexError: root index out of [-8, 7] range, got 8

When gmpy2 is installed, the index is even passed as complex number:

sage -t --long src/sage/functions/other.py
**********************************************************************
File "src/sage/functions/other.py", line 2862, in sage.functions.other.Function_crootof
Failed example:
    c.n()
Exception raised:
    Traceback (most recent call last):
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 517, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 920, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.functions.other.Function_crootof[1]>", line 1, in <module>
        c.n()
      File "sage/structure/element.pyx", line 865, in sage.structure.element.Element.n (build/cythonized/sage/structure/element.c:8131)
        return self.numerical_approx(prec, digits, algorithm)
      File "sage/symbolic/expression.pyx", line 5824, in sage.symbolic.expression.Expression.numerical_approx (build/cythonized/sage/symbolic/expression.cpp:36286)
        x = x._convert(kwds)
      File "sage/symbolic/expression.pyx", line 1259, in sage.symbolic.expression.Expression._convert (build/cythonized/sage/symbolic/expression.cpp:10663)
        res = self._gobj.evalf(0, kwds)
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/functions/other.py", line 2920, in _evalf_
        sobj = CRootOf(Poly(poly._sympy_()), int(index))
      File "sage/rings/complex_number.pyx", line 1058, in sage.rings.complex_number.ComplexNumber.__int__ (build/cythonized/sage/rings/complex_number.c:10918)
        raise TypeError("can't convert complex to int; use int(abs(z))")
    TypeError: can't convert complex to int; use int(abs(z))
**********************************************************************
File "src/sage/functions/other.py", line 2864, in sage.functions.other.Function_crootof
Failed example:
    c.n(100)
Exception raised:
    Traceback (most recent call last):
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 517, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 920, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.functions.other.Function_crootof[2]>", line 1, in <module>
        c.n(Integer(100))
      File "sage/structure/element.pyx", line 865, in sage.structure.element.Element.n (build/cythonized/sage/structure/element.c:8131)
        return self.numerical_approx(prec, digits, algorithm)
      File "sage/symbolic/expression.pyx", line 5824, in sage.symbolic.expression.Expression.numerical_approx (build/cythonized/sage/symbolic/expression.cpp:36286)
        x = x._convert(kwds)
      File "sage/symbolic/expression.pyx", line 1259, in sage.symbolic.expression.Expression._convert (build/cythonized/sage/symbolic/expression.cpp:10663)
        res = self._gobj.evalf(0, kwds)
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/functions/other.py", line 2920, in _evalf_
        sobj = CRootOf(Poly(poly._sympy_()), int(index))
      File "sage/rings/complex_number.pyx", line 1058, in sage.rings.complex_number.ComplexNumber.__int__ (build/cythonized/sage/rings/complex_number.c:10918)
        raise TypeError("can't convert complex to int; use int(abs(z))")
    TypeError: can't convert complex to int; use int(abs(z))
**********************************************************************
File "src/sage/functions/other.py", line 2866, in sage.functions.other.Function_crootof
Failed example:
    (c^6 + c + 1).n(100) < 1e-25
Exception raised:
    Traceback (most recent call last):
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 517, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 920, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.functions.other.Function_crootof[3]>", line 1, in <module>
        (c**Integer(6) + c + Integer(1)).n(Integer(100)) < RealNumber('1e-25')
      File "sage/structure/element.pyx", line 865, in sage.structure.element.Element.n (build/cythonized/sage/structure/element.c:8131)
        return self.numerical_approx(prec, digits, algorithm)
      File "sage/symbolic/expression.pyx", line 5824, in sage.symbolic.expression.Expression.numerical_approx (build/cythonized/sage/symbolic/expression.cpp:36286)
        x = x._convert(kwds)
      File "sage/symbolic/expression.pyx", line 1259, in sage.symbolic.expression.Expression._convert (build/cythonized/sage/symbolic/expression.cpp:10663)
        res = self._gobj.evalf(0, kwds)
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/functions/other.py", line 2920, in _evalf_
        sobj = CRootOf(Poly(poly._sympy_()), int(index))
      File "sage/rings/complex_number.pyx", line 1058, in sage.rings.complex_number.ComplexNumber.__int__ (build/cythonized/sage/rings/complex_number.c:10918)
        raise TypeError("can't convert complex to int; use int(abs(z))")
    TypeError: can't convert complex to int; use int(abs(z))
**********************************************************************
File "src/sage/functions/other.py", line 2908, in sage.functions.other.Function_crootof._evalf_
Failed example:
    complex_root_of(x^2-2, 1).n()
Exception raised:
    Traceback (most recent call last):
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 517, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 920, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.functions.other.Function_crootof._evalf_[0]>", line 1, in <module>
        complex_root_of(x**Integer(2)-Integer(2), Integer(1)).n()
      File "sage/structure/element.pyx", line 865, in sage.structure.element.Element.n (build/cythonized/sage/structure/element.c:8131)
        return self.numerical_approx(prec, digits, algorithm)
      File "sage/symbolic/expression.pyx", line 5824, in sage.symbolic.expression.Expression.numerical_approx (build/cythonized/sage/symbolic/expression.cpp:36286)
        x = x._convert(kwds)
      File "sage/symbolic/expression.pyx", line 1259, in sage.symbolic.expression.Expression._convert (build/cythonized/sage/symbolic/expression.cpp:10663)
        res = self._gobj.evalf(0, kwds)
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/functions/other.py", line 2920, in _evalf_
        sobj = CRootOf(Poly(poly._sympy_()), int(index))
      File "sage/rings/complex_number.pyx", line 1058, in sage.rings.complex_number.ComplexNumber.__int__ (build/cythonized/sage/rings/complex_number.c:10918)
        raise TypeError("can't convert complex to int; use int(abs(z))")
    TypeError: can't convert complex to int; use int(abs(z))
**********************************************************************
2 items had failures:
   3 of   5 in sage.functions.other.Function_crootof
   1 of   3 in sage.functions.other.Function_crootof._evalf_
    [622 tests, 4 failures, 17.27 s]  
sage -t --long src/sage/interfaces/sympy.py
**********************************************************************
File "src/sage/interfaces/sympy.py", line 617, in sage.interfaces.sympy._sympysage_crootof
Failed example:
    (sols[0]+1)._sage_().n()
Exception raised:
    Traceback (most recent call last):
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 517, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 920, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.interfaces.sympy._sympysage_crootof[6]>", line 1, in <module>
        (sols[Integer(0)]+Integer(1))._sage_().n()
      File "sage/structure/element.pyx", line 865, in sage.structure.element.Element.n (build/cythonized/sage/structure/element.c:8131)
        return self.numerical_approx(prec, digits, algorithm)
      File "sage/symbolic/expression.pyx", line 5824, in sage.symbolic.expression.Expression.numerical_approx (build/cythonized/sage/symbolic/expression.cpp:36286)
        x = x._convert(kwds)
      File "sage/symbolic/expression.pyx", line 1259, in sage.symbolic.expression.Expression._convert (build/cythonized/sage/symbolic/expression.cpp:10663)
        res = self._gobj.evalf(0, kwds)
      File "/home/patchbot/sage-patchbot/local/lib/python2.7/site-packages/sage/functions/other.py", line 2920, in _evalf_
        sobj = CRootOf(Poly(poly._sympy_()), int(index))
      File "sage/rings/complex_number.pyx", line 1058, in sage.rings.complex_number.ComplexNumber.__int__ (build/cythonized/sage/rings/complex_number.c:10918)
        raise TypeError("can't convert complex to int; use int(abs(z))")
    TypeError: can't convert complex to int; use int(abs(z))
**********************************************************************
1 item had failures:
   1 of   8 in sage.interfaces.sympy._sympysage_crootof
    [218 tests, 1 failure, 3.27 s]

CC: @rwst @EmmanuelCharpentier

Component: symbolics

Author: Ralf Stephan

Branch/Commit: 277a403

Reviewer: Jeroen Demeyer

Issue created by migration from https://trac.sagemath.org/ticket/24378

[rwst]

Branch: u/rws/doctest_failures_related_to_sympy_crootof

[rwst]

comment:4

That exact arguments are made inexact is a bug in itself. But that they are made complex (EDIT: in some machines) is beyond me.

---

New commits:

a93662f

24378: Doctest failures related to sympy

[rwst]

Commit: a93662f

[rwst]

Author: Ralf Stephan

[jdemeyer]

comment:5

Do you have an idea why this depends on the system?

[jdemeyer]

comment:6

Replying to @rwst:

That exact arguments are made inexact is a bug in itself. But that they are made complex (EDIT: in some machines) is beyond me.

Do you know where this happens? It seems to me that it is Pynac doing this.

[videlec]

comment:8

Some sympy behavior depends on the presence/absence of gmpy2. We had this trouble before the upgrade.

[jdemeyer]

comment:10

Replying to @rwst:

That exact arguments are made inexact is a bug in itself.

Right, this ticket should just fix that.

[videlec]

comment:15

Replying to @jdemeyer:

Replying to @rwst:

That exact arguments are made inexact is a bug in itself.

Right, this ticket should just fix that.

Indeed numerical_approximation of symbolic expression is lazily converting all arguments to the same parent. Which is very wrong when a function is defined on R x N.

Perhaps it would be good to add in _evalf_ the check

if not isinstance(index, numbers.Integral):
    raise ValueError

Though I am curious about this sympy misbehavior.

[videlec]

comment:16

Indeed there is a sympy bug that is now tracked at #24380.

[videlec]

comment:17

numerical_approx is very wrong when evaluating. It converts x^2 - 2 to x^2 - 2.0 and hence loosing precision for no good reason.

[videlec]

comment:18

There was indeed a bug in sympy: #24380 needs review!

[rwst]

comment:19

I suggest accepting my quick fix to resolve the blocker. Meanwhile I'm looking into Pynac.

[jdemeyer]

comment:20

If your only goal is to resolve the blocker doctest failures, then I think it is better to use # known bug. The fact that the index is made floating-point is the real bug, whether it is real or complex is just a small variation.

[rwst]

comment:21

Replying to @videlec:

numerical_approx is very wrong when evaluating. It converts x^2 - 2 to x^2 - 2.0 and hence loosing precision for no good reason.

I disagree in this case. The result is exactly what was asked for.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

8c3f951

24378: set minimum digits; convert to given prec

[jdemeyer]

comment:39

The expression prec*3/10 will behave differently on Python 2 and Python 3. You should either use // or from future import division such that it works the same on Python 2 and Python 3.

[jdemeyer]

Reviewer: Jeroen Demeyer

[jdemeyer]

comment:40

What is the meaning of the factor 3/10 anyway?

[rwst]

comment:41

Replying to @jdemeyer:

What is the meaning of the factor 3/10 anyway?

An approximation to log(2,10) (EDITED) which is good enough until about 1000 bits precision.

[jdemeyer]

comment:42

Replying to @rwst:

Replying to @jdemeyer:

What is the meaning of the factor 3/10 anyway?

An approximation to log(2,10) (EDITED) which is good enough until about 1000 bits precision.

Then why don't use the actual value 0.3010299956639812? That avoids the problem with division also.

[sagetrac-git]

Changed commit from 8c3f951 to 8e65608

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

8e65608

24378: don't prematurely optimize

[rwst]

comment:45

Ping?

[videlec]

comment:46

ceil(prec*log(2,10))) is terrible. Why not using 0.3010299956639812 as suggested in comment:42? A possible alternative would be

from math import log10
int(prec * log10(2))

You definitely do not want to use two symbolic functions here.

[sagetrac-git]

Changed commit from 8e65608 to 14ed7c6

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

14ed7c6

24378: fix previous commit

[jdemeyer]

comment:48

Or better yet, use the sympy function prec_to_dps which is meant to convert bits to digits:

from sympy.core.evalf import prec_to_dps

[rwst]

comment:49

Thanks both. I'll make a fresh branch.

[rwst]

Changed branch from u/rws/24378-1 to u/rws/24378-2

[rwst]

Changed commit from 14ed7c6 to 277a403

[rwst]

comment:51

A minor note is that the results from prec_dps(n) are not identical to the previously proposed formulae at small values, even with a suitable shift.

---

New commits:

277a403

24378: complex_root_of uses inexact index

[jdemeyer]

comment:52

Good for me if this passes patchbot testing.

[vbraun]

Changed branch from u/rws/24378-2 to 277a403