The default __invert__ method of an element should avoid coercion

[Stefan]

Currently, the __invert__ methods in element.pyx do

    return 1/self

This results in a coercion of the integer 1 into the appropriate parent structure. Better would be to do

    return self.parent().one() / self

Additionally, the __invert__ method in MultiplicativeGroupElement relies on a method is_one() that is not provided by the class itself.

[vdelecroix]

cc'ing me (+ formatting in the description)

[vdelecroix]

New commits:

​d3e1ad5	trac #17694: upgrade the category of polyhedra
​c0a0bbb	trac #17694: one_element->one and zero_element->zero
​e3aa703	trac #17692: rewrite __invert__ (and delete some)

[jdemeyer]

Why do you add

if self.is_zero():
    raise ZeroDivisionError("division by zero in a ring")

I would say it's the division code which should raise this error, not __invert__.

[git]

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

​387ff8f

trac #17692: remove zero test + override -> overwrite

[vdelecroix]

Replying to jdemeyer:

Why do you add

...

I would say it's the division code which should raise this error, not __invert__.

Right. Removed in the last commit.

[mmezzarobba]

**********************************************************************
File "src/sage/structure/coerce.pyx", line 463, in sage.structure.coerce.CoercionModel_cache_maps.explain
Failed example:
    cm.explain(ZZ['x'], QQ['x'], operator.div)
Expected:
    Coercion on left operand via
        Ring morphism:
          From: Univariate Polynomial Ring in x over Integer Ring
          To:   Univariate Polynomial Ring in x over Rational Field
          Defn: Induced from base ring by
                Natural morphism:
                  From: Integer Ring
                  To:   Rational Field
    Arithmetic performed after coercions.
    Result lives in Fraction Field of Univariate Polynomial Ring in x over Rational Field
    Fraction Field of Univariate Polynomial Ring in x over Rational Field
Got:
    Coercion on left operand via
        Ring morphism:
          From: Univariate Polynomial Ring in x over Integer Ring
          To:   Univariate Polynomial Ring in x over Rational Field
          Defn: Induced from base ring by
                Natural morphism:
                  From: Integer Ring
                  To:   Rational Field
    Arithmetic performed after coercions.
    Result lives in Univariate Polynomial Ring in x over Rational Field
    Univariate Polynomial Ring in x over Rational Field
**********************************************************************
File "src/sage/structure/coerce.pyx", line 684, in sage.structure.coerce.CoercionModel_cache_maps.division_parent
Failed example:
    cm.division_parent(ZZ['x'])
Expected:
    Fraction Field of Univariate Polynomial Ring in x over Integer Ring
Got:
    Univariate Polynomial Ring in x over Integer Ring
**********************************************************************

**********************************************************************
File "src/sage/interfaces/maxima_abstract.py", line 2299, in sage.interfaces.maxima_abstract.MaximaAbstractElementFunction.__inv__
Failed example:
    ~f
Expected:
    1/sin(x)
Got:
    one()/sin(x)
**********************************************************************

**********************************************************************
File "src/sage/interfaces/r.py", line 22, in sage.interfaces.r
Failed example:
    ~x
Expected:
    [1] 0.09615385 0.17857143 0.32258065 0.15625000 0.04608295
Got:
    [1] 0 0 0 0 0
**********************************************************************

[git]

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

​06af245	trac #17692: fix interfaces
​16f36b0	trac #17692: remove a special case (for coercion)

[jdemeyer]

Wouldn't it be better to add the zero()/one() functions in the base class src/sage/interfaces/interface.py?

[vdelecroix]

Replying to jdemeyer:

Wouldn't it be better to add the zero()/one() functions in the base class src/sage/interfaces/interface.py?

True. Will do.

[git]

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

​310f284

trac #17692: move .one and .zero into Interface

[mmezzarobba]

More doctest failures.

**********************************************************************
File "src/sage/rings/infinity.py", line 93, in sage.rings.infinity
Failed example:
    unsigned_oo/0
Expected:
    Traceback (most recent call last):
    ...
    ValueError: unsigned oo times smaller number not defined
Got:
      ...
      File "sage/structure/coerce.pyx", line 798, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (build/cythonized/sage/structure/coerce.c:7153)
        return PyObject_CallObject(op, xy)
      File "sage/structure/element.pyx", line 2013, in sage.structure.element.RingElement.__div__ (build/cythonized/sage/structure/element.c:18317)
        return (<RingElement>self)._div_(<RingElement>right)
      File "sage/structure/element.pyx", line 2017, in sage.structure.element.RingElement._div_ (build/cythonized/sage/structure/element.c:18420)
        cpdef RingElement _div_(self, RingElement right):
      File "/home/marc/co/sage/local/lib/python2.7/site-packages/sage/rings/infinity.py", line 458, in _div_
        return self * ~other
      File "sage/structure/element.pyx", line 2073, in sage.structure.element.RingElement.__invert__ (build/cythonized/sage/structure/element.c:19009)
        return self._parent.one() / self
      File "sage/structure/element.pyx", line 2013, in sage.structure.element.RingElement.__div__ (build/cythonized/sage/structure/element.c:18317)
        return (<RingElement>self)._div_(<RingElement>right)
      File "sage/structure/element.pyx", line 2017, in sage.structure.element.RingElement._div_ (build/cythonized/sage/structure/element.c:18420)
        cpdef RingElement _div_(self, RingElement right):
      File "/home/marc/co/sage/local/lib/python2.7/site-packages/sage/rings/infinity.py", line 814, in _div_
        raise ValueError("quotient of number < oo by number < oo not defined")
    ValueError: quotient of number < oo by number < oo not defined
**********************************************************************

sage -t --warn-long 30.1 src/sage/schemes/elliptic_curves/formal_group.py
**********************************************************************
File "src/sage/schemes/elliptic_curves/formal_group.py", line 431, in sage.schemes.elliptic_curves.formal_group.EllipticCurveFormalGroup.inverse
Failed example:
    F = E.formal_group().group_law(6)
Exception raised:
    ...
    TypeError: unsupported operand parent(s) for '*': 'Multivariate Polynomial Ring in a1, a2, a3, a4, a6 over Rational Field' and 'Multivariate Polynomial Ring in t1, t2 over Multivariate Polynomial Ring in a1, a2, a3, a4, a6 over Integer Ring'
**********************************************************************

**********************************************************************
File "src/sage/schemes/elliptic_curves/formal_group.py", line 523, in sage.schemes.elliptic_curves.formal_group.EllipticCurveFormalGroup.group_law
Failed example:
    F(t1, 0)
Expected:
    t1 + O(t1, t2)^5
Got:
    t1 + O(t1, t2)^7
**********************************************************************

[vdelecroix]

Hello,

Indeed! The coercion with polynomial is to blame here... see ​this sage-devel thread. Several people fixed some issue locally (e.g. #7711). In order to go further, I need the coercion to be fixed. I will open a subsequent ticket if it is not yet here.

Vincent

[jdemeyer]

I actually propose to close this as "wontfix" since we need to get rid of __invert__ anyway.

[vdelecroix]

Why? Where?

[jdemeyer]

Well, everywhere really because __invert__ is supposed to return the bitwise inverse, not the mathematical inverse. It's the whole reason why I came up with the idea of a unary division.