# Revision history [back]

### Rename xbar, ybar

When generating fraction fields, is it possible to rename xbar to x?

### Rename xbar, ybar

When generating fraction fields, is it possible to rename xbar to x?? Consider the following example:

sage: R=PolynomialRing(QQ, ['x','y','a4','a6'])
sage: R.inject_variables()
Defining x, y, a4, a6
sage: I=R.ideal(x^3+a4*x+a6-y^2)
sage: Q=R.quotient(I)
sage: F=Q.fraction_field()
sage: E=EllipticCurve(F,[a4,a6])
sage: E.discriminant()
-64*a4bar^3 - 432*a6bar^2
sage: _.factor()
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-149-995262737325> in <module>()
----> 1 _.factor()

/usr/lib/python2.7/site-packages/sage/categories/quotient_fields.pyc in factor(self, *args, **kwds)
352                 (x + y)^-1 * y * x
353             """
--> 354             return (self.numerator().factor(*args, **kwds) /
355                     self.denominator().factor(*args, **kwds))
356

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.__getattr__ (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4290)()
457             AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
458         """
--> 459         return self.getattr_from_category(name)
460
461     cdef getattr_from_category(self, name):

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.getattr_from_category (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4399)()
470         else:
471             cls = P._abstract_element_class
--> 472         return getattr_from_other_class(self, cls, name)
473
474     def __dir__(self):

/usr/share/sage/source/sage/structure/misc.pyx in sage.structure.misc.getattr_from_other_class (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/misc.c:1927)()
292         dummy_error_message.cls = type(self)
293         dummy_error_message.name = name
--> 294         raise dummy_attribute_error
295     cdef PyObject* attr = _PyType_Lookup(<type>cls, name)
296     if attr is NULL:

AttributeError: 'QuotientRing_generic_with_category.element_class' object has no attribute 'factor'


I want to have -16(4a4^3 - 27*a6^2) as an output. Is this possible?

### Rename xbar, ybar

When generating fraction fields, is it possible to rename xbar to x? Consider the following example:

sage: R=PolynomialRing(QQ, ['x','y','a4','a6'])
sage: R.inject_variables()
Defining x, y, a4, a6
sage: I=R.ideal(x^3+a4*x+a6-y^2)
sage: Q=R.quotient(I)
sage: F=Q.fraction_field()
sage: E=EllipticCurve(F,[a4,a6])
sage: E.discriminant()
-64*a4bar^3 - 432*a6bar^2
sage: _.factor()
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-149-995262737325> in <module>()
----> 1 _.factor()

/usr/lib/python2.7/site-packages/sage/categories/quotient_fields.pyc in factor(self, *args, **kwds)
352                 (x + y)^-1 * y * x
353             """
--> 354             return (self.numerator().factor(*args, **kwds) /
355                     self.denominator().factor(*args, **kwds))
356

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.__getattr__ (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4290)()
457             AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
458         """
--> 459         return self.getattr_from_category(name)
460
461     cdef getattr_from_category(self, name):

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.getattr_from_category (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4399)()
470         else:
471             cls = P._abstract_element_class
--> 472         return getattr_from_other_class(self, cls, name)
473
474     def __dir__(self):

/usr/share/sage/source/sage/structure/misc.pyx in sage.structure.misc.getattr_from_other_class (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/misc.c:1927)()
292         dummy_error_message.cls = type(self)
293         dummy_error_message.name = name
--> 294         raise dummy_attribute_error
295     cdef PyObject* attr = _PyType_Lookup(<type>cls, name)
296     if attr is NULL:

AttributeError: 'QuotientRing_generic_with_category.element_class' object has no attribute 'factor'


I want to have -16(4a4^3 - 27*a6^2) as an output. Is this possible?

### Rename xbar, ybarybar and factorize/simplify

When generating fraction fields, is it possible to rename xbar to x? Consider the following example:

sage: R=PolynomialRing(QQ, ['x','y','a4','a6'])
sage: R.inject_variables()
Defining x, y, a4, a6
sage: I=R.ideal(x^3+a4*x+a6-y^2)
sage: Q=R.quotient(I)
sage: F=Q.fraction_field()
sage: E=EllipticCurve(F,[a4,a6])
sage: E.discriminant()
-64*a4bar^3 - 432*a6bar^2
sage: _.factor()
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-149-995262737325> in <module>()
----> 1 _.factor()

/usr/lib/python2.7/site-packages/sage/categories/quotient_fields.pyc in factor(self, *args, **kwds)
352                 (x + y)^-1 * y * x
353             """
--> 354             return (self.numerator().factor(*args, **kwds) /
355                     self.denominator().factor(*args, **kwds))
356

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.__getattr__ (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4290)()
457             AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
458         """
--> 459         return self.getattr_from_category(name)
460
461     cdef getattr_from_category(self, name):

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.getattr_from_category (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4399)()
470         else:
471             cls = P._abstract_element_class
--> 472         return getattr_from_other_class(self, cls, name)
473
474     def __dir__(self):

/usr/share/sage/source/sage/structure/misc.pyx in sage.structure.misc.getattr_from_other_class (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/misc.c:1927)()
292         dummy_error_message.cls = type(self)
293         dummy_error_message.name = name
--> 294         raise dummy_attribute_error
295     cdef PyObject* attr = _PyType_Lookup(<type>cls, name)
296     if attr is NULL:

AttributeError: 'QuotientRing_generic_with_category.element_class' object has no attribute 'factor'


I want to have -16(4a4^3 -16*(4*a4^3 - 27*a6^2) 27*a6^2) as an the output. Is this possible?

### Rename xbar, ybar and factorize/simplify

When generating fraction fields, is it possible to rename xbar to x? Consider the following example:

sage: R=PolynomialRing(QQ, ['x','y','a4','a6'])
sage: R.inject_variables()
Defining x, y, a4, a6
sage: I=R.ideal(x^3+a4*x+a6-y^2)
sage: Q=R.quotient(I)
sage: F=Q.fraction_field()
sage: E=EllipticCurve(F,[a4,a6])
sage: E.discriminant()
-64*a4bar^3 - 432*a6bar^2
sage: _.factor()
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-149-995262737325> in <module>()
----> 1 _.factor()

/usr/lib/python2.7/site-packages/sage/categories/quotient_fields.pyc in factor(self, *args, **kwds)
352                 (x + y)^-1 * y * x
353             """
--> 354             return (self.numerator().factor(*args, **kwds) /
355                     self.denominator().factor(*args, **kwds))
356

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.__getattr__ (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4290)()
457             AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
458         """
--> 459         return self.getattr_from_category(name)
460
461     cdef getattr_from_category(self, name):

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.getattr_from_category (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4399)()
470         else:
471             cls = P._abstract_element_class
--> 472         return getattr_from_other_class(self, cls, name)
473
474     def __dir__(self):

/usr/share/sage/source/sage/structure/misc.pyx in sage.structure.misc.getattr_from_other_class (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/misc.c:1927)()
292         dummy_error_message.cls = type(self)
293         dummy_error_message.name = name
--> 294         raise dummy_attribute_error
295     cdef PyObject* attr = _PyType_Lookup(<type>cls, name)
296     if attr is NULL:

AttributeError: 'QuotientRing_generic_with_category.element_class' object has no attribute 'factor'


I want to have -16*(4*a4^3 - + 27*a6^2) as the output. Is this possible?

### Rename xbar, ybar and factorize/simplify

When generating fraction fields, is it possible to rename xbar to x? Consider the following example:

sage: R=PolynomialRing(QQ, ['x','y','a4','a6'])
sage: R.inject_variables()
Defining x, y, a4, a6
sage: I=R.ideal(x^3+a4*x+a6-y^2)
sage: Q=R.quotient(I)
sage: F=Q.fraction_field()
sage: E=EllipticCurve(F,[a4,a6])
sage: E.discriminant()
-64*a4bar^3 - 432*a6bar^2
sage: _.factor()
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-149-995262737325> in <module>()
----> 1 _.factor()

/usr/lib/python2.7/site-packages/sage/categories/quotient_fields.pyc in factor(self, *args, **kwds)
352                 (x + y)^-1 * y * x
353             """
--> 354             return (self.numerator().factor(*args, **kwds) /
355                     self.denominator().factor(*args, **kwds))
356

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.__getattr__ (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4290)()
457             AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
458         """
--> 459         return self.getattr_from_category(name)
460
461     cdef getattr_from_category(self, name):

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.getattr_from_category (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4399)()
470         else:
471             cls = P._abstract_element_class
--> 472         return getattr_from_other_class(self, cls, name)
473
474     def __dir__(self):

/usr/share/sage/source/sage/structure/misc.pyx in sage.structure.misc.getattr_from_other_class (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/misc.c:1927)()
292         dummy_error_message.cls = type(self)
293         dummy_error_message.name = name
--> 294         raise dummy_attribute_error
295     cdef PyObject* attr = _PyType_Lookup(<type>cls, name)
296     if attr is NULL:

AttributeError: 'QuotientRing_generic_with_category.element_class' object has no attribute 'factor'


I want to have -16*(4*a4^3 + 27*a6^2) as the output. Is this possible?

### Rename xbar, ybar xbar and factorize/simplify

When generating fraction fields, is it possible to rename xbar to x? and do a factorization? Consider the following example:

sage: R=PolynomialRing(QQ, ['x','y','a4','a6'])
sage: R.inject_variables()
Defining x, y, a4, a6
sage: I=R.ideal(x^3+a4*x+a6-y^2)
sage: Q=R.quotient(I)
sage: F=Q.fraction_field()
sage: E=EllipticCurve(F,[a4,a6])
sage: E.discriminant()
-64*a4bar^3 - 432*a6bar^2
sage: _.factor()
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-149-995262737325> in <module>()
----> 1 _.factor()

/usr/lib/python2.7/site-packages/sage/categories/quotient_fields.pyc in factor(self, *args, **kwds)
352                 (x + y)^-1 * y * x
353             """
--> 354             return (self.numerator().factor(*args, **kwds) /
355                     self.denominator().factor(*args, **kwds))
356

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.__getattr__ (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4290)()
457             AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
458         """
--> 459         return self.getattr_from_category(name)
460
461     cdef getattr_from_category(self, name):

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.getattr_from_category (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4399)()
470         else:
471             cls = P._abstract_element_class
--> 472         return getattr_from_other_class(self, cls, name)
473
474     def __dir__(self):

/usr/share/sage/source/sage/structure/misc.pyx in sage.structure.misc.getattr_from_other_class (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/misc.c:1927)()
292         dummy_error_message.cls = type(self)
293         dummy_error_message.name = name
--> 294         raise dummy_attribute_error
295     cdef PyObject* attr = _PyType_Lookup(<type>cls, name)
296     if attr is NULL:

AttributeError: 'QuotientRing_generic_with_category.element_class' object has no attribute 'factor'


I want to have -16*(4*a4^3 + 27*a6^2) as the output. Is this possible?

### Rename xbar and factorize/simplify

When generating fraction fields, is it possible to rename xbar to x and do a factorization? Consider the following example:

sage: R=PolynomialRing(QQ, ['x','y','a4','a6'])
sage: R.inject_variables()
Defining x, y, a4, a6
sage: I=R.ideal(x^3+a4*x+a6-y^2)
sage: Q=R.quotient(I)
sage: F=Q.fraction_field()
sage: E=EllipticCurve(F,[a4,a6])
sage: E.discriminant()
-64*a4bar^3 - 432*a6bar^2
sage: _.factor()
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-149-995262737325> in <module>()
----> 1 _.factor()

/usr/lib/python2.7/site-packages/sage/categories/quotient_fields.pyc in factor(self, *args, **kwds)
352                 (x + y)^-1 * y * x
353             """
--> 354             return (self.numerator().factor(*args, **kwds) /
355                     self.denominator().factor(*args, **kwds))
356

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.__getattr__ (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4290)()
457             AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
458         """
--> 459         return self.getattr_from_category(name)
460
461     cdef getattr_from_category(self, name):

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.getattr_from_category (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4399)()
470         else:
471             cls = P._abstract_element_class
--> 472         return getattr_from_other_class(self, cls, name)
473
474     def __dir__(self):

/usr/share/sage/source/sage/structure/misc.pyx in sage.structure.misc.getattr_from_other_class (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/misc.c:1927)()
292         dummy_error_message.cls = type(self)
293         dummy_error_message.name = name
--> 294         raise dummy_attribute_error
295     cdef PyObject* attr = _PyType_Lookup(<type>cls, name)
296     if attr is NULL:

AttributeError: 'QuotientRing_generic_with_category.element_class' object has no attribute 'factor'


I want to have -16*(4*a4^3 + 27*a6^2) as the output. Is this possible?possible? Another try:

sage: factor(_)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-173-af2394367aae> in <module>()
----> 1 factor(_)

/usr/lib/python2.7/site-packages/sage/arith/misc.pyc in factor(n, proof, int_, algorithm, verbose, **kwds)
2279             return n.factor(proof=proof, **kwds)
2280         except AttributeError:
-> 2281             raise TypeError("unable to factor n")
2282         except TypeError:
2283             # Just in case factor method doesn't have a proof option.

TypeError: unable to factor n
sage: factor(_, proof=false)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-174-78e3719752df> in <module>()
----> 1 factor(_, proof=false)

/usr/lib/python2.7/site-packages/sage/arith/misc.pyc in factor(n, proof, int_, algorithm, verbose, **kwds)
2279             return n.factor(proof=proof, **kwds)
2280         except AttributeError:
-> 2281             raise TypeError("unable to factor n")
2282         except TypeError:
2283             # Just in case factor method doesn't have a proof option.

TypeError: unable to factor n


### Rename xbar and factorize/simplify

When generating fraction fields, is it possible to rename xbar to x and do a factorization? Consider the following example:

sage: R=PolynomialRing(QQ, ['x','y','a4','a6'])
sage: R.inject_variables()
Defining x, y, a4, a6
sage: I=R.ideal(x^3+a4*x+a6-y^2)
sage: Q=R.quotient(I)
sage: F=Q.fraction_field()
sage: E=EllipticCurve(F,[a4,a6])
sage: E.discriminant()
-64*a4bar^3 - 432*a6bar^2
sage: _.factor()
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-149-995262737325> in <module>()
----> 1 _.factor()

/usr/lib/python2.7/site-packages/sage/categories/quotient_fields.pyc in factor(self, *args, **kwds)
352                 (x + y)^-1 * y * x
353             """
--> 354             return (self.numerator().factor(*args, **kwds) /
355                     self.denominator().factor(*args, **kwds))
356

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.__getattr__ (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4290)()
457             AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
458         """
--> 459         return self.getattr_from_category(name)
460
461     cdef getattr_from_category(self, name):

/usr/share/sage/source/sage/structure/element.pyx in sage.structure.element.Element.getattr_from_category (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/element.c:4399)()
470         else:
471             cls = P._abstract_element_class
--> 472         return getattr_from_other_class(self, cls, name)
473
474     def __dir__(self):

/usr/share/sage/source/sage/structure/misc.pyx in sage.structure.misc.getattr_from_other_class (/build/sagemath/src/sage-8.0/src/src/build/cythonized/sage/structure/misc.c:1927)()
292         dummy_error_message.cls = type(self)
293         dummy_error_message.name = name
--> 294         raise dummy_attribute_error
295     cdef PyObject* attr = _PyType_Lookup(<type>cls, name)
296     if attr is NULL:

AttributeError: 'QuotientRing_generic_with_category.element_class' object has no attribute 'factor'


I want to have -16*(4*a4^3 + 27*a6^2) as the output. Is this possible? Another try:

sage: factor(_)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-173-af2394367aae> in <module>()
----> 1 factor(_)

/usr/lib/python2.7/site-packages/sage/arith/misc.pyc in factor(n, proof, int_, algorithm, verbose, **kwds)
2279             return n.factor(proof=proof, **kwds)
2280         except AttributeError:
-> 2281             raise TypeError("unable to factor n")
2282         except TypeError:
2283             # Just in case factor method doesn't have a proof option.

TypeError: unable to factor n
sage: factor(_, proof=false)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-174-78e3719752df> in <module>()
----> 1 factor(_, proof=false)

/usr/lib/python2.7/site-packages/sage/arith/misc.pyc in factor(n, proof, int_, algorithm, verbose, **kwds)
2279             return n.factor(proof=proof, **kwds)
2280         except AttributeError:
-> 2281             raise TypeError("unable to factor n")
2282         except TypeError:
2283             # Just in case factor method doesn't have a proof option.

TypeError: unable to factor n
`