When generating fraction fields, is it possible to rename xbar to x?
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Rename xbar, ybar
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 as the output. Is this possible?- + 27*a6^2)
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
See below (my answer)
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
