On Mon, Nov 19, 2018 at 11:58 AM John Cremona <john.crem...@gmail.com> wrote:
>
> I recommend importing anything you need from sage.all since the details of
> where everything is might change in time. This works perfectly well:
>
> $ sage -python # so we use Sage's python not my system-wide one
> Python 2.7.15 (default, Nov 2 2018, 14:32:42)
> [GCC 4.8.5 20150623 (Red Hat 4.8.5-28)] on linux2
> Type "help", "copyright", "credits" or "license" for more information.
> >>> from sage.all import PolynomialRing, QQ
> >>> R = PolynomialRing(QQ,'x')
> >>> x = R.gen()
> >>> f = x^3+1 # no good as no preparser
> Traceback (most recent call last):
> File "<stdin>", line 1, in <module>
> File "sage/structure/element.pyx", line 944, in
> sage.structure.element.Element.__xor__
> (build/cythonized/sage/structure/element.c:9006)
> RuntimeError: Use ** for exponentiation, not '^', which means xor
> in Python, and has the wrong precedence.
>
> # Now we can work with this:
>
> >>> f = x**3+1 # that's better
> >>> f.factor()
> (x + 1) * (x^2 - x + 1)
>
> Another thing I do is to put my commands into a .py file and run pyflakes on
> it, as that reveals what things need to be imported. Then import them all
> from sage.all.
you can also find out exactly what you need to import:
sage: import_statements("QQ")
from sage.rings.rational_field import QQ
>
> John Cremona
>
> On Mon, 19 Nov 2018 at 11:48, Kolen Cheung <christian.ko...@gmail.com> wrote:
>>
>> Thank you both for the answers. However, I’m still stuck:
>>
>> Focusing on just translating the first line: R.<x> = QQ[]
>>
>> In sage,
>>
>> >>> preparse("R.<x> = QQ[]")
>> "R = QQ['x']; (x,) = R._first_ngens(1)"
>> >>> import_statements(QQ)
>> # ** Warning **: several names for that object: Q, QQ
>> from sage.rings.rational_field import Q
>> >>> import_statements(R)
>> from sage.rings.qqbar import QQx
>>
>> Immediately I have a question: how come the import_statements of QQ is ...
>> import Q, and the import statement of R is ... import QQx? In either case
>> the namespace in question is not imported. Does it mean ... import Q as QQ
>> and ... import QQx as R respectively?
>>
>> Then I’ve a problem: In sage, I can import them using these import
>> statements. But when entering these 2 import statements in Python,
>>
>> >>> from sage.rings.rational_field import Q
>> ---------------------------------------------------------------------------
>> ImportError Traceback (most recent call last)
>> <ipython-input-1-0fb4c40d1a13> in <module>()
>> ----> 1 from sage.rings.rational_field import Q
>>
>> /usr/lib/python2.7/site-packages/sage/rings/rational_field.py in <module>()
>> 62 _long_type = int
>> 63
>> ---> 64 from .rational import Rational
>> 65 from .integer import Integer
>> 66
>>
>> /usr/lib/python2.7/site-packages/sage/rings/rational.pyx in init
>> sage.rings.rational (build/cythonized/sage/rings/rational.c:40976)()
>> 94
>> 95
>> ---> 96 import sage.rings.real_mpfr
>> 97 import sage.rings.real_double
>> 98 from libc.stdint cimport uint64_t
>>
>> /usr/lib/python2.7/site-packages/sage/rings/real_mpfr.pyx in init
>> sage.rings.real_mpfr (build/cythonized/sage/rings/real_mpfr.c:44298)()
>> ----> 1 r"""
>> 2 Arbitrary Precision Real Numbers
>> 3
>> 4 AUTHORS:
>> 5
>>
>> /usr/lib/python2.7/site-packages/sage/rings/complex_number.pxd in init
>> sage.libs.mpmath.utils (build/cythonized/sage/libs/mpmath/utils.c:8831)()
>> 4 from .real_mpfr cimport RealNumber
>> 5
>> ----> 6 cdef class ComplexNumber(sage.structure.element.FieldElement):
>> 7 cdef mpfr_t __re
>> 8 cdef mpfr_t __im
>>
>> /usr/lib/python2.7/site-packages/sage/rings/complex_double.pxd in init
>> sage.rings.complex_number
>> (build/cythonized/sage/rings/complex_number.c:24212)()
>> 8
>> 9
>> ---> 10 cdef class ComplexDoubleField_class(sage.rings.ring.Field):
>> 11 pass
>> 12
>>
>> /usr/lib/python2.7/site-packages/sage/rings/complex_double.pyx in init
>> sage.rings.complex_double
>> (build/cythonized/sage/rings/complex_double.c:24230)()
>> 96 from cypari2.convert cimport new_gen_from_double,
>> new_t_COMPLEX_from_double
>> 97
>> ---> 98 from . import complex_number
>> 99
>> 100 from .complex_field import ComplexField
>>
>> ImportError: cannot import name complex_number
>> >>> from sage.rings.qqbar import QQx
>> ---------------------------------------------------------------------------
>> ImportError Traceback (most recent call last)
>> <ipython-input-1-4809457c5588> in <module>()
>> ----> 1 from sage.rings.qqbar import QQx
>>
>> /usr/lib/python2.7/site-packages/sage/rings/qqbar.py in <module>()
>> 512 rich_to_bool, richcmp_not_equal,
>> 513 op_EQ, op_NE)
>> --> 514 from sage.rings.real_mpfr import RR
>> 515 from sage.rings.real_mpfi import RealIntervalField, RIF,
>> is_RealIntervalFieldElement, RealIntervalField_class
>> 516 from sage.rings.complex_field import ComplexField
>>
>> /usr/lib/python2.7/site-packages/sage/rings/real_mpfr.pyx in init
>> sage.rings.real_mpfr (build/cythonized/sage/rings/real_mpfr.c:44298)()
>> ----> 1 r"""
>> 2 Arbitrary Precision Real Numbers
>> 3
>> 4 AUTHORS:
>> 5
>>
>> /usr/lib/python2.7/site-packages/sage/rings/complex_number.pxd in init
>> sage.libs.mpmath.utils (build/cythonized/sage/libs/mpmath/utils.c:8831)()
>> 4 from .real_mpfr cimport RealNumber
>> 5
>> ----> 6 cdef class ComplexNumber(sage.structure.element.FieldElement):
>> 7 cdef mpfr_t __re
>> 8 cdef mpfr_t __im
>>
>> /usr/lib/python2.7/site-packages/sage/rings/complex_double.pxd in init
>> sage.rings.complex_number
>> (build/cythonized/sage/rings/complex_number.c:24212)()
>> 8
>> 9
>> ---> 10 cdef class ComplexDoubleField_class(sage.rings.ring.Field):
>> 11 pass
>> 12
>>
>> /usr/lib/python2.7/site-packages/sage/rings/complex_double.pyx in init
>> sage.rings.complex_double
>> (build/cythonized/sage/rings/complex_double.c:24230)()
>> 96 from cypari2.convert cimport new_gen_from_double,
>> new_t_COMPLEX_from_double
>> 97
>> ---> 98 from . import complex_number
>> 99
>> 100 from .complex_field import ComplexField
>>
>> ImportError: cannot import name complex_number
>>
>> Thanks.
>>
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