abs floor ceil for quadratic number field

[vdelecroix]

Implementation of absolute value (abs), floor (floor) and ceiling (ceil) function for elements in quadratic number field.

The implementation uses only manipulation of (mpz) integers.

The function abs depends on the function sign implemented in ticket #13213.

[kcrisman]

Does the removal of

K.<a> = NumberField(x^2+1, embedding=CDF.gen()) 

as an example mean that one couldn't use this syntax at all any more? Would number fields from quadratics not automatically be quadratic fields (when mathematically appropriate, I'm excluding x^2-1 and the like) and inherit these methods, or would that simply not work now?

[vdelecroix]

Replying to kcrisman:

Does the removal of

K.<a> = NumberField(x^2+1, embedding=CDF.gen()) 

as an example mean that one couldn't use this syntax at all any more?

This syntax is still available. The patch only aims to implement methods abs, floor and ceil for quadratic elements. As an example

sage: K.<sqrt2> = QuadraticField(2)
sage: sqrt2.floor()
1

It is yet possible (without the patch) to do

sage: K.<sqrt2> = QuadraticField(2)
sage: floor(sqrt2)
1

But there is a simpler and faster way to do it compared to what floor does (using the real interval field with finer and finer approximations). Note that if the method .floor is present, the the function floor will use it!

Would number fields from quadratics not automatically be quadratic fields (when mathematically appropriate, I'm excluding x^2-1 and the like) and inherit these methods, or would that simply not work now?

Yes, it is the way it is

sage: type(NumberField(x^2 + 1, 'a'))
<class 'sage.rings.number_field.number_field.NumberField_quadratic_with_category'>

[vdelecroix]

The patch now takes care of the new doctest framework (ie replace "..." by "....:" for multiline tests).

[chapoton]

I have made a short review patch, with correct links to trac and raise statements.

[chapoton]

ok, looks good to me. Positive review.

[vdelecroix]

Replying to chapoton:

ok, looks good to me. Positive review.

Cool. Thanks Frédéric.