sign and more truncation functions on real intervals

[vdelecroix]

Real intervals are missing truncation functions:

• frac
• trunc
• round
• unique_sign
• unique_trunc

We also add some more documentation to truncation methods.

see also: #18337

[vdelecroix]

New commits:

​d96885c

Trac 18334: sign and truncations for real intervals

[jdemeyer]

The frac() of an interval is not the same as

self.parent()(self.lower().frac(), self.upper().frac())

For example, the frac() of RIF(6,7) should be the whole interval RIF(0,1).

[jdemeyer]

The following would be a good doctest:

sage: RIF(-0.9, 0.9).unique_trunc()
0

[jdemeyer]

For frac(), you should check specifically if -1 or 1 should be contained in the result:

• if the interval ]a,b] contains a positive integer: frac() must contain [0,1]
• if the interval [a,b[ contains a negative integer: frac() must contain [-1,0]

If you add the frac() of the endpoints, you should get everything.

[git]

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

​10067b5

Trac 18334: fixed frac + doctests

[vdelecroix]

Replying to jdemeyer:

For frac(), you should check specifically if -1 or 1 should be contained in the result:

• if the interval ]a,b] contains a positive integer (check if floor(b) > max(a,0)): frac() must contain [0,1]
• if the interval [a,b[ contains a negative integer (check if ceil(a) < min(b,0)): frac() must contain [-1,0]

If you add the frac() of the endpoints, you should get everything.

Of course. This was completely wrong! Thanks.

[jdemeyer]

Add some comments like I wrote in 6. I would also like to see doctests where one endpoint is an integer:

sage: RIF(0.5, 1).frac()
sage: RIF(1, 1.5).frac()

[git]

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

​3aa1904

Trac 18334: more doctests

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​7fe18d6

Trac 18334: more doctests

[vdelecroix]

Thanks Jeroen!