[Positive review] improve doctest coverage for Factorization; fix several critical bugs

[williamstein]

Component: doctest coverage

Issue created by migration from https://trac.sagemath.org/ticket/1805

[williamstein]

comment:1

Before:

sage@modular:~/d/sage/sage/structure$ sage -coverage factorization.py 
----------------------------------------------------------------------
factorization.py
SCORE factorization.py: 28% (6 of 21)

Missing documentation:
	 * __init__(self, x, unit=None, cr=False, sort=True)
	 * _set_cr(self, cr)
	 * sort(self)
	 * _cmp(f,g)
	 * _cmp(f,g)
	 * _cmp(f,g)
	 * __reduce__(self)
	 * _cr(self)
	 * _repr_(self)
	 * _latex_(self)
	 * __pow__(self, n)
	 * __invert__(self)
	 * Factorization_deduce_unit(x, mul)


Missing doctests:
	 * unit_part(self)
	 * expand(self)

After:

teragon:structure was$ sage -coverage factorization.py
----------------------------------------------------------------------
factorization.py
SCORE factorization.py: 100% (22 of 22)
----------------------------------------------------------------------

and I fixed numerous conceptual bugs/mistakes in that file.

[williamstein]

comment:2

Attachment: trac-1805.patch.gz

This is a preliminary patch. I'm now doctesting all of sage-2.10 with this patch applied to see what else is broke. I'll post another patch that fixes the problems later.

[williamstein]

Attachment: trac-1805-part2.patch.gz

this part 2 fixes some additional issues, typos, etc., I saw when proofreading my patch.

[ncalexan]

comment:4

I fixed 1804 not knowing that 1805 did a lot of the same work. Damn! They should both be applied but of course they need to be merged. I'll try to do it tomorrow.

[sagetrac-mabshoff]

comment:5

Nick, can you give this another review?

Cheers,

Michael