Symbolic factor_list() should do integer factorisation of integers/rationals

[rwst]

Let symbolic factor_list() do integer factorisation if given an integer or fraction.

sage: SR(50).factor_list()
[(50, 1)]
sage: SR(49/100).factor_list()
[(49/100, 1)]

Too much surprise for new users.

Component: symbolics

Author: Ralf Stephan, Vincent Delecroix

Branch/Commit: u/rws/21067 @ a821fb6

Reviewer: Daniel Krenn

Issue created by migration from https://trac.sagemath.org/ticket/21067

[rwst]

Branch: u/rws/symbolic_factor___should_do_integer_factorisation_of_integers_rationals

[rwst]

Author: Ralf Stephan

[rwst]

New commits:

ac3d7cb

21067: do ZZ/QQ factorization in ex.factor_list()

[rwst]

Description changed:

--- 
+++ 
@@ -1,10 +1,10 @@
-Let symbolic `factor()` do integer factorisation if given an integer or fraction.
+Let symbolic `factor_list()` do integer factorisation if given an integer or fraction.
 
 ```
-sage: SR(50).factor()
-50
-sage: SR(100/49).factor()
-100/49
+sage: SR(50).factor_list()
+[(50, 1)]
+sage: SR(49/100).factor_list()
+[(49/100, 1)]
 ```
 
 Too much surprise for new users.

[rwst]

Commit: ac3d7cb

[tscrim]

comment:4

One minor thing: could you move the import into the factor_list method? I worry that this could lead to import hell.

[nbruin]

comment:5

Two comments:

• I don't think SR needs to be imported at all. The very fact that we land in this factor_list implementation should mean that self.parent() should be SR. And if it isn't, that's probably the better parent to use anyway.

• If we're going to do this anyway, I think it's better if we have

sage: (5/3*x/(x+1)).factor_list()
[(x + 1, -1), (x, 1), (5, 1), (3,-1)]

because it's closer to the idea that the factorisation of a product U*V has a tendency to be the concatenation of the factorisations of U and V.

It should be clear that factor_list just returns a factorisation:

sage: ((sqrt(5)+1)^2*(x^2-5)).expand_rational().factor_list()
[(x^2 - 5, 1), (sqrt(5) + 3, 1), (2, 1)]

but keeping the convention that we factor rational numbers into their prime factors should be fine and could be nice for newbies.

[sagetrac-git]

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

eca869e

21067: extend functionality