bug in coercion and cyclotomic fields

[AlexGhitza]

This should work automagically:

----------------------------------------------------------------------
| Sage Version 4.2.1, Release Date: 2009-11-14                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: a = CyclotomicField(3).random_element()
sage: b = CyclotomicField(4).random_element()
sage: a + b
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/home/ghitza/.sage/temp/artin/9098/_home_ghitza__sage_init_sage_0.py in <module>()

/home/ghitza/sage-devel/local/lib/python2.6/site-packages/sage/structure/element.so in sage.structure.element.ModuleElement.__add__ (sage/structure/element.c:6989)()

/home/ghitza/sage-devel/local/lib/python2.6/site-packages/sage/structure/coerce.so in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:7021)()

TypeError: unsupported operand parent(s) for '+': 'Cyclotomic Field of order 3 and degree 2' and 'Cyclotomic Field of order 4 and degree 2'
sage: a * b
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/home/ghitza/.sage/temp/artin/9098/_home_ghitza__sage_init_sage_0.py in <module>()

/home/ghitza/sage-devel/local/lib/python2.6/site-packages/sage/structure/element.so in sage.structure.element.RingElement.__mul__ (sage/structure/element.c:10248)()

/home/ghitza/sage-devel/local/lib/python2.6/site-packages/sage/structure/coerce.so in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:7021)()

TypeError: unsupported operand parent(s) for '*': 'Cyclotomic Field of order 3 and degree 2' and 'Cyclotomic Field of order 4 and degree 2'

I think it's a coercion problem. If someone knows better, please change the trac component accordingly.

[vripoll]

Has anyone looked at this ticket? I ran into this today and discover that the issue has been reported 4 years ago... This bug is particularly confusing for the user, especially when you read the doc that says "Due to their default embedding into CC, cyclotomic number fields are all compatible", and goes on to show the following example:

      sage: cf30 = CyclotomicField(30)
      sage: cf5 = CyclotomicField(5)
      sage: cf3 = CyclotomicField(3)
      sage: cf30.gen() + cf5.gen() + cf3.gen()
      zeta30^6 + zeta30^5 + zeta30 - 1

It turns out Sage is able to compute that only because the first field contains the next two! Note the following test:

      ┌────────────────────────────────────────────────────────────────────┐
      │ Sage Version 6.2.beta7, Release Date: 2014-04-08                   │
      │ Type "notebook()" for the browser-based notebook interface.        │
      │ Type "help()" for help.                                            │
      └────────────────────────────────────────────────────────────────────┘
      sage: cf15=CyclotomicField(15)
      sage: cf5=CyclotomicField(5)
      sage: cf3=CyclotomicField(3)
      
      sage: cf15.gen()+cf5.gen()+cf3.gen()
      zeta15^5 + zeta15^3 + zeta15
      
      sage: cf5.gen()+cf3.gen()+cf15.gen()
      Traceback (most recent call last)
      ...
      TypeError: unsupported operand parent(s) for '+': 'Cyclotomic Field of order 5 and degree 4'   and 'Cyclotomic Field of order 3 and degree 2'
      
      sage: cf5.gen()+cf3.gen()
      Traceback (most recent call last)
      ...
      TypeError: unsupported operand parent(s) for '+': 'Cyclotomic Field of order 5 and degree 4' and 'Cyclotomic Field of order 3 and degree 2'
      
      sage: 0*cf15.gen()+cf5.gen()+cf3.gen()
      zeta15^5 + zeta15^3

[vdelecroix]

see also the somehow related #20746

[chapoton]

first tentative, let us see what patchbot says

---

New commits:

​0a00b44

pushout for cyclotomic fields

[vdelecroix]

You should take care of embeddings. The map add: CF(p) x CF(q) -> CF(lcm(p,q)) is not uniquely defined.

[chapoton]

Well. What we just add here is the information that we need to go through CF(lcm). No responsability is taken on the existence of a canonical coercion from CF(p) to CF(lcm). I guess that this already an existing thing..

[tscrim]

As Frederic said, this does not change the (canonical) coercions between cyclotomic fields but allows the analogous computation to

sage: R.<x,y> = ZZ[]
sage: S.<y> = QQ[]
sage: R.an_element() + S.an_element()
x + y
sage: _.parent()
Multivariate Polynomial Ring in x, y over Rational Field