[with patch, needs work] Cannot create distinct polynomial rings over p-adic rings with different print_modes

[ncalexan]

The issue is in the caching:

sage: R = Qp(7, print_mode='val-unit')
sage: S = Qp(7)
sage: R(7^2 + 1)
7^2 * 1 + O(7^22)
sage: S(7^2)
7^2 + O(7^22)
sage: R(7^2 + 1)
50 + O(7^20)
sage: S(7^2 + 1)
1 + 7^2 + O(7^20)
sage: R is S
False
sage: R['x'] is S['x']
True

The issue manifests itself in polynomial_ring_constructor, which fails because the cache is keyed by ==, not identity, and

sage: R == S
True

[roed]

Use this one instead

[ncalexan]

I have lots of doctest failures... wrong versions? The argument "print_pos" does not appear anywhere in my sage/rings/padics directory, btw.

----------------------------------------------------------------------
| Sage Version 3.3.alpha0, Release Date: 2009-01-19                  |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
Loading Sage library. Current Mercurial branch is: nca
sage: import sage_emacs as emacs
sage: R = Qp(7, print_mode='digits', print_pos=True)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/home/ncalexan/.sage/temp/sage.math.washington.edu/16970/_home_ncalexan__sage_init_sage_0.py in <module>()
----> 1 
      2 
      3 
      4 
      5 

/scratch/nca/sage-3.3.alpha1-sage.math-only-x86_64-Linux/local/lib/python2.5/site-packages/sage/structure/factory.so in sage.structure.factory.UniqueFactory.__call__ (sage/structure/factory.c:579)()
    106 
    107 
--> 108 
    109 
    110 

/scratch/nca/sage-3.3.alpha1-sage.math-only-x86_64-Linux/local/lib/python2.5/site-packages/sage/structure/factory.so in sage.structure.factory.UniqueFactory.create_key_and_extra_args (sage/structure/factory.c:1373)()
    193 
    194 
--> 195 
    196 
    197 

TypeError: create_key() got an unexpected keyword argument 'print_pos'
sage: S = Qp(7, print_mode='digits', print_pos=False)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/home/ncalexan/.sage/temp/sage.math.washington.edu/16970/_home_ncalexan__sage_init_sage_0.py in <module>()
----> 1 
      2 
      3 
      4 
      5 

/scratch/nca/sage-3.3.alpha1-sage.math-only-x86_64-Linux/local/lib/python2.5/site-packages/sage/structure/factory.so in sage.structure.factory.UniqueFactory.__call__ (sage/structure/factory.c:579)()
    106 
    107 
--> 108 
    109 
    110 

/scratch/nca/sage-3.3.alpha1-sage.math-only-x86_64-Linux/local/lib/python2.5/site-packages/sage/structure/factory.so in sage.structure.factory.UniqueFactory.create_key_and_extra_args (sage/structure/factory.c:1373)()
    193 
    194 
--> 195 
    196 
    197 

TypeError: create_key() got an unexpected keyword argument 'print_pos'
sage: 

[mabshoff]

David, Nick: Has this problem been fixed due to the work by David merged in 3.4.1.rc3?

Cheers,

Michael

[kedlaya]

Replying to mabshoff:

David, Nick: Has this problem been fixed due to the work by David merged in 3.4.1.rc3?

Cheers,

Michael

It would appear so. Consider:

sage: R = Qp(7, print_mode='val-unit')
sage: S = Qp(7)
sage: R(7^2 + 1)
7^2 * 1 + O(7^22)
sage: S(7^2)
7^2 + O(7^22)
sage: R(7^2 + 1)
50 + O(7^20)
sage: S(7^2 + 1)
1 + 7^2 + O(7^20)
sage: R is S
False
sage: R['x'] is S['x']
False # this is now fixed
sage: R['x'](7^2)
(7^2 * 1 + O(7^22))
sage: S['x'](7^2)
(7^2 + O(7^22))
sage: R['x'](7^2+1)
(50 + O(7^20))
sage: S['x'](7^2+1)
(1 + 7^2 + O(7^20))

However, this is still puzzling:

sage: R['x'] == S['x']
False

[tscrim]

I get with 5.9.beta1:

sage: sage: R = Qp(7, print_mode='val-unit')
sage: sage: S = Qp(7)
sage: R is S
False
sage: R == S
False
sage: R['x'] == S['x']
False
sage: R['x'] is S['x']
False

which is the expected behavior due to UniqueRepresentation parents.

[aapitzsch]

Replying to tscrim:

I get with 5.9.beta1:

sage: sage: R = Qp(7, print_mode='val-unit')
sage: sage: S = Qp(7)
sage: R is S
False
sage: R == S
False
sage: R['x'] == S['x']
False
sage: R['x'] is S['x']
False

which is the expected behavior due to UniqueRepresentation parents.

It should be due to UniqueFactory (in 6.2.beta3). But anyway, documentation of Qp says

PRINTING:

    There are many different ways to print `p`-adic elements.
    ...
    Note that the printing options affect whether different
    `p`-adic fields are considered equal.