characteristic() should be an integer

[saraedum]

Currently characteristic() does not return an Integer for some rings:

sage: type(ZZ.characteristic())
<type 'int'>

This is annoying because one cannot for example do:

sage: ZZ.characteristic().is_prime()
AttributeError: 'int' object has no attribute 'is_prime'

I don't see a good reason not to make characteristic always an Integer. The minimal performance loss should not be an issue in any computation that I can imagine.

Depends on #13043

Component: algebra

Keywords: ZZ characteristic sd40.5

Author: Julian Rueth

Reviewer: David Roe, Jeroen Demeyer

Merged: sage-5.1.beta2

Issue created by migration from https://trac.sagemath.org/ticket/12988

[saraedum]

comment:1

I believe it is easiest to check that this is correct through the test framework of the categories.

I added a test to Rings and also one to Fields() checking that it's a prime or zero.

[jdemeyer]

Changed keywords from ZZ, characteristic to ZZ characteristic sd40.5

[jdemeyer]

Author: Julian Rueth

[saraedum]

comment:4

That's strange. I'll run the doctests again to see if this also happens here.

Actually _test_characteristic didn't catch wrong characteristic() implementations in some cases which is related to #13043. I'll upload an updated patch soon.

[saraedum]

Dependencies: #13043

[saraedum]

Attachment: trac_12988.patch.gz

move characteristic() to the category of rings and check that it is in ZZ

[roed314]

comment:7

This looks good to me.

[jdemeyer]

Reviewer: David Roe

[jdemeyer]

comment:9

3 doctest failures with sage-5.1.beta1:

sage -t  "devel/sage-main/sage/rings/padics/padic_base_leaves.py"
**********************************************************************
File "/usr/local/src/sage-5.1.beta1/devel/sage-main/sage/rings/padics/padic_base_leaves.py", line 168:
    sage: TestSuite(R).run()
Expected nothing
Got:
    Failure in _test_characteristic:
    Traceback (most recent call last):
      File "/usr/local/src/sage-5.1.beta1/local/lib/python/site-packages/sage/misc/sage_unittest.py", line 275, in run
        test_method(tester = tester)
      File "/usr/local/src/sage-5.1.beta1/local/lib/python/site-packages/sage/categories/rings.py", line 258, in _test_characteristic
        tester.assertEqual(type(characteristic),sage.rings.integer.Integer)
      File "/usr/local/src/sage-5.1.beta1/local/lib/python2.7/unittest/case.py", line 509, in assertEqual
        assertion_func(first, second, msg=msg)
      File "/usr/local/src/sage-5.1.beta1/local/lib/python2.7/unittest/case.py", line 502, in _baseAssertEqual
        raise self.failureException(msg)
    AssertionError: <type 'int'> != <type 'sage.rings.integer.Integer'>
    ------------------------------------------------------------
    The following tests failed: _test_characteristic
**********************************************************************
File "/usr/local/src/sage-5.1.beta1/devel/sage-main/sage/rings/padics/padic_base_leaves.py", line 175:
    sage: TestSuite(R).run()
Expected nothing
Got:
    Failure in _test_characteristic:
    Traceback (most recent call last):
      File "/usr/local/src/sage-5.1.beta1/local/lib/python/site-packages/sage/misc/sage_unittest.py", line 275, in run
        test_method(tester = tester)
      File "/usr/local/src/sage-5.1.beta1/local/lib/python/site-packages/sage/categories/rings.py", line 258, in _test_characteristic
        tester.assertEqual(type(characteristic),sage.rings.integer.Integer)
      File "/usr/local/src/sage-5.1.beta1/local/lib/python2.7/unittest/case.py", line 509, in assertEqual
        assertion_func(first, second, msg=msg)
      File "/usr/local/src/sage-5.1.beta1/local/lib/python2.7/unittest/case.py", line 502, in _baseAssertEqual
        raise self.failureException(msg)
    AssertionError: <type 'int'> != <type 'sage.rings.integer.Integer'>
    ------------------------------------------------------------
    The following tests failed: _test_characteristic
**********************************************************************
File "/usr/local/src/sage-5.1.beta1/devel/sage-main/sage/rings/padics/padic_base_leaves.py", line 182:
    sage: TestSuite(R).run()
Expected nothing
Got:
    Failure in _test_characteristic:
    Traceback (most recent call last):
      File "/usr/local/src/sage-5.1.beta1/local/lib/python/site-packages/sage/misc/sage_unittest.py", line 275, in run
        test_method(tester = tester)
      File "/usr/local/src/sage-5.1.beta1/local/lib/python/site-packages/sage/categories/rings.py", line 258, in _test_characteristic
        tester.assertEqual(type(characteristic),sage.rings.integer.Integer)
      File "/usr/local/src/sage-5.1.beta1/local/lib/python2.7/unittest/case.py", line 509, in assertEqual
        assertion_func(first, second, msg=msg)
      File "/usr/local/src/sage-5.1.beta1/local/lib/python2.7/unittest/case.py", line 502, in _baseAssertEqual
        raise self.failureException(msg)
    AssertionError: <type 'int'> != <type 'sage.rings.integer.Integer'>
    ------------------------------------------------------------
    The following tests failed: _test_characteristic
**********************************************************************

[saraedum]

Attachment: trac_12988_padic.patch.gz

fix characteristic for padics

[jdemeyer]

Changed reviewer from David Roe to David Roe, Jeroen Demeyer

[jdemeyer]

Merged: sage-5.1.beta2