#1956: implement multivariate truncated power series arithmetic
-------------------------------------------+--------------------------------
   Reporter:  was                          |          Owner:  pernici           
       
       Type:  enhancement                  |         Status:  needs_work        
       
   Priority:  major                        |      Milestone:  sage-4.7.1        
       
  Component:  commutative algebra          |       Keywords:  multivariate 
power series
Work_issues:                               |       Upstream:  N/A               
       
   Reviewer:  Martin Albrecht, Simon King  |         Author:  Niles Johnson     
       
     Merged:                               |   Dependencies:                    
       
-------------------------------------------+--------------------------------
Changes (by jdemeyer):

  * status:  needs_review => needs_work


Comment:

 Please rebase properly to sage-4.7.rc2:
 {{{
 sage -t  -force_lib
 devel/sage/sage/rings/multi_power_series_ring_element.py
 **********************************************************************
 File "/mnt/usb1/scratch/jdemeyer/merger/sage-4.7.1.alpha1/devel/sage-
 main/sage/rings/multi_power_series_ring_element.py", line 1299:
     sage: f.sqrt()
 Expected:
     Traceback (most recent call last):
     ...
     AttributeError:
 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'
 object has no attribute 'sqrt'
 Got:
     Traceback (most recent call last):
       File
 "/mnt/usb1/scratch/jdemeyer/merger/sage-4.7.1.alpha1/local/bin/ncadoctest.py",
 line 1231, in run_one_test
         self.run_one_example(test, example, filename, compileflags)
       File
 "/mnt/usb1/scratch/jdemeyer/merger/sage-4.7.1.alpha1/local/bin/sagedoctest.py",
 line 38, in run_one_example
         OrigDocTestRunner.run_one_example(self, test, example, filename,
 compileflags)
       File
 "/mnt/usb1/scratch/jdemeyer/merger/sage-4.7.1.alpha1/local/bin/ncadoctest.py",
 line 1172, in run_one_example
         compileflags, 1) in test.globs
       File "<doctest __main__.example_39[4]>", line 1, in <module>
         f.sqrt()###line 1299:
     sage: f.sqrt()
       File
 "/mnt/usb1/scratch/jdemeyer/merger/sage-4.7.1.alpha1/local/lib/python
 /site-packages/sage/rings/multi_power_series_ring_element.py", line 1304,
 in sqrt
         return self.parent(self._bg_value.sqrt())
       File "power_series_ring_element.pyx", line 1205, in
 sage.rings.power_series_ring_element.PowerSeries.sqrt
 (sage/rings/power_series_ring_element.c:8919)
         s = u[0].sqrt(extend=False)
       File "element.pyx", line 2003, in
 sage.structure.element.CommutativeRingElement.sqrt
 (sage/structure/element.c:14899)
       File "element.pyx", line 1906, in
 sage.structure.element.CommutativeRingElement.is_square
 (sage/structure/element.c:14740)
     NotImplementedError: is_square() not implemented for elements of
 Multivariate Polynomial Ring in a, b over Integer Ring
 **********************************************************************
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1956#comment:130>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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