#18654: reduce Integer 0 in letterplace FreeAlgebra
---------------------------+----------------------------
   Reporter:  nantel       |            Owner:
       Type:  enhancement  |           Status:  new
   Priority:  trivial      |        Milestone:  sage-6.8
  Component:  algebra      |         Keywords:
  Merged in:               |          Authors:
  Reviewers:               |  Report Upstream:  N/A
Work issues:               |           Branch:
     Commit:               |     Dependencies:
   Stopgaps:               |
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 Would be nice the "reduce" method handle the Integer 0
 It is not really a bug but one often built polynomials from Integer "0"

 {{{
 FreeA.<a,b> = FreeAlgebra(QQ, implementation='letterplace')
 I = FreeA*[a+b]*FreeA
 G=I.groebner_basis()
 P=a*a*a*a
 P.reduce(G)

 ︡{"stdout":"b*b*b*b\n"}︡

 Q=P-P
 Q
 ︡
 {"stdout":"0\n"}︡

 Q.reduce(G)
 ︡
 {"stdout":"0\n"}︡
 ︠
 Q=0
 ︡Q.reduce(G)
 ︡
 {"stderr":"Error in lines 1-1\nTraceback (most recent call last):\n  File
 \"/projects/5d2319d7-b6e9-4ea8-984f-
 57412ea9d711/.sagemathcloud/sage_server.py\", line 879, in execute\n
 exec compile(block+'\\n', '', 'single') in namespace, locals\n  File \"\",
 line 1, in <module>\n  File \"sage/structure/element.pyx\", line 431, in
 sage.structure.element.Element.__getattr__
 (build/cythonized/sage/structure/element.c:4644)\n    return
 getattr_from_other_class(self, P._abstract_element_class, name)\n  File
 \"sage/structure/misc.pyx\", line 259, in
 sage.structure.misc.getattr_from_other_class
 (build/cythonized/sage/structure/misc.c:1670)\n    raise
 dummy_attribute_error\nAttributeError: 'sage.rings.integer.Integer' object
 has no attribute 'reduce'\n"}︡
 ︠}}}

--
Ticket URL: <http://trac.sagemath.org/ticket/18654>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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