Changes between Version 1 and Version 2 of Ticket #13347


Ignore:
Timestamp:
08/07/12 09:04:55 (8 years ago)
Author:
tfeulner
Comment:

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  • Ticket #13347 – Description

    v1 v2  
    88    ``x-I.reduce(x) in I``, for all `x,y\in R`.
    99
    10 - sage/categories/pushout.py : line 2393
    11 - sage/categories/rings.py : lines 446, 482, 522
    12 - sage/structure/category_object.pyx : line 473
    13 - sage/rings/quotient_ring_element.py : lines 56, 98, 208
    14 - sage/rings/morphism.pyx : line 465
    15 - sage/rings/ring.pyx: lines 409, 708, 792
     10- sage/categories/pushout.py :
     11 - QuotientFunctor.__cmp__
     12{{{
     13            sage: P.<x> = QQ[]
     14            sage: F = P.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0]
     15            sage: F == loads(dumps(F))
     16            True
     17            sage: P2.<x,y> = QQ[]
     18            sage: F == P2.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0]
     19            False
     20            sage: P3.<x> = ZZ[]
     21            sage: F == P3.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0]
     22            True
     23}}}
     24
     25
     26- sage/categories/rings.py :
     27 - Rings.quotient
     28{{{
     29                sage: F.<x,y,z> = FreeAlgebra(QQ, 3)
     30                sage: I = F*[x*y+y*z,x^2+x*y-y*x-y^2]*F
     31                sage: Q = Rings().parent_class.quotient(F,I); Q
     32}}}
     33 - Rings.quo
     34{{{             
     35                sage: MS = MatrixSpace(QQ,2)
     36                sage: MS.full_category_initialisation()
     37                sage: I = MS*MS.gens()*MS   
     38                sage: MS.quo(I,names = ['a','b','c','d'])
     39}}}
     40 - Rings.quotient_ring
     41{{{
     42                sage: MS = MatrixSpace(QQ,2)
     43                sage: I = MS*MS.gens()*MS
     44                sage: MS.quotient_ring(I,names = ['a','b','c','d'])
     45}}}
     46- sage/structure/category_object.pyx :
     47 - CategoryObject.__temporarily_change_names
     48{{{
     49            sage: MS = MatrixSpace(GF(5),2,2)
     50            sage: I = MS*[MS.0*MS.1,MS.2+MS.3]*MS
     51            sage: Q.<a,b,c,d> = MS.quo(I)
     52}}}
     53
     54- sage/rings/quotient_ring_element.py :
     55 - QuotientRingElement
     56{{{
     57        sage: R.<x> = PolynomialRing(ZZ)
     58        sage: S.<xbar> = R.quo((4 + 3*x + x^2, 1 + x^2)); S
     59}}}
     60 - QuotientRingElement.__init__
     61{{{
     62            sage: R.<x> = PolynomialRing(ZZ)
     63            sage: S.<xbar> = R.quo((4 + 3*x + x^2, 1 + x^2)); S
     64}}}
     65 - QuotientRingElement._repr_
     66{{{ 
     67            sage: S = SteenrodAlgebra(2)
     68            sage: I = S*[S.0+S.1]*S
     69            sage: Q = S.quo(I)
     70}}}
     71
     72- sage/rings/morphism.pyx :
     73 - RingMap_lift
     74{{{
     75        sage: MS = MatrixSpace(GF(5),2,2)
     76        sage: I = MS*[MS.0*MS.1,MS.2+MS.3]*MS
     77        sage: Q = MS.quo(I)
     78}}}
     79- sage/rings/ring.pyx:
     80 - Ring.ideal_monoid
     81{{{
     82            sage: F.<x,y,z> = FreeAlgebra(ZZ, 3)
     83            sage: I = F*[x*y+y*z,x^2+x*y-y*x-y^2]*F
     84            sage: Q = sage.rings.ring.Ring.quotient(F,I)
     85}}}
     86 - Ring.quotient
     87{{{
     88            sage: R.<x> = PolynomialRing(ZZ)
     89            sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2])
     90            sage: S = R.quotient(I, 'a')
     91}}}
     92 - Ring.quotient_ring
     93{{{
     94            sage: R.<x> = PolynomialRing(ZZ)
     95            sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2])
     96            sage: S = R.quotient_ring(I, 'a')
     97            sage: S.gens()
     98}}}
    1699 
    17100These examples have to be modified, one possibility is that they use quotient rings which fulfill the assumption or the reduce function of the corresponding ideal class must be provided.