# Changes between Version 1 and Version 2 of Ticket #13347

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Timestamp:
08/07/12 09:04:55 (10 years ago)
Comment:

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• ## Ticket #13347 – Description

 v1 x-I.reduce(x) in I, for all x,y\in R. - sage/categories/pushout.py : line 2393 - sage/categories/rings.py : lines 446, 482, 522 - sage/structure/category_object.pyx : line 473 - sage/rings/quotient_ring_element.py : lines 56, 98, 208 - sage/rings/morphism.pyx : line 465 - sage/rings/ring.pyx: lines 409, 708, 792 - sage/categories/pushout.py : - QuotientFunctor.__cmp__ {{{ sage: P. = QQ[] sage: F = P.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0] sage: F == loads(dumps(F)) True sage: P2. = QQ[] sage: F == P2.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0] False sage: P3. = ZZ[] sage: F == P3.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0] True }}} - sage/categories/rings.py : - Rings.quotient {{{ sage: F. = FreeAlgebra(QQ, 3) sage: I = F*[x*y+y*z,x^2+x*y-y*x-y^2]*F sage: Q = Rings().parent_class.quotient(F,I); Q }}} - Rings.quo {{{ sage: MS = MatrixSpace(QQ,2) sage: MS.full_category_initialisation() sage: I = MS*MS.gens()*MS sage: MS.quo(I,names = ['a','b','c','d']) }}} - Rings.quotient_ring {{{ sage: MS = MatrixSpace(QQ,2) sage: I = MS*MS.gens()*MS sage: MS.quotient_ring(I,names = ['a','b','c','d']) }}} - sage/structure/category_object.pyx : - CategoryObject.__temporarily_change_names {{{ sage: MS = MatrixSpace(GF(5),2,2) sage: I = MS*[MS.0*MS.1,MS.2+MS.3]*MS sage: Q. = MS.quo(I) }}} - sage/rings/quotient_ring_element.py : - QuotientRingElement {{{ sage: R. = PolynomialRing(ZZ) sage: S. = R.quo((4 + 3*x + x^2, 1 + x^2)); S }}} - QuotientRingElement.__init__ {{{ sage: R. = PolynomialRing(ZZ) sage: S. = R.quo((4 + 3*x + x^2, 1 + x^2)); S }}} - QuotientRingElement._repr_ {{{ sage: S = SteenrodAlgebra(2) sage: I = S*[S.0+S.1]*S sage: Q = S.quo(I) }}} - sage/rings/morphism.pyx : - RingMap_lift {{{ sage: MS = MatrixSpace(GF(5),2,2) sage: I = MS*[MS.0*MS.1,MS.2+MS.3]*MS sage: Q = MS.quo(I) }}} - sage/rings/ring.pyx: - Ring.ideal_monoid {{{ sage: F. = FreeAlgebra(ZZ, 3) sage: I = F*[x*y+y*z,x^2+x*y-y*x-y^2]*F sage: Q = sage.rings.ring.Ring.quotient(F,I) }}} - Ring.quotient {{{ sage: R. = PolynomialRing(ZZ) sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2]) sage: S = R.quotient(I, 'a') }}} - Ring.quotient_ring {{{ sage: R. = PolynomialRing(ZZ) sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2]) sage: S = R.quotient_ring(I, 'a') sage: S.gens() }}} These 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.