mstreng
commented
12 years ago comment:1
Wow, that's a long list of faulty quotient rings in the documentation! Can you add the examples themselves, as line numbers tend to change a lot as Sage evolves?
Open 38e5cd24-729d-4c04-b48f-518277c23402 opened 12 years ago
mstreng
commented
12 years ago Wow, that's a long list of faulty quotient rings in the documentation! Can you add the examples themselves, as line numbers tend to change a lot as Sage evolves?
mstreng
commented
12 years ago Description changed:
---
+++
@@ -16,4 +16,4 @@
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.
-See also trac:13345 and https://groups.google.com/d/topic/sage-devel/s5y604ZPiQ8/discussion.
+See also ticket:13345 and https://groups.google.com/d/topic/sage-devel/s5y604ZPiQ8/discussion.
38e5cd24-729d-4c04-b48f-518277c23402
commented
12 years ago Description changed:
---
+++
@@ -7,12 +7,107 @@
``I.reduce(x)==I.reduce(y)`` `\iff x-y \in I`, and
``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.<x> = 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.<x,y> = QQ[]
+ sage: F == P2.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0]
+ False
+ sage: P3.<x> = 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.<x,y,z> = 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.<a,b,c,d> = MS.quo(I)
+```
+
+- sage/rings/quotient_ring_element.py :
+ - QuotientRingElement
+
+```
+ sage: R.<x> = PolynomialRing(ZZ)
+ sage: S.<xbar> = R.quo((4 + 3*x + x^2, 1 + x^2)); S
+```
+- QuotientRingElement.__init__
+
+```
+ sage: R.<x> = PolynomialRing(ZZ)
+ sage: S.<xbar> = 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.<x,y,z> = 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.<x> = 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.<x> = 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.
saraedum
commented
9 years ago Description changed:
---
+++
@@ -2,10 +2,10 @@
ASSUMPTION:
- ``I`` has a method ``I.reduce(x)`` returning the normal form
+ `I` has a method `I.reduce(x)` returning the normal form
of elements `x\in R`. In other words, it is required that
- ``I.reduce(x)==I.reduce(y)`` `\iff x-y \in I`, and
- ``x-I.reduce(x) in I``, for all `x,y\in R`.
+ `I.reduce(x)==I.reduce(y)` `\iff x-y \in I`, and
+ `x-I.reduce(x) in I`, for all `x,y\in R`.
- sage/categories/pushout.py :
- QuotientFunctor.__cmp__
The following files use quotient rings in their doctest examples, which contradict the assumption on the defining ideal:
ASSUMPTION:
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.
See also ticket:13345 and https://groups.google.com/d/topic/sage-devel/s5y604ZPiQ8/discussion.
CC: @mstreng
Component: doctest coverage
Issue created by migration from https://trac.sagemath.org/ticket/13347