#18624: Implement the lift theorem for linear matroids
-------------------------------------+-------------------------------------
Reporter: Rudi | Owner: Rudi
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.8
Component: matroid theory | Resolution:
Keywords: | Merged in:
Authors: Rudi Pendavingh | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/Rudi/implement_the_lift_theorem_for_linear_matroids|
3ec5a71913b27dac70de9ca9d2fe0bc71e6ebb43
Dependencies: | Stopgaps:
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Comment (by yomcat):
A few more typos/formatting changes. I think this is the correct way to
format them:
{{{
#!diff
--- Version 1
+++ Version 2
@@ -1,15 +1,15 @@
For a lift map `f` and a matrix `A` these conditions are as follows.
First of all
`f: S \rightarrow T`, where `S` is a set of invertible elements of
the source ring and
`T` is a set of invertible elements of the target ring. The matrix
`A` has entries
- from the source ring, and each crossratio of `A` is contained in `S`.
Moreover:
+ from the source ring, and each cross ratio of `A` is contained in `S`.
Moreover:
- - `1 \in S`, `1\in T`;
+ - `1 \in S`, `1 \in T`;
- for all `x \in S`: `f(x) = 1` if and only if `x = 1`;
- - for all `x, y\in S`: if `x+y = 0` then `f(x)+f(y)=0`;
- - for all `x, y\in S`: if `x+y = 1` then `f(x)+f(y)=1`;
- - for all `x, y, z\in S`: if `xy = z` then `f(x)f(y)=f(z)`.
+ - for all `x, y \in S`: if `x + y = 0` then `f(x) + f(y) = 0`;
+ - for all `x, y \in S`: if `x + y = 1` then `f(x) + f(y) = 1`;
+ - for all `x, y, z \in S`: if `xy = z` then `f(x)f(y) = f(z)`.
- Any ring homorphism `h: P \rightarrow R` induces a lift map from the
set of units `S` of
+ Any ring homomorphism `h: P \rightarrow R` induces a lift map from the
set of units `S` of
`P` to the set of units `T` of `R`. There exist lift maps which do
not arise in
this manner. Several such maps can be created by the function
:meth:`lift_map() <sage.matroids.utilities.lift_map>`.
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/18624#comment:34>
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