Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision | ||
extensions:polytropes [2020/03/18 12:38] – joswig | extensions:polytropes [2021/01/12 14:34] (current) – external edit 127.0.0.1 | ||
---|---|---|---|
Line 9: | Line 9: | ||
===== Download ===== | ===== Download ===== | ||
- | [[http:// | + | [[http:// |
===== Installation ===== | ===== Installation ===== | ||
Line 21: | Line 21: | ||
Suppose this ends up at ''/ | Suppose this ends up at ''/ | ||
< | < | ||
- | import_extension "/ | + | import_extension "/ |
</ | </ | ||
- | Do not forget to use an absolute path! Afterwards you are good to run the code. This import needs to be performed only once. The reference to the extension is permanently stored in '' | + | Do not forget to use an absolute path! Afterwards you are good to run the code. This import needs to be performed only once. The reference to the extension is permanently stored in '' |
===== Examples ===== | ===== Examples ===== | ||
Line 37: | Line 37: | ||
> $G = new GraphAdjacency< | > $G = new GraphAdjacency< | ||
</ | </ | ||
- | The edges are defined along with their weights. | + | [For polymake 4.0 use '' |
< | < | ||
> $Weights = new EdgeMap< | > $Weights = new EdgeMap< | ||
Line 132: | Line 132: | ||
In the first solution, e.g., we see that $c$ and $d$ go through $b$ to reach $a$. | In the first solution, e.g., we see that $c$ and $d$ go through $b$ to reach $a$. | ||
The next part of the output for each solution are the distances from each node to the target, written in the form $\alpha + \beta x$, where $x$ is the variable weight of the arc from $b$ to $a$. | The next part of the output for each solution are the distances from each node to the target, written in the form $\alpha + \beta x$, where $x$ is the variable weight of the arc from $b$ to $a$. | ||
- | The distance from $a$ to itself is zero; the output " | + | The distance from $a$ to itself is zero; the output " |
The distance from $b$ to $a$ is $x$. | The distance from $b$ to $a$ is $x$. | ||
The distance from $c$ to $a$ is $2+x$. | The distance from $c$ to $a$ is $2+x$. | ||
Line 142: | Line 142: | ||
The second solution (which is the one shown in Figure 3) is subject to the conditions $-3+x\geq 0$ and $1-x\geq 0$, i.e., $x \geq 3$ and $x\leq 1$, which is impossible. | The second solution (which is the one shown in Figure 3) is subject to the conditions $-3+x\geq 0$ and $1-x\geq 0$, i.e., $x \geq 3$ and $x\leq 1$, which is impossible. | ||
The feasibility can be checked via an LP oracle. | The feasibility can be checked via an LP oracle. | ||
+ | |||
+ | The sparse matrix notation works as follows: each row is a sparse vector. Each sparse vector starts with its length (in parantheses), | ||