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luke naylor latex documents
research
Max Destabilizer Rank
Commits
1de605fb
Commit
1de605fb
authored
1 year ago
by
Luke Naylor
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Fix size issue of characteristic curves plots
parent
d4b66856
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main.tex
+55
-33
55 additions, 33 deletions
main.tex
with
55 additions
and
33 deletions
main.tex
+
55
−
33
View file @
1de605fb
...
...
@@ -121,67 +121,89 @@ $\Delta(v) \geq 0$ and positive rank.
\begin{sagesilent}
def charact
_
curves(v):
var("alpha beta")
coords
_
range = (beta, -10, 10), (alpha, 0, 8)
alpha = stability.Tilt().alpha
beta = stability.Tilt().beta
coords
_
range = (beta, -4, 5), (alpha, 0, 4)
p = (
implicit
_
plot(stability.Tilt().degree(v), *coords
_
range )
+ line([(mu(v),0),(mu(v),5)], linestyle = "dashed")
+ text(r"
$
ch
_
2
^{
\alpha
,
\beta
}
(
v
)=
0
$
",[3.5, 2], rotation=45, fontsize="large")
+ text(r"
$
ch
_
1
^{
\alpha
,
\beta
}
(
v
)=
0
$
", [0.45, 1.5], rotation=90, fontsize="large")
+ text(r"
$
ch
_
2
^{
\alpha
,
\beta
}
(
v
)=
0
$
", [-2, 2], rotation=-45, fontsize="large")
+ text(r"
$
\nu
_{
\alpha
,
\beta
}
(
v
)
>
0
$
", [-3, 1], rgbcolor="black", fontsize="large")
+ text(r"
$
\nu
_{
\alpha
,
\beta
}
(
v
)
<
0
$
", [-1, 3], rgbcolor="black", fontsize="large")
+ text(r"
$
\nu
_{
\alpha
,
\beta
}
(-
v
)
>
0
$
", [2, 3], rgbcolor="black", fontsize="large")
+ text(r"
$
\nu
_{
\alpha
,
\beta
}
(-
v
)
<
0
$
", [4, 1], rgbcolor="black", fontsize="large")
+ text(r"
$
ch
_
2
^{
\alpha
,
\beta
}
(
v
)=
0
$
",[3.5, 2], rotation=45, fontsize="
x-
large"
, clip=True
)
+ text(r"
$
ch
_
1
^{
\alpha
,
\beta
}
(
v
)=
0
$
", [0.45, 1.5], rotation=90, fontsize="
x-
large"
, clip=True
)
+ text(r"
$
ch
_
2
^{
\alpha
,
\beta
}
(
v
)=
0
$
", [-2, 2], rotation=-45, fontsize="
x-
large"
, clip=True
)
+ text(r"
$
\nu
_{
\alpha
,
\beta
}
(
v
)
>
0
$
", [-3, 1], rgbcolor="black", fontsize="
x-
large"
, clip=True
)
+ text(r"
$
\nu
_{
\alpha
,
\beta
}
(
v
)
<
0
$
", [-1, 3], rgbcolor="black", fontsize="
x-
large"
, clip=True
)
+ text(r"
$
\nu
_{
\alpha
,
\beta
}
(-
v
)
>
0
$
", [2, 3], rgbcolor="black", fontsize="
x-
large"
, clip=True
)
+ text(r"
$
\nu
_{
\alpha
,
\beta
}
(-
v
)
<
0
$
", [4, 1], rgbcolor="black", fontsize="
x-
large"
, clip=True
)
)
p.xmax(5)
p.xmin(-4)
p.ymax(4)
p.axes
_
labels([r"
$
\beta
$
", r"
$
\alpha
$
"])
p.tick
_
label
_
color("white")
return p
v1 = Chern
_
Char(3, 2, -2)
v2 = Chern
_
Char(3, 2, 2/3)
\end{sagesilent}
%\begin{figure}
% \centering
% \sageplot[width=\textwidth]{charact_curves(v1)}
% \caption{}
% \label{fig:charact_curves_vis}
%\end{figure}
\begin{figure}
\centering
\resizebox
{
\textwidth
}{
!
}{
\sageplot
{
charact
_
curves(v1)
}
\begin{subfigure}
{
.49
\textwidth
}
\centering
\sageplot
[width=\textwidth]
{
charact
_
curves(v1)
}
\caption
{$
\Delta
(
v
)
>
0
$}
\label
{
fig:charact
_
curves
_
vis
_
bgmvlPos
}
\end{subfigure}
%
\hfill
\begin{subfigure}
{
.49
\textwidth
}
\centering
\sageplot
[width=\textwidth]
{
charact
_
curves(v2)
}
\caption
{$
\Delta
(
v
)=
0
$}
\label
{
fig:charact
_
curves
_
vis
_
bgmlv0
}
\end{subfigure}
\caption
{
Characteristic curves (
$
\chern
_
i
^{
\alpha
,
\beta
}
(
v
)=
0
$
) of stability conditions
associated to Chern characters
$
v
$
with
$
\Delta
(
v
)
\geq
0
$
and positive rank.
}
\caption
{
capt 1
}
\label
{
fig:charact
_
curves
_
vis
}
\end{figure}
\begin{sagesilent}
v = Chern
_
Char(3, 2, -2)
u = Chern
_
Char(1, 0, 0)
alpha = stability.Tilt().alpha
beta = stability.Tilt().beta
coords
_
range = (beta, -5, 5), (alpha, 0, 5)
charact
_
curve
_
plot = (
implicit
_
plot(stability.Tilt().degree(u), *coords
_
range , rgbcolor = "red")
+ implicit
_
plot(stability.Tilt().degree(v), *coords
_
range )
+ line([(mu(v),0),(mu(v),5)], linestyle = "dashed", legend
_
label =
r"
$
(
3
,
2
\ell
,
-
4
\ell
^
2
/
2
)
$
")
+ line([(mu(u),0),(mu(u),5)], rgbcolor = "red", linestyle =
"dashed", legend
_
label = r"
$
(
1
,
0
,
0
)
$
")
+ implicit
_
plot(stability.Tilt().wall
_
eqn(u,v)/alpha,
*coords
_
range , rgbcolor = "black")
)
charact
_
curve
_
plot.xmax(1)
charact
_
curve
_
plot.xmin(-2)
charact
_
curve
_
plot.ymax(1.5)
charact
_
curve
_
plot.axes
_
labels([r"
$
\beta
$
", r"
$
\alpha
$
"])
def charact
_
curve
_
with
_
wall
_
plot(u,v):
alpha = stability.Tilt().alpha
beta = stability.Tilt().beta
coords
_
range = (beta, -5, 5), (alpha, 0, 5)
charact
_
curve
_
plot = (
implicit
_
plot(stability.Tilt().degree(u), *coords
_
range , rgbcolor = "red")
+ implicit
_
plot(stability.Tilt().degree(v), *coords
_
range )
+ line([(mu(v),0),(mu(v),5)], linestyle = "dashed", legend
_
label =
r"
$
(
3
,
2
\ell
,
-
4
\ell
^
2
/
2
)
$
")
+ line([(mu(u),0),(mu(u),5)], rgbcolor = "red", linestyle =
"dashed", legend
_
label = r"
$
(
1
,
0
,
0
)
$
")
+ implicit
_
plot(stability.Tilt().wall
_
eqn(u,v)/alpha,
*coords
_
range , rgbcolor = "black")
)
charact
_
curve
_
plot.xmax(1)
charact
_
curve
_
plot.xmin(-2)
charact
_
curve
_
plot.ymax(1.5)
charact
_
curve
_
plot.axes
_
labels([r"
$
\beta
$
", r"
$
\alpha
$
"])
return charact
_
curve
_
plot
\end{sagesilent}
\begin{figure}
\centering
\sageplot
[width=\linewidth]
{
charact
_
curve
_
plot
}
\sageplot
[width=\linewidth]
{
charact
_
curve
_
with
_
wall
_
plot(u,v)
}
\caption
{}
\label
{
fig:characteristic-curves-example
}
\end{figure}
...
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