Paper Size
1in = 2.54cm
A4 | = 21.0cm × 29.7cm | = 8.27in × 11.69in |
A4 − 1in margins | = 15.92cm × 24.62cm | = 6.27in × 9.69in |
Letter | = 21.59cm × 27.94cm | = 8.5in × 11in |
theoretical and applied randomness by betaveros
1in = 2.54cm
A4 | = 21.0cm × 29.7cm | = 8.27in × 11.69in |
A4 − 1in margins | = 15.92cm × 24.62cm | = 6.27in × 9.69in |
Letter | = 21.59cm × 27.94cm | = 8.5in × 11in |
Cheaply, using an Iverson bracket expression:
\[ \begin{aligned} \lim_{a \to \infty} \lim_{b \to \infty} [a > b] &= 0 \\ \lim_{b \to \infty} \lim_{a \to \infty} [a > b] &= 1 \end{aligned} \]
For more continuity, use \(\frac{a}{a + b}\) instead (Rudin Example 7.2).
Uniform convergence on one limit suffices to allow this exchange, almost by definition.
Let
\[ f_\epsilon(x) = \begin{cases} 0 & \text{if } |x| \geq \epsilon \\ 1 - \left|\frac{x}{\epsilon}\right| &\text{if } |x| < \epsilon \end{cases}. \]
(Ported from betaveros.stash. Wow, I get syntax highlighting and footnotes! Probably years out of date though. I probably wrote this somewhere in 2012–2014, but am editing this parenthetical in 2021.)
A quick brief guide. At least, that’s how I planned it.
A lot of stuff is in the package java.awt.datatransfer
. Class Toolkit
is in java.awt
.
Some basic classes. The class Clipboard
is a clipboard, obviously. Its content is/will be an instance of the class Transferable
. Some content can be read as different types of objects depending on what you want; to choose which type you use an instance of DataFlavor
. It provides three basic ones: DataFlavor.imageFlavor
, DataFlavor.javaFileListFlavor
, and DataFlavor.stringFlavor
.
Okay, now step by step. This is the low-level method.
Clipboard clipboard = Toolkit.getDefaultToolkit().getSystemClipboard();
Transferable content = clipboard.getContents(null);
^{1}content
can be read as the kind of object you want with (content != null) && content.isDataFlavorSupported(someFlavor)
content.getTransferData(someFlavor)
^{2}.If you just want a quick-and-dirty function:
db.tt
).vimrc
if necessary.Editor’s note: This is almost certainly years out of date. cabal has v2 commands and stuff now? Sorry.
diagrams
is a nifty Haskell library for making vector diagrams. I keep coming back to it to generate graphics for puzzles:
I got sick of relearning it every time, and I think there’s some small chance other people will find it useful too, so I wrote something up. This post is a sort of reference that tries to compromise between the quick start tutorial and manual on one hand, and the API reference on the other, to try to be deeper and more comprehensive than the former, but also flow better and be easier to navigate than the latter. Some types are just really intimidating when fully written out…
To avoid unhelpfully generic types, I will deal concretely with two-dimensional diagrams that measure everything in Double
, and will frequently abbreviate complex types with an asterisk, like I will write V2*
for V2 Double
. I will introduce these aliases along the way for easy greppability. They’re not legal Haskell, of course.
This reference assumes basic-to-intermediate Haskell knowledge. Some of the more intermediate stuff includes:
Monoid
operator is <>
TrailLike
is a typeclass, and I might say or write that a function returns TrailLike
when I really mean TrailLike t => t
, any type t
that is in that typeclass.van Laarhoven lenses may help, but mostly I’ll try to black-box them.
It seems like a rite of passage to create one of these because there are so many Coq tactic cheat sheets out there and there’s just so much to learn. Here’s mine.
This is mostly about tactics but I realized not really.
Links:
Other Coq cheat sheets found by Googling “Coq cheat sheets”:
Meta-notes: I cover a lot of weak tactics because I like knowing exactly what my tools are doing. I try to use the variants of tactics that explicitly name things produced when possible. I am sure there is nomenclature I don’t understand precisely and use sloppily in this list; I am also sloppy with metavariables. Even things that are correct might be horrible style. There are likely other errors and omissions. They might be fixed one day. I’m putting this up nevertheless because it’s personally useful.
remember expr as X eqn:Hname.
easier to work with than set (X := expr).
pose proof expr as Hname.
adds expr
to the context, with name Hname
. Modus ponens where you know H1
and H2
, which is “H1
implies H3
”, is just pose proof (H2 H1) as H3
.1:
, 2:
etc., which can really help limit nesting depth. 2: (tactic that solves subgoal 2).
If you want more bullets, there are infinitely many, not just three. After -
+
*
you can use --
++
**
---
etc.Bruce Lindbloom has a ton of equations, but I just want the big ones on one page. We’ll assume sRGB, which implies using D65 as white (if you’re using Bruce Lindbloom’s calculator to check your implementation, make sure to set these).
Let \(\Xi\) (one of \(R\), \(G\), and \(B\)) be an RGB component in the range \([0, 1]\). (This is an obnoxious variable choice, but I’m trying to not overload any variable names in this entire post.) If you have RGB values in \([0, 255]\), divide them by 255. It can be converted to/from the linearized component \(\xi\) (one of \(r\), \(g\), and \(b\)) as:
\[\xi = \begin{cases} \Xi/12.92 & \text{if }\Xi \leq 0.04045 \\ ((\Xi + 0.055)/1.055)^{2.4} & \text{if }\Xi > 0.04045 \end{cases}\]
\[\Xi = \begin{cases} 12.92\xi & \text{if }\xi \leq 0.0031308 \\ 1.055v^{1/2.4} - 0.055 & \text{if }\xi > 0.0031308 \end{cases}\]
This is called “companding”.
However, you can use \(\xi = \Xi^{2.4}\) and \(\Xi = \xi^{1/2.4}\) in a pinch.
Convert between XYZ and linearized RGB. Again, this assumes sRGB and D65.
\[\begin{align*} X &= 0.4124564r + 0.3575761g + 0.1804375b \\ Y &= 0.2126729r + 0.7151522g + 0.0721750b \\ Z &= 0.0193339r + 0.1191920g + 0.9503041b \end{align*}\]