OpenLLM-France/wikimedia huggingface dataset:
# Should we have a Wikiversity specific discord server?

Discord is a collaborative platform that gives communities the space to communicate with each other via voice calls, video chats, platformed stage presentations etc etc. So would it be a useful tool to encourage communication and bring fresh editors to The WMF?

## We should use a Discord server

Relevant details, definitions and assumptions regarding the first possibility.

### Pro

* Pro The use of a discord server would widely increase communication between editors on everything that Wikiversity has to offer.
** Objection Talk pages are the proper venue for content- and policy-related discourse.
* Pro The use of a platform like discord would be a good way to train younger editors to start learning how to access the resources that Wikiversity offers. A place for younger editors to talk through the learning curves of this website would also give this older corner of the internet a very eager group of scholars to do all the tedious grunt-work the upkeep of this kind of place requires.
** Objection A new group of youths might be more trouble than it's worth and create more problems with clutter instead of cleaning it up.

### Con

* Con Using a platform outside of Wikiversity discussion boards or email to communicate would be unprofessional and confusing.
** Objection The point of the Wikimedia foundation is to be an accessible, free springboard of information that anyone can use. Using a well moderated alternative mode of communication could be a good place to ease newcomers into the learning curve of contributing to the Wikimedia Foundations sister projects.
*** Objection Don't you think that the use of an external link would make navigating Wikimedia projects more confusing?
**** Objection Wikiversity uses external links all the time, whether it's to keep their projects well sourced or for google form interviews to see if someone is worth promoting to higher editor levels.
* Con Discord is proprietary VoIP software, which raises concerns about privacy, surveillance and in general the abuse of whatever data they collect. Its use should be discouraged on this basis. One must wonder what they have to gain from offering VoIP as a "free" service. In some sense, it's a "dishonest" transaction between the average user and the people offering this service. The average user does not understand the value of data and simply believes they're getting something for free.
* Con An off-wiki communication room creates a separate locus of power, wielded by those who would rather hang around and chat than do real serious wiki work. That is a bad thing.
** Objection Wikiversity already uses IRC, and that's off-wiki. In addition, Wikipedia (or the Wikimedia Foundation in general) already has a Discord server.
* Con An IRC server with public logs would be a better, open-source alternative. Discourse is a "gated community", its servers are not managed by users.

## See Also

* Wikiversity:Discord
# Indian Law
## Constitution

The Indian Constitution is an original document and which is heavily based on and from various constitutions, as well as common law. Indian judicial system has its origins in its history, it has learned dispensing justice from great rulers like Ashoka and Akbar. True that we inherited the systematic dispensing of justice from British. Indian legal system works on the principles of checks and balances. The three wings of a Government - Executive, Judiciary and Parliament keeps it in equilibrium. It has a hierarchy of Courts. Starting from Muffasil or subdivision courts to the Supreme Court of India. The system can be divided in two parts - Lower Judiciary and Higher Judiciary. Each district has a Court, called Court of the District and Session Judge, and each provincial State has a High Court, which is basically first Appellate Court. Above all High Courts, there is Supreme Court of India. Indian Legal system, like any other system is divided in Civil and Criminal laws, which are always tested on the anvil of the Constitution of India.
For civil disputes,there are several laws divided according to subject areas but procedurally there is one Law which regulates them, called Code of Civil Procedure. For the criminal justice system, India has adopted the Laws framed in British India by Lord McKauley, namely IPC (Indian Penal Code), Cr.P.C. (Criminal Procedure Code), and Evidence Act.

## Problems

Unfortunately, proportionate to its population, Indian Legal sytem is also over burdened. About 2 million cases are pending in various Courts. One must believe that Indian Justice system, though slow but it dispenses justice.

## Resources

* Victims rights in India
# Winding number
## Definition

Let $\Gamma$ be a cycle in $\mathbb {C}$, and let $z\in \mathbb {C}$ be a point that $\Gamma$ does not intersect. Then
$n(\Gamma ,z):={\frac {1}{2\pi i}}\int _{\Gamma }{\frac {1}{w-z}}\,dw$
is called the *winding number* of $\Gamma$ around $z$.

### Motivation

First, consider the case where $\Gamma =\gamma$ consists of a single closed curve. Then $\gamma$ is homologous in $\mathbb {C} \setminus {z}$ to an $n$-fold (for some $n\in \mathbb {Z}$) traversed circle $\partial D_{r}(z)$ around $z$ with $r>0$. Now,
    $\int _{\gamma }{\frac {1}{w-z}},dw=\int _{n\cdot \partial B(z)}{\frac {1}{w-z}},dw=n\int _{\partial B(z)}{\frac {1}{w-z}},dw=2\pi i\cdot n.$
Thus, this integral counts how many times the curve $\gamma$ winds around the point $z$.

### Task

Let the closed integration path $\gamma :[-\pi ,+\pi ]\to \mathbb {C}$ be defined as:
    $\gamma (t):=\left(2+\cos(t)\right)\cdot e^{2it}.$
1. Plot the trace of the integration path.
2. Determine the winding number $n(\gamma ,1+i)$.
3. Determine the winding number $n(\gamma ,0)$.
4. Determine the winding number $n(\gamma ,1)$.

## Additivity of the Integral

For a cycle $\Gamma =\sum _{i=1}^{k}n_{i}\cdot \gamma _{i}$ with closed $\gamma _{i}$, due to the additivity of the integral, we have
    $n(\Gamma ,z)=\sum _{i=1}^{k}n_{i}\cdot n(\gamma _{i},z).$
Thus, the winding number also counts how many times the point $z$ is encircled.

## Length of the Cycle

For a cycle $\Gamma =\sum _{i=1}^{k}n_{i}\gamma _{i}$ with closed $\gamma _{i}$, the length of the cycle is defined additively over the lengths of the individual integration paths:
    $L(\Gamma ):=\sum _{i=1}^{k}n_{i}\cdot L(\gamma _{i}).$

## See Also

* Cauchy's Integral Theorem for Disks

## Page Information

You can display this page as Wiki2Reveal slides

### Wiki2Reveal

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* This page is designed as a PanDocElectron-SLIDE document type.
* Source: Wikiversity https://en.wikiversity.org/wiki/Winding%20number
* see Wiki2Reveal for the functionality of Wiki2Reveal.

### Translation and Version Control

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* Source: Kurs:Funktionentheorie/Umlaufzahl - URL:
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* Date: 12/17/2024
# Complex Analysis/Chain

A chain is a formal linear combination ofTrace of Curve, we have

## Definition - Chain

Let $G\subseteq \mathbb {C}$, let $n\in \mathbb {N}$, and let $\gamma _{i}\colon [a_{i},b_{i}]\to G$ be curves in $G$ and $n_{i}\in \mathbb {Z}$. Then the formal linear combination $\sum _{i=1}^{n}n_{i}\gamma _{i}$ is called a chain in $\mathbb {C}$. The set of all chains in $G$, which is naturally an abelian group, is denoted by $C(G)$.

## Definition - Trace of a Chain

The trace of a chain $\Gamma$ is the union of the traces of the individual curves $\gamma _{i}$, i.e.
$\mathrm {Trace} (\Gamma ):=\bigcup _{i=1}^{n}\mathrm {Trace} (\gamma _{i})$

## Cycle

A chain $\Gamma =\sum _{i=1}^{n}n_{i}\gamma _{i}\in C(G)$ with $\gamma _{i}\colon [a_{i},b_{i}]\to G$ is called a cycle if each point of $G$ occurs equally often as the starting and ending point of curves in $G$, i.e., if
$\sum _{i=1}^{n}n_{i}|\{i:\gamma _{i}(a_{i})=z\}|=\sum _{i=1}^{n}n_{i}|\{i:\gamma _{i}(b_{i})=z\}|$
holds for every $z\in G$.

### Interior and Exterior Region

Let $\Gamma$ be a cycle in $\mathbb {C}$, with the help of the winding number one can consider a decomposition of $\mathbb {C}$ into three parts determined by $\Gamma$, namely:
* The image set of $\mathrm {Trace} (\Gamma )$
* The exterior region, those points that are not traversed by $\Gamma$, i.e. $A_{\Gamma }:={z\in \mathbb {C} \setminus \mathrm {Trace} (\Gamma ):n(\Gamma ,z)=0}$
* The interior region consists of those points that are traversed by $\Gamma$, i.e. $I_{\Gamma }:={z\in \mathbb {C} \setminus \mathrm {Trace} (\Gamma ):n(\Gamma ,z)\neq 0}$

## Page Information

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* This page is designed as a PanDocElectron-SLIDE document type.

### Translation and Version Control

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# Complex Analysis/Liouville's Theorem

The Liouville Theorem is a statement about holomorphic functions defined on the entire complex plane $\mathbb {C}$.

## Statement

Let $f\colon \mathbb {C} \to \mathbb {C}$ be holomorphic and bounded. Then $f$ is constant.

## Proof

For every $R>0$ and every $z\in \mathbb {C}$, we have by the Cauchy integral formula:
${\begin{array}{rl}|f'(z)|&=\displaystyle {\frac {1}{2\pi }}\left|\int _{\partial B_{R}(z)}{\frac {f(w)}{(w-z)^{2}}}\,dw\right|\\&\leq \displaystyle {\frac {1}{2\pi }}2\pi R\cdot {\frac {1}{R^{2}}}\cdot \sup _{w\in B_{R}(z)}|f(w)|\\&\leq {\frac {M}{R}}\\&\to 0,\qquad R\to \infty \end{array}}$
Thus, $f'=0$, and therefore $f$ is constant.

## See Also

* Complex Analysis
* Cauchy's integral formula
* Wiki2Reveal

## Page Information

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### Wiki2Reveal

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### Translation and Version Control

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# Complex Analysis/Differences from real differentiability
## n-times Real Differentiability

The function
    $f:\mathbb {R} \rightarrow \mathbb {R} ,$ with $x\mapsto f(x)=|x|\cdot x$,
can be differentiated once. However, its first derivative is no longer differentiable at 0.

## Task

* Sketch the graphs of the functions $f$ and $f'$.
* Can the function $f:\mathbb {R} \rightarrow \mathbb {R}$ be extended to a holomorphic function $F:\mathbb {C} \rightarrow \mathbb {C}$, where $F_{|\mathbb {R} }=f$ (i.e., $f(x)=F(x)$ for all $x\in \mathbb {R}$)? Justify your answer using the properties of holomorphic functions!
* Show that the function
    $f_{n}:\mathbb {R} \rightarrow \mathbb {R} ,$ with $x\mapsto f(x)=|x|\cdot x^{n}$,
    can be differentiated $n$ times. However, the $n+1$-th derivative is no longer differentiable at 0.

## Remark

In complex analysis (Complex Analysis), one will see that a holomorphic function $f:U\to \mathbb {C}$ defined on $U\subseteq \mathbb {C}$ is automatically infinitely often complex differentiable if it is complex differentiable once (seeHolomorphy Criteria.
# Complex Analysis/Trace
## Definition

A curve in $\mathbb {C}$ is a continuous mapping $\gamma \colon [a,b]\to \mathbb {C}$. The image set
$\mathrm {Trace} (\gamma ):=\{\gamma (t):t\in [a,b]\}$
is called the "trace" of the curve.

### Properties of Curves

* A curve is called differentiable, $C^{k}$, etc., if the defining mapping has these properties.
* A property particularly important for the theory of Curve Integral is therectifiable curve rectifiable of a curve, rectifiable curves are curves over which integration is possible.

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# Complex Analysis/null-homologous

Definition Let $G\subseteq \mathbb {C}$ be a domain, and let $\Gamma$ be a Chain in $G$. The cycle $\Gamma$ is called null-homologous in $G$ if, for every $z\in \mathbb {C} \setminus G$, the Winding number vanishes. In other words, this means that $\mathbb {C} \setminus G\subseteq A_{\Gamma }={z\in \mathbb {C} :n(\Gamma ,z)=0}$.

### Translation and Version Control

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# Riemann Removability Theorem
## Statement

Let $G\subseteq \mathbb {C}$ be a domain, $z_{0}\in G$, and $f\colon G\setminus {z_{0}}\to \mathbb {C}$ be holomorphic. Then $f$ can be holomorphically extended to $z_{0}$ if and only if there exists a neighborhood $U\subseteq G$ of $z_{0}$ such that $f$ is bounded on $U\setminus {z_{0}}$.

## Proof

Let $r>0$ be chosen such that ${\bar {B}}_{r}(z_{0})\subseteq U$, and let $M$ be an upper bound for $f$ on $U$.
We consider the Laurent Series of $f$ around $z_{0}$. It is
$f(z)=\sum _{n=-\infty }^{\infty }a_{n}(z-z_{0})^{n},\qquad a_{n}={\frac {1}{2\pi i}}\int _{|w-z_{0}|=r}{\frac {f(w)}{(w-z_{0})^{n+1}}}\,dw$
Estimating $a_{n}$ gives the so-called Cauchy estimates, namely
${\begin{array}{rl}|a_{n}|&=\displaystyle \left|{\frac {1}{2\pi i}}\int _{|w-z_{0}|=r}{\frac {f(w)}{(w-z_{0})^{n+1}}}\,dw\right|\\&\leq \displaystyle {\frac {1}{2\pi }}\int _{|w-z_{0}|=r}{\frac {|f(w)|}{|w-z_{0}|^{n+1}}}\,|dw|\\&\leq \displaystyle {\frac {1}{2\pi }}\int _{|w-z_{0}|=r}{\frac {M}{r^{n+1}}}\,|dw|\\&=\displaystyle {\frac {M}{r^{n}}}\\\end{array}}$
For $n<0$, it follows that
$|a_{n}|\leq {\frac {M}{r^{n}}}=Mr^{-n}\to 0,\quad r\to 0$
Thus, $a_{n}=0$ for all $n<0$, meaning we have $f(z)=\sum _{n=0}^{\infty }a_{n}(z-z_{0})^{n}$, and $f(z_{0}):=a_{0}$ is a holomorphic extension of $f$ to $z_{0}$.

### Translation and Version Control

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# Rouché's theorem

Rouché's theorem is a statement about the location of the zeros of holomorphic functions, often used to estimate the number of zeros.

## Statement

Let $U\subseteq \mathbb {C}$ be open, and let $\Gamma$ be a cycle in $U$, which is null-homologous in $U$ and winds around every point in its interior exactly once, i.e., $n(\Gamma ,z)\in {0,1}$ for each $z\in U$. Let $f,g\colon U\to \mathbb {C}$ be holomorphic functions such that
$|f(z)-g(z)|<|f(z)|,\qquad z\in \mathrm {trace} (\Gamma )$
holds. Then $f$ and $g$ have the same number of zeros (counted with multiplicity) in $I_{\Gamma }=\{z\in \mathbb {C} :n(\Gamma ,z)=1\}$.

## Proof

For each $\lambda \in [0,1]$, consider the function $f_{\lambda }:=(1-\lambda )f+\lambda g=f+\lambda (g-f)$. Since
    $|\lambda (g(z)-f(z))|=|\lambda ||g(z)-f(z)|<|f(z)|,\qquad z\in \mathrm {trace} (\Gamma )$,
$f_{\lambda }$ has no zeros on $\mathrm {trace} (\Gamma )$. Since $f_{\lambda }$ is holomorphic on $I_{\Gamma }$, it follows from the Zero and Pole counting integral that the number of zeros of $f_{\lambda }$ in $I_{\Gamma }$ is
    ${\frac {1}{2\pi i}}\int _{\Gamma }{\frac {f_{\lambda }'(z)}{f_{\lambda }(z)}},dz={\frac {1}{2\pi i}}\int _{\Gamma }{\frac {(1-\lambda )f'(z)+\lambda g'(z)}{(1-\lambda )f(z)+\lambda g(z)}},dz$.
This means it depends continuously on $\lambda$. A continuous $\mathbb {Z}$-valued function on $[0,1]$ is constant, so $f_{0}=f$ and $f_{1}=g$ have the same number of zeros in $I_{\Gamma }$.

## Application

An application of Rouché's theorem is a proof of the Fundamental Theorem of Algebra: Let $p(z)=\sum _{k=0}^{n}a_{k}z^{k}\in \mathbb {C} [z]$ be a polynomial with $n>0$ and $a_{n}\neq 0$. The idea of the proof is to compare $p$ with $q(z)=a_{n}z^{n}$ (the number of zeros of $q$ is known). It holds that
    $|p(z)-q(z)|=\left|\sum _{k=0}^{n-1}a_{k}z^{k}\right|\leq \sum _{k=0}^{n-1}|a_{k}||z|^{k}<|a_{n}||z^{n}|=|q(z)|$
for $|z|\geq R$ and a sufficiently large $R$. Hence, $p$ and $q$ have the same number of zeros, namely $n$, in $D_{R}(0)$.
# Boolf prop/3-ary/twin consul

This is the XOR of all Zhegalkin exponents, i.e. the binary places of the Zhegalkin index. Compare consul, twin prefect.
Number of blocks: 8 Integer partition: 8⋅32
| # | twin consul | block |
| 32 | 0 | [0, 1, 2, 3, 4, 5, 6, 7, 16, 17, 18, 19, 20, 21, 22, 23, 232, 233, 234, 235, 236, 237, 238, 239, 248, 249, 250, 251, 252, 253, 254, 255] |
| 32 | 4 | [8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31, 224, 225, 226, 227, 228, 229, 230, 231, 240, 241, 242, 243, 244, 245, 246, 247] |
| 32 | 2 | [32, 33, 34, 35, 36, 37, 38, 39, 48, 49, 50, 51, 52, 53, 54, 55, 200, 201, 202, 203, 204, 205, 206, 207, 216, 217, 218, 219, 220, 221, 222, 223] |
| 32 | 6 | [40, 41, 42, 43, 44, 45, 46, 47, 56, 57, 58, 59, 60, 61, 62, 63, 192, 193, 194, 195, 196, 197, 198, 199, 208, 209, 210, 211, 212, 213, 214, 215] |
| 32 | 1 | [64, 65, 66, 67, 68, 69, 70, 71, 80, 81, 82, 83, 84, 85, 86, 87, 168, 169, 170, 171, 172, 173, 174, 175, 184, 185, 186, 187, 188, 189, 190, 191] |
| 32 | 5 | [72, 73, 74, 75, 76, 77, 78, 79, 88, 89, 90, 91, 92, 93, 94, 95, 160, 161, 162, 163, 164, 165, 166, 167, 176, 177, 178, 179, 180, 181, 182, 183] |
| 32 | 3 | [96, 97, 98, 99, 100, 101, 102, 103, 112, 113, 114, 115, 116, 117, 118, 119, 136, 137, 138, 139, 140, 141, 142, 143, 152, 153, 154, 155, 156, 157, 158, 159] |
| 32 | 7 | [104, 105, 106, 107, 108, 109, 110, 111, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 144, 145, 146, 147, 148, 149, 150, 151] |
# Boolf prop/3-ary/chunky twist xors

Number of blocks: 16 Integer partition: 16⋅16
| # | chunky twist xors | chunky seminar | block |
| 16 | (0, 0, 0), (0, 0, 7), (7, 0, 0), (7, 0, 7) | 0 0 Ж 0 | [0, 1, 22, 23, 104, 105, 126, 127, 128, 129, 150, 151, 232, 233, 254, 255] |
| 16 | (1, 6, 0), (1, 6, 7), (6, 6, 0), (6, 6, 7) | 42 130 Ж 42 | [2, 3, 20, 21, 106, 107, 124, 125, 130, 131, 148, 149, 234, 235, 252, 253] |
| 16 | (2, 5, 0), (2, 5, 7), (5, 5, 0), (5, 5, 7) | 36 108 Ж 36 | [4, 5, 18, 19, 108, 109, 122, 123, 132, 133, 146, 147, 236, 237, 250, 251] |
| 16 | (3, 3, 0), (3, 3, 7), (4, 3, 0), (4, 3, 7) | 14 238 Ж 14 | [6, 7, 16, 17, 110, 111, 120, 121, 134, 135, 144, 145, 238, 239, 248, 249] |
| 16 | (0, 3, 0), (0, 3, 7), (7, 3, 0), (7, 3, 7) | 8 136 Ж 8 | [8, 9, 30, 31, 96, 97, 118, 119, 136, 137, 158, 159, 224, 225, 246, 247] |
| 16 | (1, 5, 0), (1, 5, 7), (6, 5, 0), (6, 5, 7) | 34 10 Ж 34 | [10, 11, 28, 29, 98, 99, 116, 117, 138, 139, 156, 157, 226, 227, 244, 245] |
| 16 | (2, 6, 0), (2, 6, 7), (5, 6, 0), (5, 6, 7) | 44 228 Ж 44 | [12, 13, 26, 27, 100, 101, 114, 115, 140, 141, 154, 155, 228, 229, 242, 243] |
| 16 | (3, 0, 0), (3, 0, 7), (4, 0, 0), (4, 0, 7) | 6 102 Ж 6 | [14, 15, 24, 25, 102, 103, 112, 113, 142, 143, 152, 153, 230, 231, 240, 241] |
| 16 | (0, 5, 0), (0, 5, 7), (7, 5, 0), (7, 5, 7) | 32 160 Ж 32 | [32, 33, 54, 55, 72, 73, 94, 95, 160, 161, 182, 183, 200, 201, 222, 223] |
| 16 | (1, 3, 0), (1, 3, 7), (6, 3, 0), (6, 3, 7) | 10 34 Ж 10 | [34, 35, 52, 53, 74, 75, 92, 93, 162, 163, 180, 181, 202, 203, 220, 221] |
| 16 | (2, 0, 0), (2, 0, 7), (5, 0, 0), (5, 0, 7) | 4 204 Ж 4 | [36, 37, 50, 51, 76, 77, 90, 91, 164, 165, 178, 179, 204, 205, 218, 219] |
| 16 | (3, 6, 0), (3, 6, 7), (4, 6, 0), (4, 6, 7) | 46 78 Ж 46 | [38, 39, 48, 49, 78, 79, 88, 89, 166, 167, 176, 177, 206, 207, 216, 217] |
| 16 | (0, 6, 0), (0, 6, 7), (7, 6, 0), (7, 6, 7) | 40 40 Ж 40 | [40, 41, 62, 63, 64, 65, 86, 87, 168, 169, 190, 191, 192, 193, 214, 215] |
| 16 | (1, 0, 0), (1, 0, 7), (6, 0, 0), (6, 0, 7) | 2 170 Ж 2 | [42, 43, 60, 61, 66, 67, 84, 85, 170, 171, 188, 189, 194, 195, 212, 213] |
| 16 | (2, 3, 0), (2, 3, 7), (5, 3, 0), (5, 3, 7) | 12 68 Ж 12 | [44, 45, 58, 59, 68, 69, 82, 83, 172, 173, 186, 187, 196, 197, 210, 211] |
| 16 | (3, 5, 0), (3, 5, 7), (4, 5, 0), (4, 5, 7) | 38 198 Ж 38 | [46, 47, 56, 57, 70, 71, 80, 81, 174, 175, 184, 185, 198, 199, 208, 209] |
# Boolf prop/3-ary/twist xors 1

Number of blocks: 8 Integer partition: 8⋅32
| # | twist xors 1 | block |
| 32 | 0 | [0, 8, 23, 31, 32, 40, 55, 63, 64, 72, 87, 95, 96, 104, 119, 127, 128, 136, 151, 159, 160, 168, 183, 191, 192, 200, 215, 223, 224, 232, 247, 255] |
| 32 | 7 | [1, 9, 22, 30, 33, 41, 54, 62, 65, 73, 86, 94, 97, 105, 118, 126, 129, 137, 150, 158, 161, 169, 182, 190, 193, 201, 214, 222, 225, 233, 246, 254] |
| 32 | 1 | [2, 10, 21, 29, 34, 42, 53, 61, 66, 74, 85, 93, 98, 106, 117, 125, 130, 138, 149, 157, 162, 170, 181, 189, 194, 202, 213, 221, 226, 234, 245, 253] |
| 32 | 6 | [3, 11, 20, 28, 35, 43, 52, 60, 67, 75, 84, 92, 99, 107, 116, 124, 131, 139, 148, 156, 163, 171, 180, 188, 195, 203, 212, 220, 227, 235, 244, 252] |
| 32 | 2 | [4, 12, 19, 27, 36, 44, 51, 59, 68, 76, 83, 91, 100, 108, 115, 123, 132, 140, 147, 155, 164, 172, 179, 187, 196, 204, 211, 219, 228, 236, 243, 251] |
| 32 | 5 | [5, 13, 18, 26, 37, 45, 50, 58, 69, 77, 82, 90, 101, 109, 114, 122, 133, 141, 146, 154, 165, 173, 178, 186, 197, 205, 210, 218, 229, 237, 242, 250] |
| 32 | 3 | [6, 14, 17, 25, 38, 46, 49, 57, 70, 78, 81, 89, 102, 110, 113, 121, 134, 142, 145, 153, 166, 174, 177, 185, 198, 206, 209, 217, 230, 238, 241, 249] |
| 32 | 4 | [7, 15, 16, 24, 39, 47, 48, 56, 71, 79, 80, 88, 103, 111, 112, 120, 135, 143, 144, 152, 167, 175, 176, 184, 199, 207, 208, 216, 231, 239, 240, 248] |
# Boolf prop/3-ary/great quaestor

Number of blocks: 4 Integer partition: 4⋅64
| # | great quaestor | quaestor tiling and slatting | twist xors 2 | block |
| 64 | 0 | (0, 0) | 0 | [0, 1, 14, 15, 22, 23, 24, 25, 36, 37, 42, 43, 50, 51, 60, 61, 66, 67, 76, 77, 84, 85, 90, 91, 102, 103, 104, 105, 112, 113, 126, 127, 128, 129, 142, 143, 150, 151, 152, 153, 164, 165, 170, 171, 178, 179, 188, 189, 194, 195, 204, 205, 212, 213, 218, 219, 230, 231, 232, 233, 240, 241, 254, 255] |
| 64 | 2 | (0, 1) | 6 | [2, 3, 12, 13, 20, 21, 26, 27, 38, 39, 40, 41, 48, 49, 62, 63, 64, 65, 78, 79, 86, 87, 88, 89, 100, 101, 106, 107, 114, 115, 124, 125, 130, 131, 140, 141, 148, 149, 154, 155, 166, 167, 168, 169, 176, 177, 190, 191, 192, 193, 206, 207, 214, 215, 216, 217, 228, 229, 234, 235, 242, 243, 252, 253] |
| 64 | 4 | (1, 1) | 5 | [4, 5, 10, 11, 18, 19, 28, 29, 32, 33, 46, 47, 54, 55, 56, 57, 70, 71, 72, 73, 80, 81, 94, 95, 98, 99, 108, 109, 116, 117, 122, 123, 132, 133, 138, 139, 146, 147, 156, 157, 160, 161, 174, 175, 182, 183, 184, 185, 198, 199, 200, 201, 208, 209, 222, 223, 226, 227, 236, 237, 244, 245, 250, 251] |
| 64 | 6 | (1, 0) | 3 | [6, 7, 8, 9, 16, 17, 30, 31, 34, 35, 44, 45, 52, 53, 58, 59, 68, 69, 74, 75, 82, 83, 92, 93, 96, 97, 110, 111, 118, 119, 120, 121, 134, 135, 136, 137, 144, 145, 158, 159, 162, 163, 172, 173, 180, 181, 186, 187, 196, 197, 202, 203, 210, 211, 220, 221, 224, 225, 238, 239, 246, 247, 248, 249] |