Lagmental

Math and Code Test

2026-08-29T12:45:00-06:00

Math test

Inline math:

$e^{i\pi} + 1 = 0$

Display math:

$$ q = p^n $$

A slightly more interesting one:

$$ \mathbf{F}_{p^n}^{\times} \cong C_{p^n - 1}. $$

And:

$$ \int_0^\infty e^{-x^2}\,dx = \frac{\sqrt{\pi}}{2}. $$

C++ syntax highlighting

#include <cstdint>
#include <iostream>
#include <vector>

using namespace std;

int main() {
  vector<int64_t> primes = {2, 3, 5, 7, 11};

  for (int64_t p : primes) {
    cout << "F_" << p
         << " has " << p
         << " elements." << endl;
  }

  return 0;
}

Haskell syntax highlighting

primes :: [Integer]
primes = [2, 3, 5, 7, 11]

main :: IO ()
main = mapM_ print primes

Shell syntax highlighting

pelican content
pelican --listen

Finite Fields up to Order 128

Let $\zeta_n$ denote a primitive $n$th root of unity.

For every finite field $\mathbf F_q$,

$$ \mathbf F_q^\times \cong C_{q-1}=\mu_{q-1}. $$

In particular, if $q=p^d$, then

$$ \mathbf F_q=\mathbf F_p(\zeta_{q-1}), $$

although a root of unity of much smaller order often already generates the extension.

Field	Units	Cyclotomic realizations	Why it is beautiful
$\mathbf F_2$	$\mathbf F_2^\times\cong C_1$	$\mathbf F_2=\mathbf F_2(\zeta_1)$	The atom. Its entire multiplicative group is trivial and $-1=1$. Characteristic $2$ begins its campaign against ordinary intuition.
$\mathbf F_3$	$\mathbf F_3^\times\cong C_2$	$\mathbf F_3=\mathbf F_3(\zeta_2)$	The smallest field where $1\neq-1$. The familiar pair $\{\pm1\}$ finally exists.
$\mathbf F_4$	$\mathbf F_4^\times\cong C_3$	$\mathbf F_4=\mathbf F_2(\zeta_3)$	The first genuine finite-field extension. Its three nonzero elements are exactly the cube roots of unity. Tiny perfection.
$\mathbf F_5$	$\mathbf F_5^\times\cong C_4$	$\mathbf F_5=\mathbf F_5(\zeta_4)$	Already contains a primitive fourth root of unity: $2^2=-1$. An $i$-like element appears inside the prime field itself.
$\mathbf F_7$	$\mathbf F_7^\times\cong C_6$	$\mathbf F_7=\mathbf F_7(\zeta_6)$	Contains primitive $3$rd and $6$th roots of unity. The factorization $6=2\cdot3$ gives a surprisingly rich tiny multiplicative world.
$\mathbf F_8$	$\mathbf F_8^\times\cong C_7$	$\mathbf F_8=\mathbf F_2(\zeta_7)$	The first cubic extension. Since $7$ is prime, every nonzero element except $1$ is a primitive $7$th root of unity.
$\mathbf F_9$	$\mathbf F_9^\times\cong C_8$	$\mathbf F_9=\mathbf F_3(\zeta_4)=\mathbf F_3(\zeta_8)$	The finite-field analogue of adjoining $i$: $\mathbf F_9=\mathbf F_3(i)$. Its entire unit group is $\mu_8$.
$\mathbf F_{11}$	$\mathbf F_{11}^\times\cong C_{10}$	$\mathbf F_{11}=\mathbf F_{11}(\zeta_{10})$	Primitive fifth roots of unity already live in the prime field because $5\mid10$.
$\mathbf F_{13}$	$\mathbf F_{13}^\times\cong C_{12}$	$\mathbf F_{13}=\mathbf F_{13}(\zeta_{12})$	Contains primitive roots of orders $3,4,6,$ and $12$. A very rich little cyclotomic playground.
$\mathbf F_{16}$	$\mathbf F_{16}^\times\cong C_{15}$	$\mathbf F_{16}=\mathbf F_2(\zeta_5)=\mathbf F_2(\zeta_{15})$	The famous counterintuitive step: $\zeta_3$ gives $\mathbf F_4$, $\zeta_7$ gives $\mathbf F_8$, but the smaller $\zeta_5$ needs degree $4$. It also contains $\mathbf F_4$.
$\mathbf F_{17}$	$\mathbf F_{17}^\times\cong C_{16}$	$\mathbf F_{17}=\mathbf F_{17}(\zeta_{16})$	Pure $2$-power cyclotomy: $\mathbf F_{17}^\times$ has order $2^4$. Fermat-prime elegance appears here.
$\mathbf F_{19}$	$\mathbf F_{19}^\times\cong C_{18}$	$\mathbf F_{19}=\mathbf F_{19}(\zeta_{18})$	Since $18=2\cdot3^2$, primitive $9$th and $18$th roots of unity occur naturally.
$\mathbf F_{23}$	$\mathbf F_{23}^\times\cong C_{22}$	$\mathbf F_{23}=\mathbf F_{23}(\zeta_{22})$	Its multiplicative group contains the large prime-order subgroup $\mu_{11}$. Clean and almost prime-order.
$\mathbf F_{25}$	$\mathbf F_{25}^\times\cong C_{24}$	$\mathbf F_{25}=\mathbf F_5(\zeta_3)=\mathbf F_5(\zeta_{24})$	A lovely surprise: merely adjoining a primitive cube root of unity to $\mathbf F_5$ produces the quadratic extension $\mathbf F_{25}$.
$\mathbf F_{27}$	$\mathbf F_{27}^\times\cong C_{26}$	$\mathbf F_{27}=\mathbf F_3(\zeta_{13})=\mathbf F_3(\zeta_{26})$	A primitive $13$th root creates a cubic extension because $\operatorname{ord}_{13}(3)=3$. There are no intermediate fields.
$\mathbf F_{29}$	$\mathbf F_{29}^\times\cong C_{28}$	$\mathbf F_{29}=\mathbf F_{29}(\zeta_{28})$	Since $28=2^2\cdot7$, fourth and seventh roots of unity coexist naturally.
$\mathbf F_{31}$	$\mathbf F_{31}^\times\cong C_{30}$	$\mathbf F_{31}=\mathbf F_{31}(\zeta_{30})$	The factorization $30=2\cdot3\cdot5$ gives elements of orders $2,3,5,6,10,15,$ and $30$.
$\mathbf F_{32}$	$\mathbf F_{32}^\times\cong C_{31}$	$\mathbf F_{32}=\mathbf F_2(\zeta_{31})$	An absolute jewel. Since $31$ is prime, every element of $\mathbf F_{32}\setminus\{0,1\}$ is a primitive $31$st root of unity.
$\mathbf F_{37}$	$\mathbf F_{37}^\times\cong C_{36}$	$\mathbf F_{37}=\mathbf F_{37}(\zeta_{36})$	The unit group has order $36=2^2\cdot3^2$, giving a rich mixture of $2$-power and $3$-power cyclotomy.
$\mathbf F_{41}$	$\mathbf F_{41}^\times\cong C_{40}$	$\mathbf F_{41}=\mathbf F_{41}(\zeta_{40})$	Since $40=2^3\cdot5$, eighth roots and fifth roots of unity coexist inside one prime field.
$\mathbf F_{43}$	$\mathbf F_{43}^\times\cong C_{42}$	$\mathbf F_{43}=\mathbf F_{43}(\zeta_{42})$	$42=2\cdot3\cdot7$: quadratic, cubic, and seventh-root cyclotomy all coexist.
$\mathbf F_{47}$	$\mathbf F_{47}^\times\cong C_{46}$	$\mathbf F_{47}=\mathbf F_{47}(\zeta_{46})$	Its multiplicative structure is dominated by the large prime-order subgroup $\mu_{23}$.
$\mathbf F_{49}$	$\mathbf F_{49}^\times\cong C_{48}$	$\mathbf F_{49}=\mathbf F_7(\zeta_4)=\mathbf F_7(\zeta_{48})$	Beautifully simple: adjoining $i$ to $\mathbf F_7$ produces $\mathbf F_{49}$. Its unit group has order $48=2^4\cdot3$.
$\mathbf F_{53}$	$\mathbf F_{53}^\times\cong C_{52}$	$\mathbf F_{53}=\mathbf F_{53}(\zeta_{52})$	Since $52=2^2\cdot13$, it is a natural home for primitive $13$th roots of unity.
$\mathbf F_{59}$	$\mathbf F_{59}^\times\cong C_{58}$	$\mathbf F_{59}=\mathbf F_{59}(\zeta_{58})$	Its cyclotomic structure is dominated by the large prime $29$.
$\mathbf F_{61}$	$\mathbf F_{61}^\times\cong C_{60}$	$\mathbf F_{61}=\mathbf F_{61}(\zeta_{60})$	One of the richest prime-field playgrounds in this range: $60=2^2\cdot3\cdot5$ has many divisors and therefore many root orders.
$\mathbf F_{64}$	$\mathbf F_{64}^\times\cong C_{63}$	$\mathbf F_{64}=\mathbf F_2(\zeta_9)=\mathbf F_2(\zeta_{21})=\mathbf F_2(\zeta_{63})$	A primitive $9$th root already generates the sextic extension. It contains both the $\zeta_3$ world $\mathbf F_4$ and the $\zeta_7$ world $\mathbf F_8$.
$\mathbf F_{67}$	$\mathbf F_{67}^\times\cong C_{66}$	$\mathbf F_{67}=\mathbf F_{67}(\zeta_{66})$	Since $66=2\cdot3\cdot11$, it simultaneously contains primitive $3$rd, $6$th, $11$th, $22$nd, $33$rd, and $66$th roots.
$\mathbf F_{71}$	$\mathbf F_{71}^\times\cong C_{70}$	$\mathbf F_{71}=\mathbf F_{71}(\zeta_{70})$	$70=2\cdot5\cdot7$, so fifth- and seventh-root cyclotomy meet naturally.
$\mathbf F_{73}$	$\mathbf F_{73}^\times\cong C_{72}$	$\mathbf F_{73}=\mathbf F_{73}(\zeta_{72})$	$72=2^3\cdot3^2$ gives unusually rich simultaneous $2$-power and $3$-power root-of-unity structure.
$\mathbf F_{79}$	$\mathbf F_{79}^\times\cong C_{78}$	$\mathbf F_{79}=\mathbf F_{79}(\zeta_{78})$	Since $78=2\cdot3\cdot13$, primitive $13$th roots coexist with cubic structure.
$\mathbf F_{81}$	$\mathbf F_{81}^\times\cong C_{80}$	$\mathbf F_{81}=\mathbf F_3(\zeta_5)=\mathbf F_3(\zeta_{16})=\mathbf F_3(\zeta_{80})$	A primitive fifth root already generates the quartic extension because $\operatorname{ord}_5(3)=4$. It also contains $\mathbf F_9$ as a proper subfield.
$\mathbf F_{83}$	$\mathbf F_{83}^\times\cong C_{82}$	$\mathbf F_{83}=\mathbf F_{83}(\zeta_{82})$	Its unit group has order $82=2\cdot41$, dominated by the large prime cyclotomic subgroup $\mu_{41}$.
$\mathbf F_{89}$	$\mathbf F_{89}^\times\cong C_{88}$	$\mathbf F_{89}=\mathbf F_{89}(\zeta_{88})$	$88=2^3\cdot11$ combines substantial $2$-power structure with primitive $11$th roots.
$\mathbf F_{97}$	$\mathbf F_{97}^\times\cong C_{96}$	$\mathbf F_{97}=\mathbf F_{97}(\zeta_{96})$	$96=2^5\cdot3$: a remarkable amount of $2$-power cyclotomy occurs inside a prime field of fewer than $100$ elements.
$\mathbf F_{101}$	$\mathbf F_{101}^\times\cong C_{100}$	$\mathbf F_{101}=\mathbf F_{101}(\zeta_{100})$	The particularly tidy factorization $100=2^2\cdot5^2$ gives rich fifth-power cyclotomic structure.
$\mathbf F_{103}$	$\mathbf F_{103}^\times\cong C_{102}$	$\mathbf F_{103}=\mathbf F_{103}(\zeta_{102})$	Since $102=2\cdot3\cdot17$, primitive $17$th roots sit alongside cubic and sixth-root structure.
$\mathbf F_{107}$	$\mathbf F_{107}^\times\cong C_{106}$	$\mathbf F_{107}=\mathbf F_{107}(\zeta_{106})$	Its multiplicative group has the simple shape $C_{2\cdot53}$, with a large prime-order subgroup $\mu_{53}$.
$\mathbf F_{109}$	$\mathbf F_{109}^\times\cong C_{108}$	$\mathbf F_{109}=\mathbf F_{109}(\zeta_{108})$	$108=2^2\cdot3^3$, so this field is especially rich in $3$-power roots of unity, including primitive $27$th roots.
$\mathbf F_{113}$	$\mathbf F_{113}^\times\cong C_{112}$	$\mathbf F_{113}=\mathbf F_{113}(\zeta_{112})$	$112=2^4\cdot7$ combines deep $2$-power cyclotomy with primitive seventh roots.
$\mathbf F_{121}$	$\mathbf F_{121}^\times\cong C_{120}$	$\mathbf F_{121}=\mathbf F_{11}(\zeta_3)=\mathbf F_{11}(\zeta_{120})$	A primitive cube root already generates the quadratic extension of $\mathbf F_{11}$. Meanwhile $120=2^3\cdot3\cdot5$ makes its unit group spectacularly rich.
$\mathbf F_{125}$	$\mathbf F_{125}^\times\cong C_{124}$	$\mathbf F_{125}=\mathbf F_5(\zeta_{31})=\mathbf F_5(\zeta_{124})$	A primitive $31$st root creates a cubic extension because $\operatorname{ord}_{31}(5)=3$. Since the degree is prime, there are no intermediate fields.
$\mathbf F_{127}$	$\mathbf F_{127}^\times\cong C_{126}$	$\mathbf F_{127}=\mathbf F_{127}(\zeta_{126})$	$126=2\cdot3^2\cdot7$ gives a rich mixture of cubic, ninth-root, and seventh-root behavior. Also, $127$ itself is a Mersenne prime.
$\mathbf F_{128}$	$\mathbf F_{128}^\times\cong C_{127}$	$\mathbf F_{128}=\mathbf F_2(\zeta_{127})$	Peak tiny binary-field behavior. Since $127$ is prime, every element of $\mathbf F_{128}\setminus\{0,1\}$ is a primitive $127$th root of unity. The extension degree $7$ is prime, so there are no intermediate fields.

Cyclotomic Fields in Small Cases

2026-04-27T18:49:00-06:00

Cyclotomic Fields in Small Cases

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 4" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Generating Functions as Algebraic Machinery

2025-03-31T17:09:00-06:00

Generating Functions as Algebraic Machinery

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 18" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Shell Pipelines as Data Plumbing

2026-05-17T07:24:00-06:00

Shell Pipelines as Data Plumbing

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 64" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

A Tiny Tour of Galois Theory

2021-02-05T00:27:00-06:00

A Tiny Tour of Galois Theory

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 3" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Fenwick Trees Beyond Sums

2016-11-24T03:02:00-06:00

Fenwick Trees Beyond Sums

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 34" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

SSH Config for Many Hosts

2026-01-16T11:40:00-06:00

SSH Config for Many Hosts

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 75" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Nikola Notes

2013-08-14T20:16:00-05:00

Nikola Notes

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 85" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Dynamic Programming as State Design

2025-10-20T15:00:00-06:00

Dynamic Programming as State Design

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 21" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

awk as a Tiny Data Language

2025-10-17T08:24:00-06:00

awk as a Tiny Data Language

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 68" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Elliptic Curves Over Finite Fields

2022-12-21T13:33:00-06:00

Elliptic Curves Over Finite Fields

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 5" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Tailscale Behind Carrier NAT

2018-05-11T10:29:00-05:00

Tailscale Behind Carrier NAT

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 72" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Vim Text Objects

2023-11-12T19:07:00-06:00

Vim Text Objects

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 53" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Classical Sliding Window Problems

2025-08-01T18:04:00-06:00

Classical Sliding Window Problems

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 92" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Paperless ngx for Documents

2019-10-28T01:34:00-06:00

Paperless ngx for Documents

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 78" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

GDB Breakpoints That Are Actually Useful

2025-06-15T13:02:00-06:00

GDB Breakpoints That Are Actually Useful

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 56" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

The Chinese Remainder Theorem

2025-05-26T22:36:00-06:00

The Chinese Remainder Theorem

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 13" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Classifying Finite Abelian Groups

2024-03-16T04:19:00-06:00

Classifying Finite Abelian Groups

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 9" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Competitive Programming Heuristics

2025-05-16T14:52:00-06:00

Competitive Programming Heuristics

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 90" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Graph Search Heuristics

2024-10-28T11:51:00-06:00

Graph Search Heuristics

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 94" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Sliding Window Patterns

2025-01-29T13:57:00-06:00

Sliding Window Patterns

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 27" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Chinese Vocabulary Experiments

2024-12-01T15:15:00-06:00

Chinese Vocabulary Experiments

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 99" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

DP Heuristics I Want to Remember

2024-09-13T00:33:00-06:00

DP Heuristics I Want to Remember

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 93" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Connected Components Three Ways

2023-04-09T02:40:00-06:00

Connected Components Three Ways

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 32" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Two Pointers on Sorted Arrays

2024-06-05T02:50:00-06:00

Two Pointers on Sorted Arrays

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Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 26" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Prefix Sums as a Habit

2024-05-14T15:40:00-06:00

Prefix Sums as a Habit

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 29" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Coordinate Rings as Geometry

2024-04-16T08:26:00-06:00

Coordinate Rings as Geometry

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 17" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

grep for Recursive Source Searches

2016-02-14T15:51:00-06:00

grep for Recursive Source Searches

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 66" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Scheme Implementations Everywhere

2024-03-01T12:16:00-06:00

Scheme Implementations Everywhere

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 47" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

A Minimal Self Hosted Notes Stack

2011-01-05T02:16:00-06:00

A Minimal Self Hosted Notes Stack

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 77" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

C++ Ranges I Actually Use

2019-09-20T21:06:00-05:00

C++ Ranges I Actually Use

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 41" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Finite Fields by Example

2023-12-28T09:11:00-06:00

Finite Fields by Example

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 1" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Depth First Search Uses

2023-12-25T14:02:00-06:00

Depth First Search Uses

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 31" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Knapsack Without State Compression

2014-09-17T12:34:00-05:00

Knapsack Without State Compression

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 22" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Inclusive Scan and Prefix Computation

2023-11-06T02:22:00-06:00

Inclusive Scan and Prefix Computation

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 43" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

The Multiplicative Group of a Finite Field

2023-06-22T17:06:00-06:00

The Multiplicative Group of a Finite Field

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 8" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

OpenBSD Router Notes

2019-03-19T20:41:00-06:00

OpenBSD Router Notes

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 62" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Vim and CoC Notes

2020-01-01T11:42:00-06:00

Vim and CoC Notes

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 54" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Zip Files From the Command Line

2022-10-08T21:34:00-05:00

Zip Files From the Command Line

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 69" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Reverse Proxies With nginx

2022-07-21T08:06:00-05:00

Reverse Proxies With nginx

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 76" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Quaternion Group Notes

2022-03-25T19:06:00-06:00

Quaternion Group Notes

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 11" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Pelican Tags and Archives

2021-08-26T13:14:00-05:00

Pelican Tags and Archives

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 81" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Sequence DP With Local Constraints

2021-09-07T01:10:00-05:00

Sequence DP With Local Constraints

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 23" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

AtCoder Debugging Notes

2021-07-15T07:07:00-05:00

AtCoder Debugging Notes

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 95" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

find and xargs Together

2021-07-30T20:37:00-05:00

find and xargs Together

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 65" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Quadratic Extensions Without the Fog

2021-06-20T12:49:00-05:00

Quadratic Extensions Without the Fog

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 2" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Clangd Inlay Hints

2021-04-01T22:39:00-06:00

Clangd Inlay Hints

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 55" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

OpenRC Service Management

2021-03-21T20:05:00-06:00

OpenRC Service Management

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 60" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Classical Two Pointer Problems

2017-12-12T03:48:00-06:00

Classical Two Pointer Problems

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 91" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

A Few Useful rc-status Tricks

2020-09-11T01:46:00-05:00

A Few Useful rc-status Tricks

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 61" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Pandoc as the Universal Document Hammer

2017-03-28T02:35:00-06:00

Pandoc as the Universal Document Hammer

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 87" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Self Referential DP in Haskell

2020-06-03T17:21:00-05:00

Self Referential DP in Haskell

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 46" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Bridges and Articulation Points

2016-09-22T08:17:00-05:00

Bridges and Articulation Points

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 33" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Pelican Pagination Notes

2020-05-20T23:36:00-05:00

Pelican Pagination Notes

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 82" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Pelican and MathJax

2020-05-02T13:51:00-05:00

Pelican and MathJax

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 83" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Markdown and LaTeX Portability

2020-01-10T15:56:00-06:00

Markdown and LaTeX Portability

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 88" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

MathJax Versus KaTeX

2019-10-28T05:41:00-06:00

MathJax Versus KaTeX

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 89" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Interval DP in Slow Motion

2019-07-15T06:19:00-05:00

Interval DP in Slow Motion

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 24" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

RAII and Resource Lifetimes

2019-04-01T04:08:00-06:00

RAII and Resource Lifetimes

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 44" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Pygments and Monokai

2012-11-24T20:41:00-06:00

Pygments and Monokai

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 84" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Sparse Tables for Static Queries

2019-01-28T22:52:00-06:00

Sparse Tables for Static Queries

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 36" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Views iota and Index Loops

2017-12-02T21:04:00-06:00

Views iota and Index Loops

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 42" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Binary Search as an Invariant

2018-10-07T03:05:00-05:00

Binary Search as an Invariant

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 28" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Hyperelliptic Curves in One Page

2015-05-28T10:50:00-05:00

Hyperelliptic Curves in One Page

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 6" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Segment Trees and General Monoids

2018-05-07T16:39:00-05:00

Segment Trees and General Monoids

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 35" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Haskell Lists and Laziness

2018-01-24T03:11:00-06:00

Haskell Lists and Laziness

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 45" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Static Sites Behind nginx

2018-01-19T00:08:00-06:00

Static Sites Behind nginx

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 79" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

sed for Small Rewrites

2017-06-17T05:49:00-05:00

sed for Small Rewrites

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 67" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Tries for Prefix Problems

2017-05-22T13:32:00-05:00

Tries for Prefix Problems

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 38" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Learning Japanese Through Reading

2017-05-01T02:35:00-05:00

Learning Japanese Through Reading

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 97" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Heaps and Priority Queues

2016-12-28T02:08:00-06:00

Heaps and Priority Queues

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 39" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Vim Macros for Repetitive Work

2016-11-12T22:53:00-06:00

Vim Macros for Repetitive Work

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 52" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

FreeBSD and NetBSD Notes

2016-10-18T23:16:00-05:00

FreeBSD and NetBSD Notes

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 63" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Pelican Notes

2016-03-03T08:31:00-06:00

Pelican Notes

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 80" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

A Toy SQL Project

2015-11-30T11:12:00-06:00

A Toy SQL Project

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 49" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Linearity of Expectation

2015-07-04T01:42:00-05:00

Linearity of Expectation

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 19" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Lua as an Embedded Language

2015-09-14T18:49:00-05:00

Lua as an Embedded Language

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 48" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Modern C++ for Contest Code

2015-06-01T18:12:00-05:00

Modern C++ for Contest Code

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 96" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Gentoo Package Notes

2015-05-19T22:50:00-05:00

Gentoo Package Notes

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 59" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Linguistics Notes on Writing Systems

2015-04-11T16:56:00-05:00

Linguistics Notes on Writing Systems

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 100" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Rename Many Files Without Drama

2015-04-07T04:03:00-05:00

Rename Many Files Without Drama

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 70" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

WireGuard Notes

2015-03-10T10:56:00-06:00

WireGuard Notes

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 71" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Vim Registers I Keep Forgetting

2014-10-29T02:02:00-06:00

Vim Registers I Keep Forgetting

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 51" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Watchpoints and Recursive Bugs

2014-03-31T16:02:00-06:00

Watchpoints and Recursive Bugs

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 57" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Why Print Debugging Still Wins Sometimes

2014-06-18T09:24:00-05:00

Why Print Debugging Still Wins Sometimes

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 58" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Pagefind for Static Search

2014-05-28T07:35:00-05:00

Pagefind for Static Search

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 86" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Counting Inversions

2014-03-09T18:42:00-06:00

Counting Inversions

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 40" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Japanese Grammar Notes

2013-11-18T04:02:00-06:00

Japanese Grammar Notes

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 98" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

A First Look at Algebraic Geometry

2012-09-29T23:59:00-05:00

A First Look at Algebraic Geometry

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 16" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

The Klein Four Group

2012-01-30T01:43:00-06:00

The Klein Four Group

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 10" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Fermat's Little Theorem, Several Ways

2011-10-15T02:43:00-05:00

Fermat's Little Theorem, Several Ways

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 12" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Polynomial Rings and Quotients

2011-09-23T19:42:00-05:00

Polynomial Rings and Quotients

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 14" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

A Tiny Static Site Generator in C++

2011-02-20T10:11:00-06:00

A Tiny Static Site Generator in C++

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 50" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Ideals as Generalized Divisibility

2010-11-06T18:20:00-06:00

Ideals as Generalized Divisibility

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 15" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Markov Chains on Tiny State Spaces

2010-10-19T19:45:00-05:00

Markov Chains on Tiny State Spaces

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 20" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

tcpdump Filters I Reuse

2010-09-29T14:05:00-05:00

tcpdump Filters I Reuse

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 74" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Breadth First Search Uses

2010-04-12T18:38:00-05:00

Breadth First Search Uses

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 30" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Port Forwarding Through a VPN

2009-11-17T19:13:00-06:00

Port Forwarding Through a VPN

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 73" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Disjoint Sparse Tables

2009-11-13T01:22:00-06:00

Disjoint Sparse Tables

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 37" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

The Circle as a Group

2009-05-29T10:28:00-05:00

The Circle as a Group

This is synthetic Pelican test content for pagination, archives, tags, sorting, feeds, and theme rendering.

Notes

The topic is drawn from subjects that have come up in mathematics, programming, Unix, networking, static-site tooling, or language study.

Code rendering

#include <iostream>

using namespace std;

int main() {
  cout << "test post 7" << endl;
  return 0;
}

Math rendering

$$ \sum_{k=1}^n k = \frac{n(n+1)}{2}. $$

Nothing here is intended to be novel. This is harmless test data for a Pelican build.

Field	Units	Cyclotomic realizations	Why it is beautiful
\(\mathbf F_2\)	\(\mathbf F_2^\times\cong C_1\)	\(\mathbf F_2=\mathbf F_2(\zeta_1)\)	The atom. Its entire multiplicative group is trivial and \(-1=1\). Characteristic \(2\) begins its campaign against ordinary intuition.
\(\mathbf F_3\)	\(\mathbf F_3^\times\cong C_2\)	\(\mathbf F_3=\mathbf F_3(\zeta_2)\)	The smallest field where \(1\neq-1\). The familiar pair \(\{\pm1\}\) finally exists.
\(\mathbf F_4\)	\(\mathbf F_4^\times\cong C_3\)	\(\mathbf F_4=\mathbf F_2(\zeta_3)\)	The first genuine finite-field extension. Its three nonzero elements are exactly the cube roots of unity. Tiny perfection.
\(\mathbf F_5\)	\(\mathbf F_5^\times\cong C_4\)	\(\mathbf F_5=\mathbf F_5(\zeta_4)\)	Already contains a primitive fourth root of unity: \(2^2=-1\). An \(i\)-like element appears inside the prime field itself.
\(\mathbf F_7\)	\(\mathbf F_7^\times\cong C_6\)	\(\mathbf F_7=\mathbf F_7(\zeta_6)\)	Contains primitive \(3\)rd and \(6\)th roots of unity. The factorization \(6=2\cdot3\) gives a surprisingly rich tiny multiplicative world.
\(\mathbf F_8\)	\(\mathbf F_8^\times\cong C_7\)	\(\mathbf F_8=\mathbf F_2(\zeta_7)\)	The first cubic extension. Since \(7\) is prime, every nonzero element except \(1\) is a primitive \(7\)th root of unity.
\(\mathbf F_9\)	\(\mathbf F_9^\times\cong C_8\)	\(\mathbf F_9=\mathbf F_3(\zeta_4)=\mathbf F_3(\zeta_8)\)	The finite-field analogue of adjoining \(i\): \(\mathbf F_9=\mathbf F_3(i)\). Its entire unit group is \(\mu_8\).
\(\mathbf F_{11}\)	\(\mathbf F_{11}^\times\cong C_{10}\)	\(\mathbf F_{11}=\mathbf F_{11}(\zeta_{10})\)	Primitive fifth roots of unity already live in the prime field because \(5\mid10\).
\(\mathbf F_{13}\)	\(\mathbf F_{13}^\times\cong C_{12}\)	\(\mathbf F_{13}=\mathbf F_{13}(\zeta_{12})\)	Contains primitive roots of orders \(3,4,6,\) and \(12\). A very rich little cyclotomic playground.
\(\mathbf F_{16}\)	\(\mathbf F_{16}^\times\cong C_{15}\)	\(\mathbf F_{16}=\mathbf F_2(\zeta_5)=\mathbf F_2(\zeta_{15})\)	The famous counterintuitive step: \(\zeta_3\) gives \(\mathbf F_4\), \(\zeta_7\) gives \(\mathbf F_8\), but the smaller \(\zeta_5\) needs degree \(4\). It also contains \(\mathbf F_4\).
\(\mathbf F_{17}\)	\(\mathbf F_{17}^\times\cong C_{16}\)	\(\mathbf F_{17}=\mathbf F_{17}(\zeta_{16})\)	Pure \(2\)-power cyclotomy: \(\mathbf F_{17}^\times\) has order \(2^4\). Fermat-prime elegance appears here.
\(\mathbf F_{19}\)	\(\mathbf F_{19}^\times\cong C_{18}\)	\(\mathbf F_{19}=\mathbf F_{19}(\zeta_{18})\)	Since \(18=2\cdot3^2\), primitive \(9\)th and \(18\)th roots of unity occur naturally.
\(\mathbf F_{23}\)	\(\mathbf F_{23}^\times\cong C_{22}\)	\(\mathbf F_{23}=\mathbf F_{23}(\zeta_{22})\)	Its multiplicative group contains the large prime-order subgroup \(\mu_{11}\). Clean and almost prime-order.
\(\mathbf F_{25}\)	\(\mathbf F_{25}^\times\cong C_{24}\)	\(\mathbf F_{25}=\mathbf F_5(\zeta_3)=\mathbf F_5(\zeta_{24})\)	A lovely surprise: merely adjoining a primitive cube root of unity to \(\mathbf F_5\) produces the quadratic extension \(\mathbf F_{25}\).
\(\mathbf F_{27}\)	\(\mathbf F_{27}^\times\cong C_{26}\)	\(\mathbf F_{27}=\mathbf F_3(\zeta_{13})=\mathbf F_3(\zeta_{26})\)	A primitive \(13\)th root creates a cubic extension because \(\operatorname{ord}_{13}(3)=3\). There are no intermediate fields.
\(\mathbf F_{29}\)	\(\mathbf F_{29}^\times\cong C_{28}\)	\(\mathbf F_{29}=\mathbf F_{29}(\zeta_{28})\)	Since \(28=2^2\cdot7\), fourth and seventh roots of unity coexist naturally.
\(\mathbf F_{31}\)	\(\mathbf F_{31}^\times\cong C_{30}\)	\(\mathbf F_{31}=\mathbf F_{31}(\zeta_{30})\)	The factorization \(30=2\cdot3\cdot5\) gives elements of orders \(2,3,5,6,10,15,\) and \(30\).
\(\mathbf F_{32}\)	\(\mathbf F_{32}^\times\cong C_{31}\)	\(\mathbf F_{32}=\mathbf F_2(\zeta_{31})\)	An absolute jewel. Since \(31\) is prime, every element of \(\mathbf F_{32}\setminus\{0,1\}\) is a primitive \(31\)st root of unity.
\(\mathbf F_{37}\)	\(\mathbf F_{37}^\times\cong C_{36}\)	\(\mathbf F_{37}=\mathbf F_{37}(\zeta_{36})\)	The unit group has order \(36=2^2\cdot3^2\), giving a rich mixture of \(2\)-power and \(3\)-power cyclotomy.
\(\mathbf F_{41}\)	\(\mathbf F_{41}^\times\cong C_{40}\)	\(\mathbf F_{41}=\mathbf F_{41}(\zeta_{40})\)	Since \(40=2^3\cdot5\), eighth roots and fifth roots of unity coexist inside one prime field.
\(\mathbf F_{43}\)	\(\mathbf F_{43}^\times\cong C_{42}\)	\(\mathbf F_{43}=\mathbf F_{43}(\zeta_{42})\)	\(42=2\cdot3\cdot7\): quadratic, cubic, and seventh-root cyclotomy all coexist.
\(\mathbf F_{47}\)	\(\mathbf F_{47}^\times\cong C_{46}\)	\(\mathbf F_{47}=\mathbf F_{47}(\zeta_{46})\)	Its multiplicative structure is dominated by the large prime-order subgroup \(\mu_{23}\).
\(\mathbf F_{49}\)	\(\mathbf F_{49}^\times\cong C_{48}\)	\(\mathbf F_{49}=\mathbf F_7(\zeta_4)=\mathbf F_7(\zeta_{48})\)	Beautifully simple: adjoining \(i\) to \(\mathbf F_7\) produces \(\mathbf F_{49}\). Its unit group has order \(48=2^4\cdot3\).
\(\mathbf F_{53}\)	\(\mathbf F_{53}^\times\cong C_{52}\)	\(\mathbf F_{53}=\mathbf F_{53}(\zeta_{52})\)	Since \(52=2^2\cdot13\), it is a natural home for primitive \(13\)th roots of unity.
\(\mathbf F_{59}\)	\(\mathbf F_{59}^\times\cong C_{58}\)	\(\mathbf F_{59}=\mathbf F_{59}(\zeta_{58})\)	Its cyclotomic structure is dominated by the large prime \(29\).
\(\mathbf F_{61}\)	\(\mathbf F_{61}^\times\cong C_{60}\)	\(\mathbf F_{61}=\mathbf F_{61}(\zeta_{60})\)	One of the richest prime-field playgrounds in this range: \(60=2^2\cdot3\cdot5\) has many divisors and therefore many root orders.
\(\mathbf F_{64}\)	\(\mathbf F_{64}^\times\cong C_{63}\)	\(\mathbf F_{64}=\mathbf F_2(\zeta_9)=\mathbf F_2(\zeta_{21})=\mathbf F_2(\zeta_{63})\)	A primitive \(9\)th root already generates the sextic extension. It contains both the \(\zeta_3\) world \(\mathbf F_4\) and the \(\zeta_7\) world \(\mathbf F_8\).
\(\mathbf F_{67}\)	\(\mathbf F_{67}^\times\cong C_{66}\)	\(\mathbf F_{67}=\mathbf F_{67}(\zeta_{66})\)	Since \(66=2\cdot3\cdot11\), it simultaneously contains primitive \(3\)rd, \(6\)th, \(11\)th, \(22\)nd, \(33\)rd, and \(66\)th roots.
\(\mathbf F_{71}\)	\(\mathbf F_{71}^\times\cong C_{70}\)	\(\mathbf F_{71}=\mathbf F_{71}(\zeta_{70})\)	\(70=2\cdot5\cdot7\), so fifth- and seventh-root cyclotomy meet naturally.
\(\mathbf F_{73}\)	\(\mathbf F_{73}^\times\cong C_{72}\)	\(\mathbf F_{73}=\mathbf F_{73}(\zeta_{72})\)	\(72=2^3\cdot3^2\) gives unusually rich simultaneous \(2\)-power and \(3\)-power root-of-unity structure.
\(\mathbf F_{79}\)	\(\mathbf F_{79}^\times\cong C_{78}\)	\(\mathbf F_{79}=\mathbf F_{79}(\zeta_{78})\)	Since \(78=2\cdot3\cdot13\), primitive \(13\)th roots coexist with cubic structure.
\(\mathbf F_{81}\)	\(\mathbf F_{81}^\times\cong C_{80}\)	\(\mathbf F_{81}=\mathbf F_3(\zeta_5)=\mathbf F_3(\zeta_{16})=\mathbf F_3(\zeta_{80})\)	A primitive fifth root already generates the quartic extension because \(\operatorname{ord}_5(3)=4\). It also contains \(\mathbf F_9\) as a proper subfield.
\(\mathbf F_{83}\)	\(\mathbf F_{83}^\times\cong C_{82}\)	\(\mathbf F_{83}=\mathbf F_{83}(\zeta_{82})\)	Its unit group has order \(82=2\cdot41\), dominated by the large prime cyclotomic subgroup \(\mu_{41}\).
\(\mathbf F_{89}\)	\(\mathbf F_{89}^\times\cong C_{88}\)	\(\mathbf F_{89}=\mathbf F_{89}(\zeta_{88})\)	\(88=2^3\cdot11\) combines substantial \(2\)-power structure with primitive \(11\)th roots.
\(\mathbf F_{97}\)	\(\mathbf F_{97}^\times\cong C_{96}\)	\(\mathbf F_{97}=\mathbf F_{97}(\zeta_{96})\)	\(96=2^5\cdot3\): a remarkable amount of \(2\)-power cyclotomy occurs inside a prime field of fewer than \(100\) elements.
\(\mathbf F_{101}\)	\(\mathbf F_{101}^\times\cong C_{100}\)	\(\mathbf F_{101}=\mathbf F_{101}(\zeta_{100})\)	The particularly tidy factorization \(100=2^2\cdot5^2\) gives rich fifth-power cyclotomic structure.
\(\mathbf F_{103}\)	\(\mathbf F_{103}^\times\cong C_{102}\)	\(\mathbf F_{103}=\mathbf F_{103}(\zeta_{102})\)	Since \(102=2\cdot3\cdot17\), primitive \(17\)th roots sit alongside cubic and sixth-root structure.
\(\mathbf F_{107}\)	\(\mathbf F_{107}^\times\cong C_{106}\)	\(\mathbf F_{107}=\mathbf F_{107}(\zeta_{106})\)	Its multiplicative group has the simple shape \(C_{2\cdot53}\), with a large prime-order subgroup \(\mu_{53}\).
\(\mathbf F_{109}\)	\(\mathbf F_{109}^\times\cong C_{108}\)	\(\mathbf F_{109}=\mathbf F_{109}(\zeta_{108})\)	\(108=2^2\cdot3^3\), so this field is especially rich in \(3\)-power roots of unity, including primitive \(27\)th roots.
\(\mathbf F_{113}\)	\(\mathbf F_{113}^\times\cong C_{112}\)	\(\mathbf F_{113}=\mathbf F_{113}(\zeta_{112})\)	\(112=2^4\cdot7\) combines deep \(2\)-power cyclotomy with primitive seventh roots.
\(\mathbf F_{121}\)	\(\mathbf F_{121}^\times\cong C_{120}\)	\(\mathbf F_{121}=\mathbf F_{11}(\zeta_3)=\mathbf F_{11}(\zeta_{120})\)	A primitive cube root already generates the quadratic extension of \(\mathbf F_{11}\). Meanwhile \(120=2^3\cdot3\cdot5\) makes its unit group spectacularly rich.
\(\mathbf F_{125}\)	\(\mathbf F_{125}^\times\cong C_{124}\)	\(\mathbf F_{125}=\mathbf F_5(\zeta_{31})=\mathbf F_5(\zeta_{124})\)	A primitive \(31\)st root creates a cubic extension because \(\operatorname{ord}_{31}(5)=3\). Since the degree is prime, there are no intermediate fields.
\(\mathbf F_{127}\)	\(\mathbf F_{127}^\times\cong C_{126}\)	\(\mathbf F_{127}=\mathbf F_{127}(\zeta_{126})\)	\(126=2\cdot3^2\cdot7\) gives a rich mixture of cubic, ninth-root, and seventh-root behavior. Also, \(127\) itself is a Mersenne prime.
\(\mathbf F_{128}\)	\(\mathbf F_{128}^\times\cong C_{127}\)	\(\mathbf F_{128}=\mathbf F_2(\zeta_{127})\)	Peak tiny binary-field behavior. Since \(127\) is prime, every element of \(\mathbf F_{128}\setminus\{0,1\}\) is a primitive \(127\)th root of unity. The extension degree \(7\) is prime, so there are no intermediate fields.