A Formalization of Elementary Linear Algebra: Part I

Fuente: arXiv

Gespeichert in:

Bibliographische Detailangaben
1. Verfasser:	Russinoff, David
Format:	Preprint
Veröffentlicht:	2025
Schlagworte:	Discrete Mathematics
Online-Zugang:	Acceder al recurso
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Ähnliche Einträge

A Formalization of Elementary Linear Algebra: Part II
von: Russinoff, David
Veröffentlicht: (2025)

A Course of Algebra (PART I)
von: Frasser, Carlos E.
Veröffentlicht: (2024)

Relational Algebras for Subset Selection and Optimisation
von: Pratten, David Robert, et al.
Veröffentlicht: (2025)

On the Convergence of Elementary Cellular Automata under Sequential Update Modes
von: Donoso-Leiva, Isabel, et al.
Veröffentlicht: (2025)

Elementary methods for splitting representations of Rook monoids: a gentle introduction to groupoids
von: Duchamp, Gérard Henry Edmond, et al.
Veröffentlicht: (2024)

Revisiting Linear Width: Rethinking the Relationship between Single Ideal and Linear Obstacle
von: Fujita, Takaaki
Veröffentlicht: (2023)

Cycles of Well-Linked Sets II: an Elementary Bound for the Directed Grid Theorem
von: Hatzel, Meike, et al.
Veröffentlicht: (2026)

On Connectedness of Solutions to Integer Linear Systems
von: Shigenobu, Takasugu, et al.
Veröffentlicht: (2024)

Linear Search with Probabilistic Detection and Variable Speeds
von: Coleman, Jared, et al.
Veröffentlicht: (2025)

An Integer Linear Program for Periodic Scheduling in Universities
von: Moradi, Sina
Veröffentlicht: (2024)

Linear Search for an Escaping Target with Unknown Speed
von: Coleman, Jared, et al.
Veröffentlicht: (2024)

Linear Extensions of Rotor-Routing in Directed Graphs: Reachability Problems
von: Auger, David, et al.
Veröffentlicht: (2024)

A Proof of the 2004 Albert-Grossman-Nowakowski-Wolfe Conjecture on Alternating Linear Clobber
von: Chen, Xinyue, et al.
Veröffentlicht: (2025)

Sparse String Graphs and Region Intersection Graphs over Minor-Closed Classes have Linear Expansion
von: Karol, Nikolai, et al.
Veröffentlicht: (2026)

Linear colorings of graphs
von: Hilaire, Claire, et al.
Veröffentlicht: (2025)

A Necessary Condition for Connectedness of Solutions to Integer Linear Systems
von: Shigenobu, Takasugu, et al.
Veröffentlicht: (2025)

Bounds on Linear Turán Number for Trees
von: Adak, Rajat, et al.
Veröffentlicht: (2026)

Linear versus centred chromatic numbers
von: Bose, Prosenjit, et al.
Veröffentlicht: (2022)

Forbidden Patterns in Mixed Linear Layouts
von: Haun, Deborah, et al.
Veröffentlicht: (2024)

An Upper Bound on the Linear Turán Number of $k$-Crowns
von: Adak, Rajat
Veröffentlicht: (2026)

Remote control system of a binary tree of switches -- I. constraints and inequalities
von: Golinelli, Olivier
Veröffentlicht: (2024)

Elementary Cellular Automata as Multiplicative Automata
von: McKinley, Daniel
Veröffentlicht: (2025)

Linear Layouts of Graphs with Priority Queues
von: Di Giacomo, Emilio, et al.
Veröffentlicht: (2025)

Geometry of the Reformulation-Linearization-Technique: Domination of Disjunctions
von: Hof, Hugo A., et al.
Veröffentlicht: (2025)

Combinatorial Algorithm for Tropical Linearly Factorized Programming
von: Nishida, Yuki
Veröffentlicht: (2025)

Linear Programming Hierarchies Collapse under Symmetry
von: Faenza, Yuri, et al.
Veröffentlicht: (2025)

New Solutions to Delsarte's Dual Linear Programs
von: Chailloux, André, et al.
Veröffentlicht: (2024)

Characterizing and Transforming DAGs within the I-LCA Framework
von: Hellmuth, Marc, et al.
Veröffentlicht: (2024)

Characterization of Chordal Circular-arc Graphs: I. Split Graphs
von: Cao, Yixin, et al.
Veröffentlicht: (2024)

Binary constraints on one additional variable can create exponential ascents
von: Cohen, David A., et al.
Veröffentlicht: (2026)

Monk Algebras and Representability
von: Alm, Jeremy F.
Veröffentlicht: (2025)

Linear Exact Repair in MDS Array Codes: A General Lower Bound and Its Attainability
von: Liu, Hai, et al.
Veröffentlicht: (2026)

Fast and Furious: A study on Monotonicity and Speed in Cops-and-Robber Games
von: Fluck, Eva, et al.
Veröffentlicht: (2025)

Algorithmic methods of finite discrete structures. Topological graph drawing (part I)
von: Kurapov, Sergey, et al.
Veröffentlicht: (2024)

A Linear Kernel for Planar Vector Domination
von: Sahili, Mahabba El, et al.
Veröffentlicht: (2023)

Graph Homomorphisms and Universal Algebra
von: Bodirsky, Manuel
Veröffentlicht: (2026)

String Graph Obstacles of High Girth and of Bounded Degree
von: Chudnovsky, Maria, et al.
Veröffentlicht: (2025)

Mixed Unit Interval Bigraphs : A Characterization
von: Das, Ashok Kumar, et al.
Veröffentlicht: (2026)

A note on hardness of promise hypergraph colouring
von: Wrochna, Marcin
Veröffentlicht: (2022)

HyP-ASO: A Hybrid Policy-based Adaptive Search Optimization Framework for Large-Scale Integer Linear Programs
von: Xu, Ning, et al.
Veröffentlicht: (2025)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
VUFIND_SESSION	"d5ec67625d0f721368567eb415586b5e"
language	"de"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790899836.2348 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "d5ec67625d0f721368567eb415586b5e" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; VUFIND_SESSION=d5ec67625d0f721368567eb415586b5e; language=de"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.142"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"33177"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2507_19006/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2507_19006/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790899836.2303
REQUEST_TIME	1790899836

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler