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Eine Ergänzung für Quantum Algebra - Problemstellung

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Problemstellung

Bei meiner Beschäftigung mit der Quantenphysik studiere ich auch das Buch "Student Friendly Quantum Field Theory" von Robert D. Klauber. Hierbei ergab sich die Frage bzw. die Idee, ob nicht einige der darin aufgeführten Rechnungen durch Mathematica erleichtert werden könnten.

Als Mathematica Paket zur Unterstützung der Rechungen schien mir Quantum Algebra geeignet - zumindest ansatzweise. Aber einige der mathematischen Symbole, die im Buch Verwendung fanden, wurden von Quantum Algebra nicht unterstützt. Quantum Algebra mußte also erweitert werden. Als Ergebnis ergab sich eine erweiterte Anwendung. Diese Erweiterung und was sie leistet soll im folgenden vorgestellt werden.

Im Wesentlichen handelt es sich dabei um Summations-, Integrations- und Ableitungssymbole, die schon im Basispaket vorhandene Operatornotation und die Unterstützung von Matrizen. Alle werden durch entsprechende Regeln zur Vereinfachung und Umformung unterstützt - so, wie man es eigentlich auch manuell machen würde.

Details
Kategorie: Quantum Algebra
Zugriffe: 14880

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  • SELECT `id`,`home`,`template`,`s`.`params`,`inheritable`,`parent` FROM `jos_template_styles` AS `s` LEFT JOIN `jos_extensions` AS `e` ON `e`.`element` = `s`.`template` AND `e`.`type` = 'template' AND `e`.`client_id` = `s`.`client_id` WHERE `s`.`client_id` = 0 AND `e`.`enabled` = 11.79ms864B/administrator/components/com_templates/src/Model/StyleModel.php:775Copy
  • SELECT `id`,`name`,`rules`,`parent_id` FROM `jos_assets` WHERE `name` IN (:preparedArray1,:preparedArray2,:preparedArray3,:preparedArray4,:preparedArray5,:preparedArray6,:preparedArray7,:preparedArray8,:preparedArray9,:preparedArray10,:preparedArray11,:preparedArray12,:preparedArray13,:preparedArray14,:preparedArray15,:preparedArray16,:preparedArray17,:preparedArray18,:preparedArray19,:preparedArray20,:preparedArray21,:preparedArray22,:preparedArray23,:preparedArray24,:preparedArray25,:preparedArray26,:preparedArray27,:preparedArray28,:preparedArray29,:preparedArray30,:preparedArray31,:preparedArray32,:preparedArray33,:preparedArray34,:preparedArray35,:preparedArray36,:preparedArray37,:preparedArray38,:preparedArray39,:preparedArray40,:preparedArray41,:preparedArray42,:preparedArray43,:preparedArray44,:preparedArray45,:preparedArray46)2.78ms8.44KBParams/libraries/src/Access/Access.php:357Copy
  • SELECT `id`,`name`,`rules`,`parent_id` FROM `jos_assets` WHERE `name` LIKE :asset OR `name` = :extension OR `parent_id` = 01.87ms3.23KBParams/libraries/src/Access/Access.php:301Copy
  • SHOW FULL COLUMNS FROM `jos_content`6.19ms1.77KB/libraries/vendor/joomla/database/src/Mysqli/MysqliDriver.php:587Copy
  • UPDATE `jos_content` SET `hits` = (`hits` + 1) WHERE `id` = '49'6.92ms48B/libraries/src/Table/Table.php:1348Copy
  • SELECT `a`.`id`,`a`.`asset_id`,`a`.`title`,`a`.`alias`,`a`.`introtext`,`a`.`fulltext`,`a`.`state`,`a`.`catid`,`a`.`created`,`a`.`created_by`,`a`.`created_by_alias`,`a`.`modified`,`a`.`modified_by`,`a`.`checked_out`,`a`.`checked_out_time`,`a`.`publish_up`,`a`.`publish_down`,`a`.`images`,`a`.`urls`,`a`.`attribs`,`a`.`version`,`a`.`ordering`,`a`.`metakey`,`a`.`metadesc`,`a`.`access`,`a`.`hits`,`a`.`metadata`,`a`.`featured`,`a`.`language`,`fp`.`featured_up`,`fp`.`featured_down`,`c`.`title` AS `category_title`,`c`.`alias` AS `category_alias`,`c`.`access` AS `category_access`,`c`.`language` AS `category_language`,`fp`.`ordering`,`u`.`name` AS `author`,`parent`.`title` AS `parent_title`,`parent`.`id` AS `parent_id`,`parent`.`path` AS `parent_route`,`parent`.`alias` AS `parent_alias`,`parent`.`language` AS `parent_language`,ROUND(`v`.`rating_sum` / `v`.`rating_count`, 1) AS `rating`,`v`.`rating_count` AS `rating_count` FROM `jos_content` AS `a` INNER JOIN `jos_categories` AS `c` ON `c`.`id` = `a`.`catid` LEFT JOIN `jos_content_frontpage` AS `fp` ON `fp`.`content_id` = `a`.`id` LEFT JOIN `jos_users` AS `u` ON `u`.`id` = `a`.`created_by` LEFT JOIN `jos_categories` AS `parent` ON `parent`.`id` = `c`.`parent_id` LEFT JOIN `jos_content_rating` AS `v` ON `a`.`id` = `v`.`content_id` WHERE ( (`a`.`id` = :pk AND `c`.`published` > 0 AND `a`.`language` IN (:preparedArray1,:preparedArray2)) AND (`a`.`publish_up` IS NULL OR `a`.`publish_up` <= :publishUp)) AND (`a`.`publish_down` IS NULL OR `a`.`publish_down` >= :publishDown) AND `a`.`state` IN (:preparedArray3,:preparedArray4)2.36ms22.19KBParams/components/com_content/src/Model/ArticleModel.php:215Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `jos_categories` AS `s` INNER JOIN `jos_categories` AS `c` ON (`s`.`lft` < `c`.`lft` AND `c`.`lft` < `s`.`rgt` AND `c`.`language` IN (:preparedArray3,:preparedArray4)) OR (`c`.`lft` <= `s`.`lft` AND `s`.`rgt` <= `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1,:preparedArray2) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`1.98ms4KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT `m`.`tag_id`,`t`.* FROM `jos_contentitem_tag_map` AS `m` INNER JOIN `jos_tags` AS `t` ON `m`.`tag_id` = `t`.`id` WHERE `m`.`type_alias` = :contentType AND `m`.`content_item_id` = :id AND `t`.`published` = 1 AND `t`.`access` IN (:preparedArray1,:preparedArray2)1.59ms3.97KBParams/libraries/src/Helper/TagsHelper.php:388Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `jos_categories` AS `s` INNER JOIN `jos_categories` AS `c` ON (`s`.`lft` < `c`.`lft` AND `c`.`lft` < `s`.`rgt` AND `c`.`language` IN (:preparedArray3,:preparedArray4)) OR (`c`.`lft` <= `s`.`lft` AND `s`.`rgt` <= `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1,:preparedArray2) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`2.19ms4KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT DISTINCT a.id, a.title, a.name, a.checked_out, a.checked_out_time, a.note, a.state, a.access, a.created_time, a.created_user_id, a.ordering, a.language, a.fieldparams, a.params, a.type, a.default_value, a.context, a.group_id, a.label, a.description, a.required, a.only_use_in_subform,l.title AS language_title, l.image AS language_image,uc.name AS editor,ag.title AS access_level,ua.name AS author_name,g.title AS group_title, g.access as group_access, g.state AS group_state, g.note as group_note FROM jos_fields AS a LEFT JOIN `jos_languages` AS l ON l.lang_code = a.language LEFT JOIN jos_users AS uc ON uc.id=a.checked_out LEFT JOIN jos_viewlevels AS ag ON ag.id = a.access LEFT JOIN jos_users AS ua ON ua.id = a.created_user_id LEFT JOIN jos_fields_groups AS g ON g.id = a.group_id LEFT JOIN `jos_fields_categories` AS fc ON fc.field_id = a.id WHERE ( (`a`.`context` = :context AND (`fc`.`category_id` IS NULL OR `fc`.`category_id` IN (:preparedArray1,:preparedArray2,:preparedArray3,:preparedArray4)) AND `a`.`access` IN (:preparedArray5,:preparedArray6)) AND (`a`.`group_id` = 0 OR `g`.`access` IN (:preparedArray7,:preparedArray8)) AND `a`.`state` = :state) AND (`a`.`group_id` = 0 OR `g`.`state` = :gstate) AND `a`.`only_use_in_subform` = :only_use_in_subform AND `a`.`language` IN (:preparedArray9,:preparedArray10) ORDER BY a.ordering ASC5.45ms6.12KBParams/libraries/src/MVC/Model/BaseDatabaseModel.php:164Copy
  • SELECT m.id, m.title, m.module, m.position, m.content, m.showtitle, m.params,am.params AS extra, 0 AS menuid, m.publish_up, m.publish_down FROM jos_modules AS m LEFT JOIN jos_extensions AS e ON e.element = m.module AND e.client_id = m.client_id LEFT JOIN jos_advancedmodules as am ON am.module_id = m.id WHERE m.published = 1 AND e.enabled = 1 AND m.client_id = 0 ORDER BY m.position, m.ordering4.54ms178.17KB/plugins/system/advancedmodules/src/Helper.php:199Copy
  • SELECT m.condition_id,m.item_id FROM jos_conditions_map as m LEFT JOIN jos_conditions as c ON c.id = m.condition_id WHERE `m`.`extension` = 'com_advancedmodules' AND `c`.`published` = 11.66ms1.19KB/administrator/components/com_conditions/src/Model/ItemModel.php:831Copy
  • SHOW FULL COLUMNS FROM `jos_conditions`2.35ms1.45KB/libraries/vendor/joomla/database/src/Mysqli/MysqliDriver.php:587Copy
  • SELECT * FROM `jos_conditions` WHERE `id` = '16'1.21ms1.44KB/libraries/src/Table/Table.php:780Copy
  • SELECT * FROM jos_conditions_groups as g WHERE g.condition_id = 161.19ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:1049Copy
  • SELECT * FROM jos_conditions_rules as r WHERE r.group_id = 81.24ms832B/administrator/components/com_conditions/src/Model/GroupModel.php:108Copy
  • SELECT m.extension,m.item_id,m.table,m.name_column FROM jos_conditions_map as m WHERE m.condition_id = 16 ORDER BY m.extension,m.item_id1.13ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:917Copy
  • SELECT `id`,`title` AS `value` FROM `jos_modules`1.11ms2.06KB/administrator/components/com_conditions/src/Helper/Helper.php:184Copy
  • SHOW FULL COLUMNS FROM `jos_modules`2.16ms1.58KB/libraries/vendor/joomla/database/src/Mysqli/MysqliDriver.php:587Copy
  • SELECT `id`,`published` AS `value` FROM `jos_modules`1.15ms2.06KB/administrator/components/com_conditions/src/Helper/Helper.php:184Copy
  • SELECT * FROM `jos_conditions` WHERE `id` = '17'2.05ms1.44KB/libraries/src/Table/Table.php:780Copy
  • SELECT * FROM jos_conditions_groups as g WHERE g.condition_id = 171.22ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:1049Copy
  • SELECT * FROM jos_conditions_rules as r WHERE r.group_id = 91.24ms848B/administrator/components/com_conditions/src/Model/GroupModel.php:108Copy
  • SELECT m.extension,m.item_id,m.table,m.name_column FROM jos_conditions_map as m WHERE m.condition_id = 17 ORDER BY m.extension,m.item_id1.32ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:917Copy
  • SELECT * FROM `jos_conditions` WHERE `id` = '29'1.26ms1.44KB/libraries/src/Table/Table.php:780Copy
  • SELECT * FROM jos_conditions_groups as g WHERE g.condition_id = 291.29ms3.19KB/administrator/components/com_conditions/src/Model/ItemModel.php:1049Copy
  • SELECT * FROM jos_conditions_rules as r WHERE r.group_id = 181.19ms832B/administrator/components/com_conditions/src/Model/GroupModel.php:108Copy
  • SELECT m.extension,m.item_id,m.table,m.name_column FROM jos_conditions_map as m WHERE m.condition_id = 29 ORDER BY m.extension,m.item_id1.31ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:917Copy
  • SELECT * FROM `jos_conditions` WHERE `id` = '28'1.21ms1.44KB/libraries/src/Table/Table.php:780Copy
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  • SELECT m.extension,m.item_id,m.table,m.name_column FROM jos_conditions_map as m WHERE m.condition_id = 28 ORDER BY m.extension,m.item_id1.29ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:917Copy
  • SELECT * FROM `jos_conditions` WHERE `id` = '35'1.24ms1.44KB/libraries/src/Table/Table.php:780Copy
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  • SELECT * FROM jos_conditions_rules as r WHERE r.group_id = 301.2ms832B/administrator/components/com_conditions/src/Model/GroupModel.php:108Copy
  • SELECT m.extension,m.item_id,m.table,m.name_column FROM jos_conditions_map as m WHERE m.condition_id = 35 ORDER BY m.extension,m.item_id1.23ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:917Copy
  • SELECT * FROM `jos_conditions` WHERE `id` = '3'1.2ms1.44KB/libraries/src/Table/Table.php:780Copy
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  • SELECT m.extension,m.item_id,m.table,m.name_column FROM jos_conditions_map as m WHERE m.condition_id = 3 ORDER BY m.extension,m.item_id1.27ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:917Copy
  • SELECT * FROM `jos_conditions` WHERE `id` = '23'1.13ms1.44KB/libraries/src/Table/Table.php:780Copy
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  • SELECT * FROM jos_conditions_rules as r WHERE r.group_id = 141.7ms832B/administrator/components/com_conditions/src/Model/GroupModel.php:108Copy
  • SELECT m.extension,m.item_id,m.table,m.name_column FROM jos_conditions_map as m WHERE m.condition_id = 23 ORDER BY m.extension,m.item_id1.4ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:917Copy
  • SELECT * FROM `jos_conditions` WHERE `id` = '22'1.23ms1.44KB/libraries/src/Table/Table.php:780Copy
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  • SELECT * FROM jos_conditions_rules as r WHERE r.group_id = 131.07ms832B/administrator/components/com_conditions/src/Model/GroupModel.php:108Copy
  • SELECT m.extension,m.item_id,m.table,m.name_column FROM jos_conditions_map as m WHERE m.condition_id = 22 ORDER BY m.extension,m.item_id1.16ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:917Copy
  • SELECT * FROM `jos_conditions` WHERE `id` = '25'1.06ms1.44KB/libraries/src/Table/Table.php:780Copy
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  • SELECT * FROM jos_conditions_rules as r WHERE r.group_id = 281.34ms832B/administrator/components/com_conditions/src/Model/GroupModel.php:108Copy
  • SELECT m.extension,m.item_id,m.table,m.name_column FROM jos_conditions_map as m WHERE m.condition_id = 25 ORDER BY m.extension,m.item_id1.15ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:917Copy
  • SELECT * FROM `jos_conditions` WHERE `id` = '27'1.13ms1.44KB/libraries/src/Table/Table.php:780Copy
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  • SELECT * FROM jos_conditions_groups as g WHERE g.condition_id = 181.08ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:1049Copy
  • SELECT * FROM jos_conditions_rules as r WHERE r.group_id = 101.09ms848B/administrator/components/com_conditions/src/Model/GroupModel.php:108Copy
  • SELECT m.extension,m.item_id,m.table,m.name_column FROM jos_conditions_map as m WHERE m.condition_id = 18 ORDER BY m.extension,m.item_id1.1ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:917Copy
  • SELECT * FROM `jos_conditions` WHERE `id` = '2'1.12ms1.44KB/libraries/src/Table/Table.php:780Copy
  • SELECT * FROM jos_conditions_groups as g WHERE g.condition_id = 21.24ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:1049Copy
  • SELECT * FROM jos_conditions_rules as r WHERE r.group_id = 11.24ms848B/administrator/components/com_conditions/src/Model/GroupModel.php:108Copy
  • SELECT m.extension,m.item_id,m.table,m.name_column FROM jos_conditions_map as m WHERE m.condition_id = 2 ORDER BY m.extension,m.item_id1.22ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:917Copy
  • SELECT * FROM `jos_conditions` WHERE `id` = '20'1.1ms1.44KB/libraries/src/Table/Table.php:780Copy
  • SELECT * FROM jos_conditions_groups as g WHERE g.condition_id = 201.1ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:1049Copy
  • SELECT * FROM jos_conditions_rules as r WHERE r.group_id = 121.3ms832B/administrator/components/com_conditions/src/Model/GroupModel.php:108Copy
  • SELECT m.extension,m.item_id,m.table,m.name_column FROM jos_conditions_map as m WHERE m.condition_id = 20 ORDER BY m.extension,m.item_id1.13ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:917Copy
  • SELECT * FROM `jos_conditions` WHERE `id` = '11'1.2ms1.44KB/libraries/src/Table/Table.php:780Copy
  • SELECT * FROM jos_conditions_groups as g WHERE g.condition_id = 111.1ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:1049Copy
  • SELECT * FROM jos_conditions_rules as r WHERE r.group_id = 31.21ms832B/administrator/components/com_conditions/src/Model/GroupModel.php:108Copy
  • SELECT m.extension,m.item_id,m.table,m.name_column FROM jos_conditions_map as m WHERE m.condition_id = 11 ORDER BY m.extension,m.item_id1.18ms704B/administrator/components/com_conditions/src/Model/ItemModel.php:917Copy
  • SELECT `a`.`id`,`a`.`title`,`a`.`catid`,`a`.`language`, CASE WHEN CHAR_LENGTH(`a`.`alias`) != 0 THEN CONCAT_WS(':', `a`.`id`, `a`.`alias`) ELSE a.id END AS `slug`, CASE WHEN CHAR_LENGTH(`cc`.`alias`) != 0 THEN CONCAT_WS(':', `cc`.`id`, `cc`.`alias`) ELSE cc.id END AS `catslug` FROM `jos_content` AS `a` LEFT JOIN `jos_categories` AS `cc` ON `cc`.`id` = `a`.`catid` WHERE `a`.`catid` = :catid AND `a`.`state` = :state AND `a`.`access` IN (:preparedArray1,:preparedArray2) AND (`publish_up` IS NULL OR `publish_up` <= :nowDate1) AND (`publish_down` IS NULL OR `publish_down` >= :nowDate2) AND `a`.`language` IN (:preparedArray3,:preparedArray4) ORDER BY `a`.`ordering`2.02ms1.78KBParams/plugins/content/pagenavigation/src/Extension/PageNavigation.php:188Copy
  • SELECT `language`,`id` FROM `jos_menu` WHERE `home` = '1' AND `published` = 1 AND `client_id` = 01.37ms624B/libraries/src/Language/Multilanguage.php:123Copy
  • SELECT `c2`.`language`,CONCAT_WS(':', `c2`.`id`, `c2`.`alias`) AS `id`,CONCAT_WS(':', `ca`.`id`, `ca`.`alias`) AS `catid` FROM `jos_content` AS `c` INNER JOIN `jos_associations` AS `a` ON `a`.`id` = `c`.`id` AND `a`.`context` = :context INNER JOIN `jos_associations` AS `a2` ON `a`.`key` = `a2`.`key` INNER JOIN `jos_content` AS `c2` ON `a2`.`id` = `c2`.`id` INNER JOIN `jos_categories` AS `ca` ON `c2`.`catid` = `ca`.`id` AND `ca`.`extension` = :extension2 WHERE `c`.`id` = :id AND c2.access IN (1,5) AND c2.language != 'de-DE' AND (c2.publish_up IS NULL OR c2.publish_up <= '2025-04-03 17:52:01') AND (c2.publish_down IS NULL OR c2.publish_down >= '2025-04-03 17:52:01') AND c2.state = 11.64ms1.48KBParams/libraries/src/Language/Associations.php:145Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `jos_categories` AS `s` INNER JOIN `jos_categories` AS `c` ON (`s`.`lft` < `c`.`lft` AND `c`.`lft` < `s`.`rgt` AND `c`.`language` IN (:preparedArray3,:preparedArray4)) OR (`c`.`lft` <= `s`.`lft` AND `s`.`rgt` <= `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1,:preparedArray2) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`1.81ms4KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT `c2`.`language`,`c2`.`id` FROM `jos_menu` AS `c` INNER JOIN `jos_associations` AS `a` ON `a`.`id` = `c`.`id` AND `a`.`context` = :context INNER JOIN `jos_associations` AS `a2` ON `a`.`key` = `a2`.`key` INNER JOIN `jos_menu` AS `c2` ON `a2`.`id` = `c2`.`id` WHERE `c`.`id` = :id1.49ms1.41KBParams/libraries/src/Language/Associations.php:145Copy
  • SELECT `a`.`id`,`a`.`title`,`a`.`alias`,`a`.`introtext`,`a`.`fulltext`,`a`.`checked_out`,`a`.`checked_out_time`,`a`.`catid`,`a`.`created`,`a`.`created_by`,`a`.`created_by_alias`,`a`.`modified`,`a`.`modified_by`,CASE WHEN `a`.`publish_up` IS NULL THEN `a`.`created` ELSE `a`.`publish_up` END AS `publish_up`,`a`.`publish_down`,`a`.`images`,`a`.`urls`,`a`.`attribs`,`a`.`metadata`,`a`.`metakey`,`a`.`metadesc`,`a`.`access`,`a`.`hits`,`a`.`featured`,`a`.`language`,LENGTH(`a`.`fulltext`) AS `readmore`,`a`.`ordering`,`fp`.`featured_up`,`fp`.`featured_down`,CASE WHEN `c`.`published` = 2 AND `a`.`state` > 0 THEN 2 WHEN `c`.`published` != 1 THEN 0 ELSE `a`.`state` END AS `state`,`c`.`title` AS `category_title`,`c`.`path` AS `category_route`,`c`.`access` AS `category_access`,`c`.`alias` AS `category_alias`,`c`.`language` AS `category_language`,`c`.`published`,`c`.`published` AS `parents_published`,`c`.`lft`,CASE WHEN `a`.`created_by_alias` > ' ' THEN `a`.`created_by_alias` ELSE `ua`.`name` END AS `author`,`ua`.`email` AS `author_email`,`uam`.`name` AS `modified_by_name`,`parent`.`title` AS `parent_title`,`parent`.`id` AS `parent_id`,`parent`.`path` AS `parent_route`,`parent`.`alias` AS `parent_alias`,`parent`.`language` AS `parent_language`,COALESCE(NULLIF(ROUND(`v`.`rating_sum` / `v`.`rating_count`, 1), 0), 0) AS `rating`,COALESCE(NULLIF(`v`.`rating_count`, 0), 0) AS `rating_count` FROM `jos_content` AS `a` LEFT JOIN `jos_categories` AS `c` ON `c`.`id` = `a`.`catid` LEFT JOIN `jos_users` AS `ua` ON `ua`.`id` = `a`.`created_by` LEFT JOIN `jos_users` AS `uam` ON `uam`.`id` = `a`.`modified_by` LEFT JOIN `jos_categories` AS `parent` ON `parent`.`id` = `c`.`parent_id` LEFT JOIN `jos_content_frontpage` AS `fp` ON `fp`.`content_id` = `a`.`id` LEFT JOIN `jos_content_rating` AS `v` ON `a`.`id` = `v`.`content_id` WHERE `a`.`access` IN (:preparedArray1,:preparedArray2) AND `c`.`access` IN (:preparedArray3,:preparedArray4) AND `c`.`published` = 1 AND `a`.`state` = :condition AND (`a`.`publish_up` IS NULL OR `a`.`publish_up` <= :publishUp) AND (`a`.`publish_down` IS NULL OR `a`.`publish_down` >= :publishDown) AND `a`.`language` IN (:preparedArray5,:preparedArray6) ORDER BY a.hits DESC LIMIT 53.46ms55.08KBParams/libraries/src/MVC/Model/BaseDatabaseModel.php:164Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `jos_categories` AS `s` INNER JOIN `jos_categories` AS `c` ON (`s`.`lft` < `c`.`lft` AND `c`.`lft` < `s`.`rgt` AND `c`.`language` IN (:preparedArray3,:preparedArray4)) OR (`c`.`lft` <= `s`.`lft` AND `s`.`rgt` <= `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1,:preparedArray2) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`1.85ms4KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `jos_categories` AS `s` INNER JOIN `jos_categories` AS `c` ON (`s`.`lft` < `c`.`lft` AND `c`.`lft` < `s`.`rgt` AND `c`.`language` IN (:preparedArray3,:preparedArray4)) OR (`c`.`lft` <= `s`.`lft` AND `s`.`rgt` <= `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1,:preparedArray2) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`1.72ms4KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `jos_categories` AS `s` INNER JOIN `jos_categories` AS `c` ON (`s`.`lft` < `c`.`lft` AND `c`.`lft` < `s`.`rgt` AND `c`.`language` IN (:preparedArray3,:preparedArray4)) OR (`c`.`lft` <= `s`.`lft` AND `s`.`rgt` <= `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1,:preparedArray2) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`3.36ms11.98KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `jos_categories` AS `s` INNER JOIN `jos_categories` AS `c` ON (`s`.`lft` < `c`.`lft` AND `c`.`lft` < `s`.`rgt` AND `c`.`language` IN (:preparedArray3,:preparedArray4)) OR (`c`.`lft` <= `s`.`lft` AND `s`.`rgt` <= `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1,:preparedArray2) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`1.61ms4.02KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT `name`,`element` FROM `jos_extensions` WHERE `type` = 'plugin' AND `folder` = 'finder' AND `enabled` = 11.19ms656B/administrator/components/com_finder/src/Helper/LanguageHelper.php:135Copy
  • SELECT `title` FROM `jos_finder_taxonomy` WHERE `parent_id` = 1 AND `state` = 1 AND `access` IN (1,5)3.78ms584B/administrator/components/com_finder/src/Indexer/Taxonomy.php:325Copy
  • SELECT a.params FROM jos_advancedmodules AS a WHERE a.module_id = 106995μs520B/plugins/system/advancedmodules/src/Helper.php:159Copy
  • SELECT a.params FROM jos_advancedmodules AS a WHERE a.module_id = 951.03ms520B/plugins/system/advancedmodules/src/Helper.php:159Copy
  • SELECT * FROM `jos_schemaorg` WHERE `itemId` = :itemId AND `context` = :context1.09ms1.55KBParams/plugins/system/schemaorg/src/Extension/Schemaorg.php:403Copy
  • SELECT `a`.`id`,`a`.`asset_id`,`a`.`title`,`a`.`alias`,`a`.`introtext`,`a`.`fulltext`,`a`.`state`,`a`.`catid`,`a`.`created`,`a`.`created_by`,`a`.`created_by_alias`,`a`.`modified`,`a`.`modified_by`,`a`.`checked_out`,`a`.`checked_out_time`,`a`.`publish_up`,`a`.`publish_down`,`a`.`images`,`a`.`urls`,`a`.`attribs`,`a`.`version`,`a`.`ordering`,`a`.`metakey`,`a`.`metadesc`,`a`.`access`,`a`.`hits`,`a`.`metadata`,`a`.`featured`,`a`.`language`,`fp`.`featured_up`,`fp`.`featured_down`,`c`.`title` AS `category_title`,`c`.`alias` AS `category_alias`,`c`.`access` AS `category_access`,`c`.`language` AS `category_language`,`fp`.`ordering`,`u`.`name` AS `author`,`parent`.`title` AS `parent_title`,`parent`.`id` AS `parent_id`,`parent`.`path` AS `parent_route`,`parent`.`alias` AS `parent_alias`,`parent`.`language` AS `parent_language`,ROUND(`v`.`rating_sum` / `v`.`rating_count`, 1) AS `rating`,`v`.`rating_count` AS `rating_count` FROM `jos_content` AS `a` INNER JOIN `jos_categories` AS `c` ON `c`.`id` = `a`.`catid` LEFT JOIN `jos_content_frontpage` AS `fp` ON `fp`.`content_id` = `a`.`id` LEFT JOIN `jos_users` AS `u` ON `u`.`id` = `a`.`created_by` LEFT JOIN `jos_categories` AS `parent` ON `parent`.`id` = `c`.`parent_id` LEFT JOIN `jos_content_rating` AS `v` ON `a`.`id` = `v`.`content_id` WHERE ( (`a`.`id` = :pk AND `c`.`published` > 0 AND `a`.`language` IN (:preparedArray1,:preparedArray2)) AND (`a`.`publish_up` IS NULL OR `a`.`publish_up` <= :publishUp)) AND (`a`.`publish_down` IS NULL OR `a`.`publish_down` >= :publishDown) AND `a`.`state` IN (:preparedArray3,:preparedArray4)3.92ms22.23KBParams/components/com_content/src/Model/ArticleModel.php:215Copy
  • SELECT `a`.`id`,`a`.`asset_id`,`a`.`title`,`a`.`alias`,`a`.`introtext`,`a`.`fulltext`,`a`.`state`,`a`.`catid`,`a`.`created`,`a`.`created_by`,`a`.`created_by_alias`,`a`.`modified`,`a`.`modified_by`,`a`.`checked_out`,`a`.`checked_out_time`,`a`.`publish_up`,`a`.`publish_down`,`a`.`images`,`a`.`urls`,`a`.`attribs`,`a`.`version`,`a`.`ordering`,`a`.`metakey`,`a`.`metadesc`,`a`.`access`,`a`.`hits`,`a`.`metadata`,`a`.`featured`,`a`.`language`,`fp`.`featured_up`,`fp`.`featured_down`,`c`.`title` AS `category_title`,`c`.`alias` AS `category_alias`,`c`.`access` AS `category_access`,`c`.`language` AS `category_language`,`fp`.`ordering`,`u`.`name` AS `author`,`parent`.`title` AS `parent_title`,`parent`.`id` AS `parent_id`,`parent`.`path` AS `parent_route`,`parent`.`alias` AS `parent_alias`,`parent`.`language` AS `parent_language`,ROUND(`v`.`rating_sum` / `v`.`rating_count`, 1) AS `rating`,`v`.`rating_count` AS `rating_count` FROM `jos_content` AS `a` INNER JOIN `jos_categories` AS `c` ON `c`.`id` = `a`.`catid` LEFT JOIN `jos_content_frontpage` AS `fp` ON `fp`.`content_id` = `a`.`id` LEFT JOIN `jos_users` AS `u` ON `u`.`id` = `a`.`created_by` LEFT JOIN `jos_categories` AS `parent` ON `parent`.`id` = `c`.`parent_id` LEFT JOIN `jos_content_rating` AS `v` ON `a`.`id` = `v`.`content_id` WHERE ( (`a`.`id` = :pk AND `c`.`published` > 0 AND `a`.`language` IN (:preparedArray1,:preparedArray2)) AND (`a`.`publish_up` IS NULL OR `a`.`publish_up` <= :publishUp)) AND (`a`.`publish_down` IS NULL OR `a`.`publish_down` >= :publishDown) AND `a`.`state` IN (:preparedArray3,:preparedArray4)1.51ms22.23KBParams/components/com_content/src/Model/ArticleModel.php:215Copy
  • SELECT SUM(CASE WHEN `a`.`next_execution` <= :now THEN 1 ELSE 0 END) AS due_count,SUM(CASE WHEN `a`.`locked` IS NULL THEN 0 ELSE 1 END) AS locked_count FROM `jos_scheduler_tasks` AS `a` WHERE `a`.`state` = 11.05ms1.37KBParams/administrator/components/com_scheduler/src/Model/TasksModel.php:465Copy
  • SELECT `session_id` FROM `jos_session` WHERE `session_id` = ?959μs1KBParams/libraries/vendor/joomla/session/src/Handler/DatabaseHandler.php:277Copy
  • UPDATE `jos_session` SET `data` = ? , `time` = ? WHERE `session_id` = ?3.2ms592BParams/libraries/vendor/joomla/session/src/Handler/DatabaseHandler.php:301Copy