Message d'erreur

  • Deprecated function: Return type of DatabaseStatementBase::execute($args = [], $options = []) should either be compatible with PDOStatement::execute(?array $params = null): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2244 of /home/laurentp/www/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::current() should either be compatible with Iterator::current(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::next() should either be compatible with Iterator::next(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::key() should either be compatible with Iterator::key(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::valid() should either be compatible with Iterator::valid(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
  • Deprecated function: Return type of DatabaseStatementEmpty::rewind() should either be compatible with Iterator::rewind(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in require_once() (line 2346 of /home/laurentp/www/includes/database/database.inc).
  • Deprecated function: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in drupal_random_bytes() (line 2268 of /home/laurentp/www/includes/bootstrap.inc).
  • Deprecated function: Optional parameter $type declared before required parameter $key is implicitly treated as a required parameter in include_once() (line 1389 of /home/laurentp/www/includes/bootstrap.inc).
  • Deprecated function: Return type of DateObject::__wakeup() should either be compatible with DateTime::__wakeup(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 143 of /home/laurentp/www/sites/all/modules/date/date_api/date_api.module).
  • Deprecated function: Return type of DateObject::format($format, $force = false) should either be compatible with DateTime::format(string $format): string, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 143 of /home/laurentp/www/sites/all/modules/date/date_api/date_api.module).
  • Deprecated function: Return type of DateObject::setTimezone($tz, $force = false) should either be compatible with DateTime::setTimezone(DateTimeZone $timezone): DateTime, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in include_once() (line 143 of /home/laurentp/www/sites/all/modules/date/date_api/date_api.module).
  • Deprecated function: Optional parameter $input declared before required parameter $form_state is implicitly treated as a required parameter in include_once() (line 1389 of /home/laurentp/www/includes/bootstrap.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : rtrim(): Passing null to parameter #1 ($string) of type string is deprecated dans url() (ligne 2349 dans /home/laurentp/www/includes/common.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property PDOException::$query_string is deprecated dans DatabaseConnection->query() (ligne 770 dans /home/laurentp/www/includes/database/database.inc).
  • Deprecated function : Creation of dynamic property PDOException::$args is deprecated dans DatabaseConnection->query() (ligne 772 dans /home/laurentp/www/includes/database/database.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : strpos(): Passing null to parameter #1 ($haystack) of type string is deprecated dans url_is_external() (ligne 2393 dans /home/laurentp/www/includes/common.inc).
  • Deprecated function : str_replace(): Passing null to parameter #3 ($subject) of type array|string is deprecated dans url_is_external() (ligne 2395 dans /home/laurentp/www/includes/common.inc).
  • Deprecated function : ltrim(): Passing null to parameter #1 ($string) of type string is deprecated dans url() (ligne 2311 dans /home/laurentp/www/includes/common.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property SelectQuery::$alterTags is deprecated dans SelectQuery->addTag() (ligne 978 dans /home/laurentp/www/includes/database/select.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).
  • Deprecated function : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans DatabaseCondition->compile() (ligne 1865 dans /home/laurentp/www/includes/database/query.inc).

Ensemble de nombres et typographie

La norme ISO 80000-2:2009 2-6.1 à 2-6.6 prescrit d'écrire les ensembles de nombres par une lettre majuscule en gras, cette convention est celle utilisée par Bourbaki.

Cela pose un problème quand on écrit sur une feuille ou au tableau, comment rendre une lettre grasse dans ce contexte.
On utilise alors traditionnellement les lettres avec double barres. Cependant la typographie utilisée nous donnera un rendu différent.

On peut utiliser la police de caractère BoldBlackboard: http://fr.wikipedia.org/wiki/Blackboard_gras
en Latex on fait précéder la lettre du \mathbb
Avantage: cette typographie est reprise par UNICODE notamment dans le BMP 2100: http://www.unicode.org/charts/PDF/U2100.pdf
Inconvénient: en manuscrit le R est compliqué à reproduire, c'est pour cela que nous sommes un certain nombre à utiliser une autre convention typographique qui a été popularisée par Ramis/Deschamps/Odoux qui se contente de doubler uniquement la partie gauche de la lettre. Ceci est plus simple et économe en encre et plus rapide.

Cette typographie peut être rendue sous Latex si on utilise la police Double Struck Font, http://www.ctex.org/documents/packages/math/dsdoc.pdf
la commande \mathds{N} affichera un N avec double barre à gauche et non sur la barre oblique comme avec la Blackboard Bold

Uncaught exception thrown in session handler.

PDOException: SQLSTATE[42000]: Syntax error or access violation: 1142 INSERT command denied to user 'laurentpabcm'@'10.2.20.129' for table 'drupclonesessions': INSERT INTO {sessions} (sid, ssid, uid, cache, hostname, session, timestamp) VALUES (:db_insert_placeholder_0, :db_insert_placeholder_1, :db_insert_placeholder_2, :db_insert_placeholder_3, :db_insert_placeholder_4, :db_insert_placeholder_5, :db_insert_placeholder_6); Array ( [:db_insert_placeholder_0] => FOqiYZa8vxd6f-aNslvPtD33jn0RLtZCLXA4W3burug [:db_insert_placeholder_1] => FOqiYZa8vxd6f-aNslvPtD33jn0RLtZCLXA4W3burug [:db_insert_placeholder_2] => 0 [:db_insert_placeholder_3] => 0 [:db_insert_placeholder_4] => 44.210.151.5 [:db_insert_placeholder_5] => messages|a:1:{s:5:"error";a:6:{i:0;s:300:"<em class="placeholder">Deprecated function</em> : Creation of dynamic property SelectQuery::$alterTags is deprecated dans <em class="placeholder">SelectQuery->addTag()</em> (ligne <em class="placeholder">978</em> dans <em class="placeholder">/home/laurentp/www/includes/database/select.inc</em>).";i:1;s:317:"<em class="placeholder">Deprecated function</em> : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans <em class="placeholder">DatabaseCondition->compile()</em> (ligne <em class="placeholder">1865</em> dans <em class="placeholder">/home/laurentp/www/includes/database/query.inc</em>).";i:2;s:317:"<em class="placeholder">Deprecated function</em> : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans <em class="placeholder">DatabaseCondition->compile()</em> (ligne <em class="placeholder">1865</em> dans <em class="placeholder">/home/laurentp/www/includes/database/query.inc</em>).";i:3;s:300:"<em class="placeholder">Deprecated function</em> : Creation of dynamic property SelectQuery::$alterTags is deprecated dans <em class="placeholder">SelectQuery->addTag()</em> (ligne <em class="placeholder">978</em> dans <em class="placeholder">/home/laurentp/www/includes/database/select.inc</em>).";i:4;s:317:"<em class="placeholder">Deprecated function</em> : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans <em class="placeholder">DatabaseCondition->compile()</em> (ligne <em class="placeholder">1865</em> dans <em class="placeholder">/home/laurentp/www/includes/database/query.inc</em>).";i:5;s:317:"<em class="placeholder">Deprecated function</em> : Creation of dynamic property DatabaseCondition::$stringVersion is deprecated dans <em class="placeholder">DatabaseCondition->compile()</em> (ligne <em class="placeholder">1865</em> dans <em class="placeholder">/home/laurentp/www/includes/database/query.inc</em>).";}} [:db_insert_placeholder_6] => 1721802906 ) in _drupal_session_write() (line 209 of /home/laurentp/www/includes/session.inc).