https://glossar.hs-augsburg.de/w/index.php?title=H%C3%A4ndler-Datenbank_(SQL-Beispiel)/Kartesisches_Produkt&feed=atom&action=history Händler-Datenbank (SQL-Beispiel)/Kartesisches Produkt - Versionsgeschichte 2024-03-29T11:19:52Z Versionsgeschichte dieser Seite in GlossarWiki MediaWiki 1.39.4 https://glossar.hs-augsburg.de/w/index.php?title=H%C3%A4ndler-Datenbank_(SQL-Beispiel)/Kartesisches_Produkt&diff=49583&oldid=prev Kowa am 26. Oktober 2019 um 07:54 Uhr 2019-10-26T07:54:42Z <p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de-x-formal"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 26. Oktober 2019, 08:54 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l21">Zeile 21:</td> <td colspan="2" class="diff-lineno">Zeile 21:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;formula&quot;&gt;&lt;math&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;formula&quot;&gt;&lt;math&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\begin{align*}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\begin{align*}</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>s :=\; &amp;\{(a_1: v_{a_1}, \ldots, a_m: v_{a_m}, b_1: v_{b_1}, \ldots, b_n: v_{b_n})\;|\\</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">r \times </ins>s :=\; &amp;\{(a_1: v_{a_1}, \ldots, a_m: v_{a_m}, b_1: v_{b_1}, \ldots, b_n: v_{b_n})\;|\\</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>       &amp;\;\;v_{a_1}\!\in\!D_{a_1} \wedge \ldots \wedge v_{a_m}\!\in\!D_{a_m} \wedge v_{b_1}\!\in\!D_{b_1} \wedge \ldots \wedge v_{b_n}\!\in\!D_{b_n} \\</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>       &amp;\;\;v_{a_1}\!\in\!D_{a_1} \wedge \ldots \wedge v_{a_m}\!\in\!D_{a_m} \wedge v_{b_1}\!\in\!D_{b_1} \wedge \ldots \wedge v_{b_n}\!\in\!D_{b_n} \\</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>       &amp;\}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>       &amp;\}</div></td></tr> </table> Kowa https://glossar.hs-augsburg.de/w/index.php?title=H%C3%A4ndler-Datenbank_(SQL-Beispiel)/Kartesisches_Produkt&diff=49582&oldid=prev Kowa am 26. Oktober 2019 um 07:52 Uhr 2019-10-26T07:52:45Z <p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de-x-formal"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 26. Oktober 2019, 08:52 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l15">Zeile 15:</td> <td colspan="2" class="diff-lineno">Zeile 15:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Das Kartesische Produkt verknüpft alle möglichen Tupelpaare zweier Relationen zu jeweils einem Tupel, das alle Attribute beider Tupel enthält.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Das Kartesische Produkt verknüpft alle möglichen Tupelpaare zweier Relationen zu jeweils einem Tupel, das alle Attribute beider Tupel enthält.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Es seien &lt;math&gt;r := r(a_1: D_{a_1}, \ldots, a_m: D_{a_m})&lt;/math&gt; und &lt;math&gt;s := s(b_1: D_{b_1}, \ldots, b_n: D_{b_n}) &lt;/math&gt; zwei Relationen,</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Es seien &lt;math&gt;r := r(a_1: D_{a_1}, \ldots, a_m: D_{a_m})&lt;/math&gt; und &lt;math&gt;s := s(b_1: D_{b_1}, \ldots, b_n: D_{b_n}) &lt;/math&gt; zwei Relationen  </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">mit [[Relationale_Algebra#Attributtupel|Attributtupeln]]</ins>,</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>wobei alle Attributbezeichner verschieden seien. Dann heißt</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>wobei alle Attributbezeichner verschieden seien. Dann heißt</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> </table> Kowa https://glossar.hs-augsburg.de/w/index.php?title=H%C3%A4ndler-Datenbank_(SQL-Beispiel)/Kartesisches_Produkt&diff=49581&oldid=prev Kowa am 25. Oktober 2019 um 12:06 Uhr 2019-10-25T12:06:10Z <p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de-x-formal"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 25. Oktober 2019, 13:06 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16">Zeile 16:</td> <td colspan="2" class="diff-lineno">Zeile 16:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Es seien &lt;math&gt;r := r(a_1: D_{a_1}, \ldots, a_m: D_{a_m})&lt;/math&gt; und &lt;math&gt;s := s(b_1: D_{b_1}, \ldots, b_n: D_{b_n}) &lt;/math&gt; zwei Relationen,</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Es seien &lt;math&gt;r := r(a_1: D_{a_1}, \ldots, a_m: D_{a_m})&lt;/math&gt; und &lt;math&gt;s := s(b_1: D_{b_1}, \ldots, b_n: D_{b_n}) &lt;/math&gt; zwei Relationen,</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>wobei alle Attributbezeichner verschieden seien.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>wobei alle Attributbezeichner verschieden seien. Dann heißt</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Dann heißt</div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;formula&quot;&gt;&lt;math&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;formula&quot;&gt;&lt;math&gt;</div></td></tr> </table> Kowa https://glossar.hs-augsburg.de/w/index.php?title=H%C3%A4ndler-Datenbank_(SQL-Beispiel)/Kartesisches_Produkt&diff=49580&oldid=prev Kowa: /* Das Kartesische Produkt */ 2019-10-25T12:05:06Z <p><span dir="auto"><span class="autocomment">Das Kartesische Produkt</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de-x-formal"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 25. Oktober 2019, 13:05 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l11">Zeile 11:</td> <td colspan="2" class="diff-lineno">Zeile 11:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Das Kartesische Produkt===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Das Kartesische Produkt===</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:Relational Algebra Cartesian Product.svg | mini|440px |links| gerahmt|Das Kartesische Produkt <del style="font-weight: bold; text-decoration: none;">verknüpft alle möglichen Tupelpaare zu jeweils einem Tupel, das alle Attribute beider Tupel enthält.</del>]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:Relational Algebra Cartesian Product.svg | mini|440px |links| gerahmt|Das Kartesische Produkt <ins style="font-weight: bold; text-decoration: none;">zweier Tabellen</ins>]]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div style=&quot;clear:both&quot;&gt;&lt;/div&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div style=&quot;clear:both&quot;&gt;&lt;/div&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Das Kartesische Produkt verknüpft alle möglichen Tupelpaare zweier Relationen zu jeweils einem Tupel, das alle Attribute beider Tupel enthält.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Das Kartesische Produkt verknüpft alle möglichen Tupelpaare zweier Relationen zu jeweils einem Tupel, das alle Attribute beider Tupel enthält.</div></td></tr> </table> Kowa https://glossar.hs-augsburg.de/w/index.php?title=H%C3%A4ndler-Datenbank_(SQL-Beispiel)/Kartesisches_Produkt&diff=49579&oldid=prev Kowa am 25. Oktober 2019 um 12:03 Uhr 2019-10-25T12:03:55Z <p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de-x-formal"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 25. Oktober 2019, 13:03 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l22">Zeile 22:</td> <td colspan="2" class="diff-lineno">Zeile 22:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\begin{align*}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\begin{align*}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>s :=\; &amp;\{(a_1: v_{a_1}, \ldots, a_m: v_{a_m}, b_1: v_{b_1}, \ldots, b_n: v_{b_n})\;|\\</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>s :=\; &amp;\{(a_1: v_{a_1}, \ldots, a_m: v_{a_m}, b_1: v_{b_1}, \ldots, b_n: v_{b_n})\;|\\</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>       &amp;\;\;v_{a_1} \in D_{a_1} \wedge \ldots \wedge v_{a_m} \in D_{a_m} \wedge v_{b_1} \in D_{b_1} \wedge \ldots \wedge v_{b_n} \in D_{b_n} \\</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>       &amp;\;\;v_{a_1}<ins style="font-weight: bold; text-decoration: none;">\!</ins>\in<ins style="font-weight: bold; text-decoration: none;">\!</ins>D_{a_1} \wedge \ldots \wedge v_{a_m}<ins style="font-weight: bold; text-decoration: none;">\!</ins>\in<ins style="font-weight: bold; text-decoration: none;">\!</ins>D_{a_m} \wedge v_{b_1}<ins style="font-weight: bold; text-decoration: none;">\!</ins>\in<ins style="font-weight: bold; text-decoration: none;">\!</ins>D_{b_1} \wedge \ldots \wedge v_{b_n}<ins style="font-weight: bold; text-decoration: none;">\!</ins>\in<ins style="font-weight: bold; text-decoration: none;">\!</ins>D_{b_n} \\</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>       &amp;\}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>       &amp;\}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{align*}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\end{align*}</div></td></tr> </table> Kowa https://glossar.hs-augsburg.de/w/index.php?title=H%C3%A4ndler-Datenbank_(SQL-Beispiel)/Kartesisches_Produkt&diff=49578&oldid=prev Kowa am 25. Oktober 2019 um 12:02 Uhr 2019-10-25T12:02:15Z <p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de-x-formal"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 25. Oktober 2019, 13:02 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l18">Zeile 18:</td> <td colspan="2" class="diff-lineno">Zeile 18:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>wobei alle Attributbezeichner verschieden seien.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>wobei alle Attributbezeichner verschieden seien.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Dann heißt</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Dann heißt</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;formula&quot;&gt;&lt;math&gt;<del style="font-weight: bold; text-decoration: none;">r </del>\<del style="font-weight: bold; text-decoration: none;">times </del>s := \{(a_1: v_{a_1}, \ldots, a_m: v_{a_m}, b_1: v_{b_1}, \ldots, b_n: v_{b_n})\;|\; v_{a_1} \in D_{a_1} \wedge \ldots \wedge v_{a_m} \in D_{a_m} \wedge v_{b_1} \in D_{b_1} \wedge \ldots \wedge v_{b_n} \in D_{b_n}\}&lt;/math&gt;&lt;/div&gt;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;formula&quot;&gt;&lt;math&gt;</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\<ins style="font-weight: bold; text-decoration: none;">begin{align*}</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>s :=<ins style="font-weight: bold; text-decoration: none;">\; &amp;</ins>\{(a_1: v_{a_1}, \ldots, a_m: v_{a_m}, b_1: v_{b_1}, \ldots, b_n: v_{b_n})\;|<ins style="font-weight: bold; text-decoration: none;">\\</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">      &amp;\;</ins>\;v_{a_1} \in D_{a_1} \wedge \ldots \wedge v_{a_m} \in D_{a_m} \wedge v_{b_1} \in D_{b_1} \wedge \ldots \wedge v_{b_n} \in D_{b_n} \<ins style="font-weight: bold; text-decoration: none;">\</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">      &amp;\}</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">\end{align*</ins>}</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;/math&gt;&lt;/div&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Kartesisches Produkt von &lt;math&gt;r&lt;/math&gt; und &lt;math&gt;s&lt;/math&gt;&#039;&#039;&#039;.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Kartesisches Produkt von &lt;math&gt;r&lt;/math&gt; und &lt;math&gt;s&lt;/math&gt;&#039;&#039;&#039;.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> </table> Kowa https://glossar.hs-augsburg.de/w/index.php?title=H%C3%A4ndler-Datenbank_(SQL-Beispiel)/Kartesisches_Produkt&diff=49577&oldid=prev Kowa: /* Das Kartesische Produkt */ 2019-10-25T11:18:08Z <p><span dir="auto"><span class="autocomment">Das Kartesische Produkt</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de-x-formal"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 25. Oktober 2019, 12:18 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l11">Zeile 11:</td> <td colspan="2" class="diff-lineno">Zeile 11:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Das Kartesische Produkt===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Das Kartesische Produkt===</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:Relational Algebra Cartesian Product.svg | mini|440px | <del style="font-weight: bold; text-decoration: none;">rechts </del>|gerahmt|Das Kartesische Produkt verknüpft alle möglichen Tupelpaare zu jeweils einem Tupel, das alle Attribute beider Tupel enthält.]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:Relational Algebra Cartesian Product.svg | mini|440px |<ins style="font-weight: bold; text-decoration: none;">links</ins>| gerahmt|Das Kartesische Produkt verknüpft alle möglichen Tupelpaare zu jeweils einem Tupel, das alle Attribute beider Tupel enthält.]]</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;div style=&quot;clear:both&quot;&gt;&lt;/div&gt;</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Das Kartesische Produkt verknüpft alle möglichen Tupelpaare zweier Relationen zu jeweils einem Tupel, das alle Attribute beider Tupel enthält.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Das Kartesische Produkt verknüpft alle möglichen Tupelpaare zweier Relationen zu jeweils einem Tupel, das alle Attribute beider Tupel enthält.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l18">Zeile 18:</td> <td colspan="2" class="diff-lineno">Zeile 18:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>wobei alle Attributbezeichner verschieden seien.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>wobei alle Attributbezeichner verschieden seien.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Dann heißt</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Dann heißt</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;formula&quot;&gt;&lt;math&gt;r \times s := \{(a_1: v_{a_1}, \ldots, a_m: v_{a_m}, b_1: v_{b_1}, \ldots, b_n: v_{b_n})| v_{a_1} \in D_{a_1} \wedge \ldots \wedge v_{a_m} \in D_{a_m}<del style="font-weight: bold; text-decoration: none;">, </del>\wedge v_{b_1} \in D_{b_1} \wedge \ldots \wedge v_{b_n} \in D_{b_n}\}&lt;/math&gt;&lt;/div&gt;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;formula&quot;&gt;&lt;math&gt;r \times s := \{(a_1: v_{a_1}, \ldots, a_m: v_{a_m}, b_1: v_{b_1}, \ldots, b_n: v_{b_n})<ins style="font-weight: bold; text-decoration: none;">\;</ins>|<ins style="font-weight: bold; text-decoration: none;">\; </ins>v_{a_1} \in D_{a_1} \wedge \ldots \wedge v_{a_m} \in D_{a_m} \wedge v_{b_1} \in D_{b_1} \wedge \ldots \wedge v_{b_n} \in D_{b_n}\}&lt;/math&gt;&lt;/div&gt;</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Kartesisches Produkt von &lt;math&gt;r&lt;/math&gt; und &lt;math&gt;s&lt;math&gt;&#039;&#039;&#039;.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Kartesisches Produkt von &lt;math&gt;r&lt;/math&gt; und &lt;math&gt;s&lt;<ins style="font-weight: bold; text-decoration: none;">/</ins>math&gt;&#039;&#039;&#039;.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Das kartesische Produkt kann analog auch für Positionstupel und attributierte Positionstupel definiert werden. Dem Attribut &lt;math&gt;b_i&lt;/math&gt;  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Das kartesische Produkt kann analog auch für Positionstupel und attributierte Positionstupel definiert werden. Dem Attribut &lt;math&gt;b_i&lt;/math&gt;  </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>wird dabei jeweils die Position &lt;math&gt;m+i&lt;/math&gt; zugeordnet. Falls zwei Relationen gleichbenannte Attribute enthalten, müssen diese zunächst mit einer  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>wird dabei jeweils die Position &lt;math&gt;m+i&lt;/math&gt; zugeordnet. Falls zwei Relationen gleichbenannte Attribute enthalten, müssen diese zunächst mit einer  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>geeigneten [[Händler-Datenbank (SQL-Beispiel)/Projektion|Projektion]] in einer der beiden Tabellen umbenannt werden.  </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>geeigneten [[Händler-Datenbank (SQL-Beispiel)/Projektion|Projektion]] in einer der beiden Tabellen umbenannt werden.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Quellen==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Quellen==</div></td></tr> </table> Kowa https://glossar.hs-augsburg.de/w/index.php?title=H%C3%A4ndler-Datenbank_(SQL-Beispiel)/Kartesisches_Produkt&diff=49576&oldid=prev Kowa: Die Seite wurde neu angelegt: „{{In Bearbeitung}} {{Qualität |correctness = 0 |extent = 0 |numberOfReferences = 3 |qualityOfReferences = 5 |conformance = 5 }}…“ 2019-10-25T11:14:44Z <p>Die Seite wurde neu angelegt: „{{In Bearbeitung}} {{Qualität |correctness = 0 |extent = 0 |numberOfReferences = 3 |qualityOfReferences = 5 |conformance = 5 }}…“</p> <p><b>Neue Seite</b></p><div>{{In Bearbeitung}}<br /> {{Qualität<br /> |correctness = 0<br /> |extent = 0<br /> |numberOfReferences = 3<br /> |qualityOfReferences = 5<br /> |conformance = 5<br /> }}<br /> Die nachfolgenden Beispiele können beispielsweise mit [[SQLite]] oder [[PostgreSQL]] getestet werden.<br /> Installieren Sie dazu die zugehörige [[Händler-Datenbank (SQL-Beispiel)|Händler-Datenbank]].<br /> <br /> ===Das Kartesische Produkt===<br /> [[Datei:Relational Algebra Cartesian Product.svg | mini|440px | rechts |gerahmt|Das Kartesische Produkt verknüpft alle möglichen Tupelpaare zu jeweils einem Tupel, das alle Attribute beider Tupel enthält.]]<br /> <br /> Das Kartesische Produkt verknüpft alle möglichen Tupelpaare zweier Relationen zu jeweils einem Tupel, das alle Attribute beider Tupel enthält.<br /> <br /> Es seien &lt;math&gt;r := r(a_1: D_{a_1}, \ldots, a_m: D_{a_m})&lt;/math&gt; und &lt;math&gt;s := s(b_1: D_{b_1}, \ldots, b_n: D_{b_n}) &lt;/math&gt; zwei Relationen,<br /> wobei alle Attributbezeichner verschieden seien.<br /> Dann heißt<br /> &lt;div class=&quot;formula&quot;&gt;&lt;math&gt;r \times s := \{(a_1: v_{a_1}, \ldots, a_m: v_{a_m}, b_1: v_{b_1}, \ldots, b_n: v_{b_n})| v_{a_1} \in D_{a_1} \wedge \ldots \wedge v_{a_m} \in D_{a_m}, \wedge v_{b_1} \in D_{b_1} \wedge \ldots \wedge v_{b_n} \in D_{b_n}\}&lt;/math&gt;&lt;/div&gt;<br /> &#039;&#039;&#039;Kartesisches Produkt von &lt;math&gt;r&lt;/math&gt; und &lt;math&gt;s&lt;math&gt;&#039;&#039;&#039;.<br /> <br /> Das kartesische Produkt kann analog auch für Positionstupel und attributierte Positionstupel definiert werden. Dem Attribut &lt;math&gt;b_i&lt;/math&gt; <br /> wird dabei jeweils die Position &lt;math&gt;m+i&lt;/math&gt; zugeordnet. Falls zwei Relationen gleichbenannte Attribute enthalten, müssen diese zunächst mit einer <br /> geeigneten [[Händler-Datenbank (SQL-Beispiel)/Projektion|Projektion]] in einer der beiden Tabellen umbenannt werden. <br /> <br /> ==Quellen==<br /> &lt;references/&gt;<br /> &lt;ol start=&quot;1&quot;&gt;<br /> &lt;li&gt;{{Quelle|Kowarschick, W. (MMDB-Skript): Skriptum zur Vorlesung Multimedia-Datenbanksysteme}}&lt;/li&gt;<br /> &lt;li&gt;{{Quelle|Kowarschick, W.: Multimedia-Datenbanksysteme}}, https://kowa.hs-augsburg.de/mmdb/mmdb-beispiele/haendler-datenbank/&lt;/li&gt;<br /> &lt;/ol&gt;<br /> [[Kategorie:PostgreSQL-Beispiel]]<br /> [[Kategorie:Praktikum:MMDB]]<br /> <br /> ==Siehe auch==<br /> * [[Händler-Datenbank (SQL-Beispiel)]]<br /> * [[Händler-Datenbank (SQL-Beispiel)/Identität]]<br /> * [[Händler-Datenbank (SQL-Beispiel)/Projektion]]<br /> * [[Händler-Datenbank (SQL-Beispiel)/Selektion]]</div> Kowa