Form [1]

Form (algebraische), eine ganze rationale Funktion von beliebig vielen homogenen Veränderlichen, heißt binär, ternär, quarternär, je nachdem die Zahl der homogenen Veränderlichen zwei, drei, vier ist. Gleich Null gesetzt, liefert eine binäre Form die Gleichung eines Punktsystems auf einer Geraden, eine ternäre diejenige einer ebenen Kurve, eine quarternäre diejenige einer Fläche im Raum. Man unterscheidet quadratische, kubische, biquadratische Formen, je nachdem die Ordnung in den Veränderlichen zwei, drei, vier ist. Die Formenlehre hat es hauptsächlich mit den durch lineare Substitution unzerstörbaren Eigenschaften der Formen zu tun (s. Invariantentheorie). Die quadratischen Formen spielen auch in der Zahlentheorie eine Rolle.

Wölffing.


http://www.zeno.org/Lueger-1904.

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