'1t 1^9 - JScholarship

Die Charakteristikentheorie. 329
pex, =y V« .pe9,2^ + 6 .p'^9'e,2 .pe%3
+ 4.5'.i28 .p'^ + 6 .p'\'^ .pe^9pi - 2 .p'^d^ .p^e"
=p'^d^ .peg,2s + 6 .y^^'i^ .p^e^ + 4.g'^ns .p'e^
+ 4.yV^j3äg2
='»' ('«'-1) {m'- 2). 2 m (to^ - 2) + 6 m' (m'- 2). m (to -1) (to - 2)
+ 4to'. m (to -1) (to-2) + 4to' (to'- 1) (to'-2) to (to.-1) (to - 2)
= 2toto' [(to^to'^ — 5m^m' + 2m^ — 2m'^ + 6m' — 4)
+ (3to^to' — 9toto' + 6to' — Qm^+ 18m — 12) + {2m^—Qm+4)
+ {2m^m'^—6m^m'—ßmm'^+4m^+4m'^+18mm'-12m—12m'+8)]
= 2toto'(3 m^m'^— 6 m^m'— 6 mm'^+ 2 m^+ 2 m'^+9 mm'—4) [Lit.Se].
Da hier unser Verfahren rücksichtlich der beiden Complexe
unsymmetrisch war, so liefert der Umstand, dass diese Formel in
m und to' symmetrisch ist, eine Bestätigung.
IV. Um aj^e zu bestimmen, verfahren wir wieder unsymmetrisch,
indem wir Formel 2 mit e multipliciren und dann ohne Weiteres
die aus § 36 bekannten Werthe der fünffachen Bedingungen substituiren;
dadurch kommt:
x^e =p'^d^. eg,23i + 6 .y V12 - e^5i.34 + 6. d^g'pu .pegesi
+ ^pi2Bi -p^e^ + 6 .p'^d^. e^gp,2 + 6 .y^e'^ .pegei2
+ 4.y V^ .pHgei + 4. d^pi23 .y 65.1 + 6 .y V.12 -y e''
= to' (m' - 1) (to' - 2) (to' - 3). 2to (6to2 - IIto - 6)
+ 6to' (to' — 2) (to' — 3). to (to — 2) (to — 3)
+ 6 to' (to' — 2) (to' — 3). to^ (to — 2) (to — 3)
+ 4»«' (3 to' — 2) (to' — 3). to (to — 1) (to — 2) (to — 3)
+ 2to' (11 to' —18). to (to — 1) (to — 2) (to — 3)
+ 6to' (to' — 1) (to' — 2) (to' — 3). to (to — 2) (to — 3)
+ 6to' (w' — 1) (to' — 2) (to' — 3). to^ (to — 2) (to - 3)
+ 4m' (to' — 1) (to' — 2) (to' — 3). to (to — 1) (to — 2) (to — 3)
+ 6to' (to' — 2) (to' — 3) . to (to — 1) (to — 2) (to — 3)
= 2to' (to' — 1) (to' - 2) (to' - 3) to . [9 to^ - 26 to + 12]
+ 2m! (9to'2 - 26to' + 12). to (to - 1) (to - 2) (to - 3)
+ 2to' (to' — 2) (to' — 3). to (to - 2) (to - 3). [3 + 3toto'
+ 2toto' —2to —2to'+2]
= 2to(to—2)(to—3).to'(to'—2)(to'-3).(5toto'-2to-2to'+5)
+ 2to (to - 1) (to - 2) (to - 3). to' (9to'2 - 26to' + 12)
+ 2to(9to2-26to+12).to'(to'-1)(to'-2)(to'-3) [Lit. 56].
V. Für % erhalten wir aus der Formel 2 nach Weglassung
derjenigen Symbole, die nuU sind, und nach Zusammenfassung der
gleichwerthigen Symbole: