Mathematische Exkursionen FAQIR Formelsprache für A über Q zur Implementierung auf Rechnern

Die vereinfachte Matrix
S0 = 1/(+1 aa + 1γ af) S3 = 1/(+1 cv + 1γ da) S6 = 1/(+1 fh)
S1 = 1/(+1 az + 1γ be) S4 = 1/(+1 ds + 1γ dw) S7 = 1/(+1 ga)
S2 = 1/(+1 bx + 1γ cc) S5 = 1/(+1 e1 + 1γ eq) S8 = 1/(+1 gq)

  e0 e1 m1 e1 m1 f1 n1 m0 n0 e0 e1 m2 e1 m2 f0 f1 f1 m2 f0 f1 n1 1
1 1

0 0 +1 ad S0
-1 aq S0
+1 ab S0
+1γ ag S0
+1γγ aj S0
+1 ac S0
+1γ ah S0
+1γγ ak S0
-1 an S0
-1γ as S0
-1γγ aw S0
-1 ap S0
-1γ au S0
-1γγ ax S0
+1 ae S0
+1γ ai S0
+1γγ al S0
-1 ao S0
-1γ at S0
-1 am S0
-1γ ar S0
-1γγ av S0
u 0 1
-1 bn S1
-1γ bs S1
+1 bb S1
-1 bo S1
+1 ay S1
+1γ bd S1
+1γγ bh S1
+1 ba S1
+1γ bf S1
+1γγ bi S1
-1 bl S1
-1γ bq S1
-1γγ bu S1
-1 bm S1
-1γ br S1
-1γγ bv S1
+1 bc S1
+1γ bg S1
+1γγ bj S1
0 -1 bk S1
-1γ bp S1
-1γγ bt S1
u² 0 1
-1 cl S2
-1γ cq S2
+1 bz S2
-1 cm S2
+1 bw S2
+1γ cb S2
+1γγ cf S2
+1 by S2
+1γ cd S2
+1γγ cg S2
-1 cj S2
-1γ co S2
-1γγ cs S2
-1 ck S2
-1γ cp S2
-1γγ ct S2
+1 ca S2
+1γ ce S2
+1γγ ch S2
0 -1 ci S2
-1γ cn S2
-1γγ cr S2
j 0 1
-1 dj S3
-1γ do S3
+1 cx S3
-1 dk S3
+1 cu S3
+1γ cz S3
+1γγ dd S3
+1 cw S3
+1γ db S3
+1γγ de S3
-1 dh S3
-1γ dm S3
-1γγ dq S3
-1 di S3
-1γ dn S3
-1γγ dr S3
+1 cy S3
+1γ dc S3
+1γγ df S3
0 -1 dg S3
-1γ dl S3
-1γγ dp S3
uj 0 1
-1 ed S4
-1γ eh S4
+1 du S4
-1 ee S4
+1 bw S4
+1γ cb S4
+1γγ cf S4
+1 dt S4
+1γ dx S4
+1γγ dz S4
-1 cj S4
-1γ co S4
-1γγ cs S4
-1 ec S4
-1γ eg S4
-1γγ ej S4
+1 dv S4
+1γ dy S4
+1γγ ea S4
0 -1 eb S4
-1γ ef S4
-1γγ ei S4
u²j 0 1
-1 ey S5
-1γ fd S5
+1 en S5
-1 ez S5
+1 ek S5
+1γ ep S5
+1γγ af S5
+1 em S5
+1γ er S5
+1γγ et S5
-1 ew S5
-1γ fb S5
-1γγ at S5
-1 ex S5
-1γ fc S5
-1γγ ff S5
+1 eo S5
+1γ es S5
+1γγ eu S5
0 -1 ev S5
-1γ fa S5
-1γγ fe S5
j² 0 1
-1 ft S6
+1 fj S6
-1 fu S6
+1 fg S6
+1γ fl S6
+1 fi S6
+1γ fm S6
+1γγ fo S6
-1 fr S6
-1γ fw S6
-1 fs S6
-1γ fx S6
-1γγ fz S6
+1 fk S6
+1γ fn S6
+1γγ fp S6
0 -1 fq S6
-1γ fv S6
-1γγ fy S6
uj² 0 1
-1 gk S7
+1 gc S7
-1 gl S7
+1 fg S7
+1γ fl S7
+1 gb S7
+1γ ge S7
+1γγ gg S7
-1 fr S7
-1γ fw S7
-1 gj S7
-1γ gn S7
-1γγ gp S7
+1 gd S7
+1γ gf S7
+1γγ gh S7
0 -1 gi S7
-1γ gm S7
-1γγ go S7
u²j² 0 1
-1 ha S8
+1 gs S8
-1 hb S8
+1 fg S8
+1γ fl S8
+1 gr S8
+1γ gu S8
+1γγ gw S8
-1 fr S8
-1γ fw S8
-1 gz S8
-1γ hd S8
-1γγ hf S8
+1 gt S8
+1γ gv S8
+1γγ gx S8
0 -1 gy S8
-1γ hc S8
-1γγ he S8

und subtrahiere von den Zeilen  
u²,  j,  uj,  u²j,  j²,  uj²   jeweils  u²j² und rechne   u²j² = u²j² - u

  e0 e1 m1 e1 m1 f1 n1 m0 n0 e0 e1 m2 e1 m2 f0 f1 f1 m2 f0 f1 n1 1
11

00+1 ad S0
-1 aq S0
+1 ab S0
+1γ ag S0
+1γγ aj S0
+1 ac S0
+1γ ah S0
+1γγ ak S0
-1 an S0
-1γ as S0
-1γγ aw S0
-1 ap S0
-1γ au S0
-1γγ ax S0
+1 ae S0
+1γ ai S0
+1γγ al S0
-1 ao S0
-1γ at S0
-1 am S0
-1γ ar S0
-1γγ av S0
u01
-1 bn S1
-1γ bs S1
+1 bb S1
-1 bo S1
+1 ay S1
+1γ bd S1
+1γγ bh S1
+1 ba S1
+1γ bf S1
+1γγ bi S1
-1 bl S1
-1γ bq S1
-1γγ bu S1
-1 bm S1
-1γ br S1
-1γγ bv S1
+1 bc S1
+1γ bg S1
+1γγ bj S1
0-1 bk S1
-1γ bp S1
-1γγ bt S1
u²00-1 cl S2
+1 ha S8
-1γ cq S2
+1 bz S2
-1 gs S8
-1 cm S2
+1 hb S8
+1 bw S2
-1 fg S8
+1γ cb S2
-1γ fl S8
+1γγ cf S2
+1 by S2
-1 gr S8
+1γ cd S2
-1γ gu S8
+1γγ cg S2
-1γγ gw S8
-1 cj S2
+1 fr S8
-1γ co S2
+1γ fw S8
-1γγ cs S2
-1 ck S2
+1 gz S8
-1γ cp S2
+1γ hd S8
-1γγ ct S2
+1γγ hf S8
+1 ca S2
-1 gt S8
+1γ ce S2
-1γ gv S8
+1γγ ch S2
-1γγ gx S8
0-1 ci S2
+1 gy S8
-1γ cn S2
+1γ hc S8
-1γγ cr S2
+1γγ he S8
j00-1 dj S3
+1 ha S8
-1γ do S3
+1 cx S3
-1 gs S8
-1 dk S3
+1 hb S8
+1 cu S3
-1 fg S8
+1γ cz S3
-1γ fl S8
+1γγ dd S3
+1 cw S3
-1 gr S8
+1γ db S3
-1γ gu S8
+1γγ de S3
-1γγ gw S8
-1 dh S3
+1 fr S8
-1γ dm S3
+1γ fw S8
-1γγ dq S3
-1 di S3
+1 gz S8
-1γ dn S3
+1γ hd S8
-1γγ dr S3
+1γγ hf S8
+1 cy S3
-1 gt S8
+1γ dc S3
-1γ gv S8
+1γγ df S3
-1γγ gx S8
0-1 dg S3
+1 gy S8
-1γ dl S3
+1γ hc S8
-1γγ dp S3
+1γγ he S8
uj00-1 ed S4
+1 ha S8
-1γ eh S4
+1 du S4
-1 gs S8
-1 ee S4
+1 hb S8
+1 bw S4
-1 fg S8
+1γ cb S4
-1γ fl S8
+1γγ cf S4
+1 dt S4
-1 gr S8
+1γ dx S4
-1γ gu S8
+1γγ dz S4
-1γγ gw S8
-1 cj S4
+1 fr S8
-1γ co S4
+1γ fw S8
-1γγ cs S4
-1 ec S4
+1 gz S8
-1γ eg S4
+1γ hd S8
-1γγ ej S4
+1γγ hf S8
+1 dv S4
-1 gt S8
+1γ dy S4
-1γ gv S8
+1γγ ea S4
-1γγ gx S8
0-1 eb S4
+1 gy S8
-1γ ef S4
+1γ hc S8
-1γγ ei S4
+1γγ he S8
u²j00-1 ey S5
+1 ha S8
-1γ fd S5
+1 en S5
-1 gs S8
-1 ez S5
+1 hb S8
+1 ek S5
-1 fg S8
+1γ ep S5
-1γ fl S8
+1γγ af S5
+1 em S5
-1 gr S8
+1γ er S5
-1γ gu S8
+1γγ et S5
-1γγ gw S8
-1 ew S5
+1 fr S8
-1γ fb S5
+1γ fw S8
-1γγ at S5
-1 ex S5
+1 gz S8
-1γ fc S5
+1γ hd S8
-1γγ ff S5
+1γγ hf S8
+1 eo S5
-1 gt S8
+1γ es S5
-1γ gv S8
+1γγ eu S5
-1γγ gx S8
0-1 ev S5
+1 gy S8
-1γ fa S5
+1γ hc S8
-1γγ fe S5
+1γγ he S8
j²00-1 ft S6
+1 ha S8
+1 fj S6
-1 gs S8
-1 fu S6
+1 hb S8
+1 fg S6
-1 fg S8
+1γ fl S6
-1γ fl S8
+1 fi S6
-1 gr S8
+1γ fm S6
-1γ gu S8
+1γγ fo S6
-1γγ gw S8
-1 fr S6
+1 fr S8
-1γ fw S6
+1γ fw S8
-1 fs S6
+1 gz S8
-1γ fx S6
+1γ hd S8
-1γγ fz S6
+1γγ hf S8
+1 fk S6
-1 gt S8
+1γ fn S6
-1γ gv S8
+1γγ fp S6
-1γγ gx S8
0-1 fq S6
+1 gy S8
-1γ fv S6
+1γ hc S8
-1γγ fy S6
+1γγ he S8
uj²00-1 gk S7
+1 ha S8
+1 gc S7
-1 gs S8
-1 gl S7
+1 hb S8
+1 fg S7
-1 fg S8
+1γ fl S7
-1γ fl S8
+1 gb S7
-1 gr S8
+1γ ge S7
-1γ gu S8
+1γγ gg S7
-1γγ gw S8
-1 fr S7
+1 fr S8
-1γ fw S7
+1γ fw S8
-1 gj S7
+1 gz S8
-1γ gn S7
+1γ hd S8
-1γγ gp S7
+1γγ hf S8
+1 gd S7
-1 gt S8
+1γ gf S7
-1γ gv S8
+1γγ gh S7
-1γγ gx S8
0-1 gi S7
+1 gy S8
-1γ gm S7
+1γ hc S8
-1γγ go S7
+1γγ he S8
u²j²00+1 bn S1
-1 ha S8
+1γ bs S1
-1 bb S1
+1 gs S8
+1 bo S1
-1 hb S8
-1 ay S1
+1 fg S8
-1γ bd S1
+1γ fl S8
-1γγ bh S1
-1 ba S1
+1 gr S8
-1γ bf S1
+1γ gu S8
-1γγ bi S1
+1γγ gw S8
+1 bl S1
-1 fr S8
+1γ bq S1
-1γ fw S8
+1γγ bu S1
+1 bm S1
-1 gz S8
+1γ br S1
-1γ hd S8
+1γγ bv S1
-1γγ hf S8
-1 bc S1
+1 gt S8
-1γ bg S1
+1γ gv S8
-1γγ bj S1
+1γγ gx S8
0+1 bk S1
-1 gy S8
+1γ bp S1
-1γ hc S8
+1γγ bt S1
-1γγ he S8
Weiter geht es ähnlich dem Gaußschen Eliminationsverfahren
 
Seite 1 - Die Konstruktion der Algebra
Seite 2 - Die Multiplikationstafel
Seite 3 - Die Addition und Multiplikation
Seite 4 - Die Inversenbildung
Seite 5 - Die Berechnung von a * b * c
Seite 6 - Der Satz
Seite 7 - Die Berechnung von  e•1/d•id•e  und  f•1/b•ib•f
Seite 8 - Die Berechnung der Punkte c1 und c2
Seite 9 - Die erste Matrix
Seite 10 - Die vereinfachte Matrix
Seite 11 - Das Ergebnis