All pastes #908008 Raw Edit
Miscellany

public text v1 · immutable
·published 2008-02-18 01:45 UTC
:"aQuad
ClrHome
a+b
Full
3→dim(L₁)
AxesOn
Lbl 0
If L₁(1)=0
Goto WV
ClrDraw
a+b
0→W
ClrHome
L₁(1)→A
L₁(2)→B
L₁(3)→C
Menu("ADVANCED QUADS","AX+BX+C=0",1,"(AX+B)(CX+D)=0",2,"A(X-H)+K=0",HK,"QUAD ANSWER",MT,"VIEW ANSWER",OO,"QUIT",Q)
Lbl WV
a+b
ClrHome
Menu("ENTER VALUES","AX+BX+C=0",1,"(AX+B)(CX+D)=0",2,"A(X-H)+K=0",HK,"QUIT",Q)
Lbl HK
ClrHome
ClrDraw
FnOff 
AxesOff
GridOff
LabelOff
0→Xmin
94→Xmax
0→Ymin
62→Ymax
Disp "A(X-H)+K=0"
Prompt A,H,K
If A=0
Goto HK
–2AH→B
K+(B/(4A))→C
{A,B,C}→L₁
Lbl VG
Menu("A(X-H)+K=0","VIEW ANSWER",IH,"MAIN MENU",0,"QUIT",Q)
Lbl IH
ClrDraw
FnOff 
A→W
–2AH→B
–K/A→Q
K+(B/(4A))→C
Text(0,0,"AX+BX+C=0
Text(6,0,"A = ",A
Text(12,0,"B = ",B
Text(18,0,"C = ",C
Text(24,0,"VERTEX:(H,K)
If B=int(B) and 2A=int(2A)
Then
gcd(abs(B),abs(2A))→N
Else
1→N
End
If 4AC-B=int(4AC-B) and 4A=int(4A)
Then
gcd(abs(4AC-B),abs(4A))→P
Else
1→P
End
Text(30,0,"H = ",H
Text(36,0,"K = ",K
Pause 
ClrDraw
–B/(2A)→H
C-(B/(4A))→K
–K→K
Text(0,17,"√(–K)
Text(4,0,"X=H+
Line(16,55,38,55)
Line(12,53,14,53)
Text(8,18,"√(A)
Text(14,0,"X=H+√(–K/A)
Line(12,43,14,43)
Pause 
1→M
1→N
For(I,1,999)
If I>abs(K)
Goto NN
Text(56,0,int(100I/abs(K)),"°/▫
abs(K)/I→L
If √(abs(K))=int(√(abs(K)))
Then
√(abs(K))→M
K/M→K
1→I
End
If L=int(L)
Then
IM→M
K/I→K
1→I
End
End
Lbl NN
Text(–1,54,0,"                
For(I,1,999)
If I>abs(A)
Goto KK
Text(56,0,int(100I/abs(A)),"°/▫
abs(A)/I→L
If √(abs(A))=int(√(abs(A)))
Then
√(abs(A))→N
A/N→A
1→I
End
If L=iPart(L)
Then
IN→N
L→A
1→I
End
End
Lbl KK
gcd(abs(M),abs(N))→O
M/O→M
N/O→N
K/A→U
If U=int(U)
Then
U→K
1→A
End
M/N→R
If R=int(R)
Then
R→M
1→N
End
Text(–1,54,0,"                
If abs(AN)≠1
Then
If M=1
Then
If K>0 and K≠1
Text(32,40,"√(",K,")
If K<0 and K≠–1
Text(32,40,"√(",abs(K),")
If K=0
Text(32,40,0
If K=1
Text(32,40,1
If K=–1
Text(32,40,"
End
If M≠1
Then
If K<0 and K≠–1
Text(32,40,M,"√(",abs(K),")
If K>0 and K≠1
Text(32,40,M,"√(",K,")
If K=0
Text(32,40,0
If K=1
Text(32,40,M
If K=–1
Text(32,40,M,"
End
If N≠1
Then
If A>0 and A≠1
Text(44,40,N,"√(",A,")
If A<0 and A≠–1
Text(44,40,N,"√(",abs(A),")
If A=0
Text(44,40,0
If A=1
Text(44,40,N
If A=–1
Text(44,40,N,"
End
If N=1
Then
If A>0 and A≠1
Text(44,40,"√(",A,")
If A<0 and A≠–1
Text(44,40,,"√(",abs(A),")
If A=0
Text(44,40,0
If A=1
Text(44,40,1
If A=–1
Text(44,40,"
End
If H≠0
Text(38,0,"X=",H,"+- =====================================================
If H=0
Then
Text(38,0,"X=+ ============================================================
Line(8,19,10,19)
End
End
If abs(AN)=1
Then
If H≠0
Then
If M≠1
Then
If U<0 and U≠–1
Text(32,0,"X=",H,"+-",M,"√(",abs(U),")
If U>0 and U≠1
Text(32,0,"X=",H,"+-",M,"√(",U,")
If U=0
Text(32,0,"X=",H
If U=1
Text(32,0,"X=",H,"+-",M
If U=–1
Text(32,0,"X=",H,"+-",M,"
End
If M=1
Then
If U>0 and U≠1
Text(32,0,"X=",H,"+-√(",U,")
If U<0 and U≠–1
Text(32,0,"X=",H,"+-√(",abs(U),")
If U=0
Text(32,0,"X=",H
If U=1
Text(32,0,"X=",H,"+-",1
If U=–1
Text(32,0,"X=",H,"+-
End
End
If H=0
Then
If M≠1
Then
If U<0 and U≠–1
Text(32,0,"X=+",M,"√(",abs(U),")
If U>0 and U≠1
Text(32,0,"X=+",M,"√(",U,")
If U=0
Text(32,0,"X=0
If U=1
Text(32,0,"X=+",M
If U=–1
Text(32,0,"X=+",M,"
End
If M=1
Then
If U>0 and U≠1
Text(32,0,"X=+√(",U,")
If U<0 and U≠–1
Text(32,0,"X=+√(",abs(U),")
If U=1
Text(32,0,"X=+1
If U=–1
Text(32,0,"X=+
End
If MU≠0
Line(8,25,10,25)
End
End
W→A
If KA≥0
Text(50,0,"X=",H+√(Q)
If KA<0
Text(50,0,"X=",H,"+",√(abs(Q)),"
If KA≥0
Text(56,0,"X=",H-√(abs(Q)
If KA<0
Text(56,0,"X=",H,"-",√(abs(Q)),"
Pause 
Goto OO
Lbl UU
ClrHome
If A=0
Goto 0
If imag(A)≠0 or imag(B)≠0 or imag(C)≠0
Goto 0
Goto OO
Lbl Q
GridOff
LabelOff
AxesOn
ClrDraw
DelVar Y₁
ZStandard
RectGC
ExprOn
–3→TblStart
1→ΔTbl
Disp 
ClrHome
Stop
Lbl 1
ClrHome
Disp "AX+BX+C=0
Prompt A,B,C
If A=0
Goto 1
a+b
{A,B,C}→L₁
Lbl UP
ClrHome
Menu("AX+BX+C=0","QUAD ANSWER",MT,"VIEW ANSWER",θ1,"MAIN MENU",0,"QUIT",Q)
Lbl OO
a+b
Menu("CURRENT QUAD","QUAD ANSWER",MT,"VIEW ANSWER",θ1,"MAIN MENU",0,"QUIT",Q)
Lbl θ1
L₁(1)→A
L₁(2)→B
L₁(3)→C
–B→D
B-4AC→I
√(B-4AC)→E
2A→F
(D+E)/F→G
(D-E)/F→H
Disp "X=
If I<0
Then
Pause GFrac
Pause HFrac
End
If I=0
Then
Pause GFrac
End
If I>0
Then
Disp GFrac,HFrac
Pause 
End
Disp "SUM OF ROOTS:
Pause G+HFrac
ClrDraw
GridOff
AxesOff
LabelOff
FnOff 
0→Xmin
94→Xmax
0→Ymin
62→Ymax
B-4AC→θ
If θ<0
–1→Z
If θ≥0
1→Z
abs(θ)→θ
Text(0,0,"DIFFERENCE OF ROOTS"
real(G-H)→L
imag(G-H)→M
If L≠0
Then
If M≠0
Text(6,0,"+",L,"+-",M,"
If M=0
Text(6,0,"+",L
End
If L=0
Then
If M=0
Text(6,0,0
If M≠0
Text(6,0,"+",M,"
End
If (L=0)+(M=0)≠2
Line(0,51,2,51)
Pause 
1→W
For(J,1,θ)
If J>θ
Goto WH
θ/J→L
If L=int(L)
Then
L→θ
JW→W
1→J
End
End
Lbl WH
If √(θ)≠int(√(θ))
Then
If Z=1
Then
If W=1
Then
Text(12,0,"√(",θ,")
Text(28,0,"–√(",θ,")
End
If W≠1
Then
Text(12,0,W,"√(",θ,")
Text(28,0,–W,"√(",θ,")
End
End
If Z=–1
Then
If W≠1
Then
Text(12,0,W,"√(",θ,")
Text(28,0,–W,"√(",θ,")
End
If W=1
Then
Text(12,0,"√(",θ,")
Text(28,0,"–√(",θ,")
End
End
If A=int(A)
Then
gcd(abs(A),W)→S
A/S→R
W/S→W
End
If A≠int(A)
A→R
Text(–1,12,0,"                
Text(–1,28,0,"                
If Z=1
Then
If W=1
Then
Text(12,0,"√(",θ,")
Text(28,0,"–√(",θ,")
End
If W≠1
Then
Text(12,0,W,"√(",θ,")
Text(28,0,–W,"√(",θ,")
End
End
If Z=–1
Then
If W=1
Then
Text(12,0,"√(",θ,")
Text(28,0,"–√(",θ,")
End
If W≠1
Then
Text(12,0,W,"√(",θ,")
Text(28,0,–W,"√(",θ,")
End
End
If R≠1 and R≠0
Then
Line(0,42,94,42)
Line(0,26,94,26)
Text(22,0,R
Text(38,0,R
End
End
If A=int(A)
Then
gcd(abs(A),W)→S
A/S→R
W/S→W
End
If A≠int(A)
A→R
If √(θ)=int(√(θ))
Then
If Z=1
Then
If (W√(θ))/R=int((W√(θ)/R))
Then
Text(12,0,(W√(θ))/R
Text(28,0,–(W√(θ))/R
End
If (W√(θ))/R≠int((W√(θ))/R)
Then
Text(12,0,W√(θ)
Text(28,0,–W√(θ)
Line(0,42,94,42)
Line(0,26,94,26)
Text(22,0,R
Text(38,0,R
End
End
If Z=–1
Then
If (W√(θ))/R=int((W√(θ))/R)
Then
Text(12,0,(W√(θ))/R,"
Text(28,0,–(W√(θ))/R,"
End
If (W√(θ))/R≠int(W√(θ)/R)
Then
Line(0,42,94,42)
Line(0,26,94,26)
Text(22,0,R
Text(38,0,R
End
End
End
If abs(int(R))>1
Then
Line(0,42,94,42)
Line(0,26,94,26)
Text(22,0,R
Text(38,0,R
End
Pause 
Disp "DIFFERENCE OF","ROOTS",(G-H)Frac,(H-G)Frac
Pause 
Disp "PRODUCT OF ROOTS
Pause GHFrac
If A=–abs(A)
Disp "OPENS DOWN
If A=abs(A)
Disp "OPENS UP
Pause 
D/F→H
C-(B/(4A))→K
Disp "VERTEX(H,K)=
Pause {H,K}Frac
Disp "AXIS OF SYMMETRY
D/F→H
Disp HFrac
Pause 
Disp "FOCUS:
C-(B/(4A))→K
K+(A/4)→O
Pause {H,O}Frac
K-(A/4)→N
Disp "DIRECTRIX","Y=
Pause NFrac
Disp "FOCAL CHORD","(LATUS RECTUM):
Pause abs(A)Frac
Disp "DISCRIMINANT:
Pause IFrac
If I=0
Disp "ONE SOLUTION
If I>0
Disp "TWO REAL","SOLUTIONS
If I<0
Disp "TWO COMPLEX","SOLUTIONS
Pause 
Lbl MT
AxesOff
GridOff
LabelOff
FnOff 
ClrDraw
ClrHome
For(θ,1,9999)
If θ≠1
Output(4,1,θ
θA→R
θB→S
θC→T
If round(R,9)=int(round(R,9)) and round(S,9)=int(round(S,9)) and round(T,9)=int(round(T,9))
Then
R→A
S→B
T→C
Goto WO
End
End
Lbl WO
If θ≠1
Then
Output(1,1,A
Output(2,1,B
Output(3,1,C
Pause 
End
gcd(gcd(abs(A),abs(B)),abs(C))→θ
A/θ→A
B/θ→B
C/θ→C
If θ≠1
Then
Output(5,1,A
Output(6,1,B
Output(7,1,C
Output(8,1,θ
Pause 
End
–B→D
√(B-4AC)→E
B-4AC→I
2A→F
(D+E)/F→G
(D-E)/F→H
D+E→J
D-E→K
√(B-4AC)→R
If I<0 or R≠int(R)
Goto MR
If I≥0 and R=int(R)
Goto MS
Lbl MS
0→Xmin
94→Xmax
0→Ymin
62→Ymax
Text(0,9,"–B+√(B-4AC)
Text(4,0,"X=
Line(17,57,19,57)
Line(8,55,94,55)
2A→V
–B→U
√(B-4AC)→T
gcd(gcd(abs(V),abs(U)),abs(T))→W
V/W→V
U/W→U
T/W→T
Text(8,25,"2A
Text(14,9,U,"+-",T
Text(18,0,"X=
Text(22,25,V
Line(8,41,94,41)
–B+√(B-4AC)→U
2A→V
–B-√(B-4AC)→W
gcd(abs(U),abs(V))→T
gcd(abs(W),abs(V))→S
U/T→O
V/T→P
W/S→Q
V/S→R
Text(28,0,P,"X+",–O,"=0
gcd(abs(O),abs(P))→N
O/N→O
P/N→P
Text(34,0,"X=",O,"/",P,"=",O/P
Text(40,0,R,"X+",–Q,"=0
gcd(abs(Q),abs(R))→N
Q/N→Q
R/N→R
Text(46,0,"X=",Q,"/",R," = ",Q/R
Text(54,0,θ,"(",P,"X+",–O,")(",R,"X+",–Q,")=0
Pause 
Goto MR
Lbl MR
ClrHome
0→Xmin
94→Xmax
0→Ymin
62→Ymax
ClrDraw
Text(0,9,"–B+√(B-4AC)
Line(17,57,19,57)
Text(4,0,"X=
Line(8,55,94,55)
Text(8,36,"2A
Pause 
Text(14,9,–B,"+-√(",B-4AC,")
Text(18,0,"X=
Text(22,24,2A
Line(8,41,94,41)
Pause 
–B→D
B-4AC→E
2A→F
a+b
If E=abs(E) or E=0
Then
1→θ
1→I
End
If E=–abs(E) and E≠0
Then
→θ
1→I
–E→E
End
1→Z
For(G,1,E)
If G>E
Goto BL
If √(E)=iPart(√(E))
Then
I√(E)→I
1→E
End
int(mean({100G/E,100G/√(E)}))→R
Text(56,0,R,"°/▫
E/(G)→H
gcd(gcd(abs(D),abs(I)),abs(F))→W
If H=int(H) and G>1
Then
H→E
GI→I
1→G
End
D/W→D
I/W→I
F/W→F
If W≠1 or H=int(H)
Then
If F=–1
Then
D/F→D
abs(I/F)→I
1→F
End
If F=1 and Z=1
Z-1→Z
End
End
Lbl BL
Text(56,0,"SIMPLIFYING......
If D≠int(D) or I≠int(I)
1→J
If D=int(D) and I=int(I)
gcd(abs(D),abs(I))→J
If F≠int(F) or J≠int(J)
1→K
If F=int(F) and J=int(J)
gcd(abs(F),abs(J))→K
If K≠1
Then
D/K→D
I/K→I
F/K→F
End
A→Q
For(R,1,9999)
RQ→P
If P=int(P)
Then
RD→D
RI→I
RF→F
Goto BC
End
End
Lbl BC
If F=–1
Then
D/F→D
I/abs(F)→I
1→F
End
Text(56,0,"LOADING ANSWER......
B-4AC→R
If D=0 and IE=0
Then
1→F
Goto θC
End
If D=0
Then
gcd(abs(I),abs(F))→θ
I/θ→I
F/θ→F
End
If I=0 or E=0
Then
gcd(abs(D),abs(F))→θ
D/θ→D
F/θ→F
End
Lbl θC
If F≠1
Then
If D≠0
Then
If I≠1
Then
If E≠0 and E≠1
Then
If R>0
Text(28,9,D,"+-",I,"√(",E,")
If R<0
Text(28,9,D,"+-",I,"√(",E,")
End
If E=0
Text(28,9,D
If E=1
Then
If R>0
Then
Text(28,9,D,"+-",I
gcd(abs(D+I),abs(F))→O
gcd(abs(D-I),abs(F))→P
If (D+I)/F=int((D+I)/F) and (D-I)/F=int((D-I)/F)
Text(42,0,"X=",(D+I)/F,",",(D-I)/F
If (D+I)/F=int((D+I)/F) and (D-I)/F≠int((D-I)/F)
Text(42,0,"X=",(D+I)/F,",",(D-I)/P,"/",F/P
If (D+I)/F≠int((D+I)/F) and (D-I)/F=int((D-I)/F)
Text(42,0,"X=",(D+I)/O,"/",F/O,",",(D-I)/F
If (D+I)/F≠int((D+I)/F) and (D-I)/F≠int((D-I)/F)
Text(42,0,"X=",(D+I)/O,"/",F/O,",",(D-I)/P,"/",F/P
End
If R<0
Then
gcd(abs(D),abs(F))→O
gcd(abs(D),abs(I))→P
Text(28,9,D,"+-",I,"
If D/F=int(D/F) and I/F=int(I/F)
Text(42,0,"X=",D/F,"+",I/F,",",D/F,"-",I/F,"
If D/F=int(D/F) and I/F≠int(I/F)
Text(42,0,"X=",D/F,"+",I,"/",F,",",D/F,"-",I,"/",F,"
If D/F≠int(D/F) and I/F=int(I/F)
Text(42,0,"X=",D,"/",F,"+",I/F,",",D,"/",F,"-",I/F,"
If D/F≠int(D/F) and I/F≠int(I/F)
Text(42,0,"X=",D,"/",F,"+",I,"/",F,",",D,"/",F,"-",I,"/",F,"
End
End
End
If I=1
Then
If E≠0 and E≠1
Then
If R>0
Text(28,9,D,"+-√(",E,")
If R<0
Text(28,9,D,"+-√(",E,")
End
If E=0
Text(28,9,D
If E=1
Then
If R>0
Then
Text(28,9,D,"+-1
gcd(abs(D+1),abs(F))→O
gcd(abs(D-1),abs(F))→P
If (D+1)/F=int((D+1)/F) and (D-1)/F=int((D-1)/F)
Text(42,0,"X=",(D+1)/F,",",(D-1)/F
If (D+1)/F=int((D+1)/F) and (D-1)/F≠int((D-1)/F)
Text(42,0,"X=",(D+1)/F,",",(D-1)/P,"/",F/P
If (D+1)/F≠int((D+1)/F) and (D-1)/F=int((D-1)/F)
Text(42,0,"X=",(D+1)/O,"/",F/O,",",(D-1)/F
If (D+1)/F≠int((D+1)/F) and (D-1)/F≠int((D-1)/F)
Text(42,0,"X=",(D+1)/O,"/",F/O,",",(D-1)/P,"/",F/P
End
If R<0
Then
gcd(abs(D),abs(F))→O
If D/F=int(D/F)
Text(28,9,D,"+-")
If D/F≠int(D/F)
Text(42,0,"X=",D/F,"+1/",F,",",D/F,"-1/",F,"
End
End
End
End
If D=0
Then
If I≠1
Then
If E≠0 and E≠1
Then
If R>0
Text(28,9,"+",I,"√(",E,")
If R<0
Text(28,9,"+",I,"√(",E,")
End
If E=0
Text(28,9,0
If E=1
Then
If R>0
Text(28,9,"+",I
If R<0
Text(28,9,"+",I,"
End
End
If I=1
Then
If E≠0 and E≠1
Then
If R>0
Text(28,9,"+√(",E,")
If R<0
Text(28,9,"+√(",E,")
End
If E=1
Then
If R>0
Text(28,9,"+1
If R<0
Text(28,9,"+
End
End
Line(9,29,11,29)
End
Text(32,0,"X=
Line(8,27,94,27)
Text(36,25,F
Text(–1,54,0,"                
Text(56,0,"DONE!!!")
Goto GZ
End
If F=1
Then
If D≠0
Then
If I≠1
Then
If E≠0 and E≠1
Then
If R>0
Text(28,0,"X=",D,"+-",I,"√(",E,")
If R<0
Text(28,0,"X=",D,"+-",I,"√(",E,")
End
If E=1
Then
If R>0
Then
Text(28,0,"X=",D,"+-",I
Text(34,0,"X=",D+I,",",D-I
End
If R<0
Then
Text(28,0,"X=",D,"+-",I,"
Text(42,0,"X=",D+I,",",D-I,"
End
End
If E=0
Text(28,0,"X=",D
End
If I=1
Then
If E≠0 and E≠1
Then
If R>0
Text(28,0,"X=",D,"+-√(",E,")
If R<0
Text(28,0,"X=",D,"+-√(",E,")
End
If E=1
Then
If R>0
Then
Text(28,0,"X=",D,"+-1
Text(34,0,"X=",D+1,",",D-1
End
If R<0
Then
Text(28,0,"X=",D,"+-
Text(42,0,"X=",D,"+,",D,"-
End
End
If E=0
Text(28,0,"X=",D
End
End
If D=0
Then
If I≠1
Then
If E≠1 and E≠0
Then
If R>0
Text(28,0,"X=+",I,"√(",E,")
If R<0
Text(28,0,"X=+",I,"√(",E,")
End
If E=1
Then
If R>0
Text(28,0,"X=+",I
If R<0
Text(28,0,"X=+",I,"
End
If E=0
Text(28,0,"X=0
End
If I=1
Then
If E≠1 and E≠0
Then
If R>0
Text(28,0,"X=+√(",E,")
If R<0
Text(28,0,"X=+√(",E,")
End
If E=0
Text(28,0,"X=0
If E=1
Then
If R>0
Text(28,0,"X=+1
If R<0
Text(28,0,"X=+
End
End
Line(8,29,10,29)
End
Text(–1,54,0,"                
Text(56,0,"DONE!!!
Goto GZ
End
Lbl GZ
Pause 
B-4AC→W
ClrDraw
Goto 0
Lbl 2
ClrHome
Disp "(AX+B)(CX+D)=0
Prompt A,B,C,D
If AC=0
Goto 2
AC→E
AD+CB→F
BD→G
{E,F,G}→L₁
Lbl PU
Menu("(AX+B)(CX+D)=0","VIEW ANSWER",OI,"MAIN MENU",0,"QUIT",Q)
Lbl OI
GridOff
AxesOff
LabelOff
ClrDraw
FnOff 
Text(0,0,"AX+BX+C=0
Text(6,0,"A = ",E
Text(12,0,"B = ",F
Text(18,0,"C = ",G
Text(24,0,E,"X+",F,"X+",G,"=0
Text(30,0,A,"X+",B," = 0
Text(36,0,"X = ",–B,"/",A," = ",–B/A
Text(42,0,C,"X+",D,"=0
Text(48,0,"X = ",–D,"/",C," = ",–D/C
Text(54,0,"(",A,"X+",B,")(",C,"X+",D,")=0
E→A
F→B
G→C
Pause 
Goto OO