1 REM KOMENIUM,n.p. PRAHA-oddeleni pocitacovych programu
2 REM 110 00 Praha 1-Truhlarska 12. (Telefon 2314934)
3 REM Evidencni cislo programu: 0113/CKL08/15
4 REM Nazev programu:LINEARNI FUNKCE
5 REM Schvaleno komisi dne: 7.3.1988
6 REM Namet navrhl:P.Nahodil
7 REM Scenar vypracoval:P.Nahodil
8 REM 2.recenzi provedl:RNDr.S.Schwabik,CSc
9 REM Metodicky text zpracoval: P.Nahodil
10 REM 1.recenzi provedl:Ing.B. Brdicka
11 REM 2.recenzi provedl:RNDr.S.Schwabik,CSc
12 REM Urceno pro-typ skoly:vsechny SOS
13 REM -predmet:matematika
14 REM -tematicky celek:lin. funkce,lin. rovnice a nerovnice a jejich soustavy
15 REM Urceno pro-typ pocitace: IQ 151
16 REM Vybaveni pocitace moduly:1001100000
18 REM Vybaveni pocitace periferiemi:000000000
90 CALL HEX(F973)
100 REM *********************
110 REM ** LINEARNI FUNKCE **
120 REM *********************
130 CLS:ERASE:AN=1:BN=1
140 REM HLAVNI MENU
145 PRINT&1,9",     ,"
150 PRINT&2,1"L I N E A R N I   F U N K C E"
153 RA=0:SL=0:S=30:V=3:GOSUB10000
155 PRINT&4,7","
160 PRINT&5,2"HLAVNI MENU";CHR$(15)&6,2"QQQQQQQQQQQ"
165 PRINT&7,14","
170 PRINT&8,4"V- vymezeni pojmu"
175 PRINT&9,16",  ,"
180 PRINT&10,4"G- graf linearni funkce"
185 PRINT&11,14","
190 PRINT&12,4"K- kresleni grafu"
200 PRINT&14,4"T- test"
210 PRINT&16,4"H- pomoc"
220 PRINT&18,4"E- konec"
230 PRINT&23,14","
240 PRINT&24,4"Stiskni klavesu"
250 PRINT&27,8"V,G,K,T,H nebo E";CHR$(7)
260 I$=INKEY$
270 IF I$="V" THEN CLS:CALLHEX(F973):GOTO400
280 IF I$="G" THEN CLS:CALLHEX(F973):GOTO1000
290 IF I$="K" THEN CLS:CALLHEX(F973):GOTO2000
300 IF I$="T" THEN CLS:CALLHEX(F973):GOTO3000
310 IF I$="H" THEN CLS:CALLHEX(F973):GOTO4000
320 IF I$="E" THEN CLS:CALLHEX(F973):GOTO5000
330 GOTO260
400 REM LIST V1
410 PRINT&4,7",  ,"
420 PRINT&5,3"Linearni funkce je funkce"
425 PRINT&8,3"tvaru:"
430 PRINT&12,10"y = ax + b"
440 RA=10:SL=8:S=13:V=4
445 GOSUB 10000
460 PRINT&16,17"v v,  v,";
470 PRINT&17,3"to je nejobecnejsi pripad"
480 PRINT&20,14",  , v,"
490 PRINT&21,3"kde a je realne cislo"
500 PRINT&22,6"o  ,"
510 PRINT&23,5"ruzne od nuly,"
520 PRINT&24,16",   ,  , v,"
530 PRINT&25,3"b je libovolne realne cislo."
560 A$="V"
570 GOSUB11000
580 REM LIST V2
590 PRINT&3,4",                  ,v  ,"
600 PRINT&4,3"Dale si projdeme zvlastni"
610 PRINT&5,4"v,      ,"
620 PRINT&6,3"pripady teto funkce:"
630 B$="1":C$="a":K=14
640 GOSUB12000
645 WAIT(10)
650 FOR I=18TO 14 STEP-1
660 PRINT&20,I"b "
665 WAIT(1)
670 NEXT I
680 WAIT(8)
690 PRINT&23,9"v"
700 PRINT&24,3"potom clen ax je roven nule."
710 PRINT&25,7", ,"
720 PRINT&26,3"Dostavame"
730 PRINT&27,19","
740 PRINT&28,5"tzv. KONSTANTNI FUNKCI"
750 WAIT(75)
760 RA=18:SL=8:S=8:V=4
770 GOSUB10000
775 WAIT(15)
780 GOSUB11000
790 REM LIST V3
800 B$="2":C$="b":K=19
810 GOSUB12000
820 PRINT&20,17" "
830 WAIT(8)
840 PRINT&15,13","
845 PRINT&16,11",mame:"
850 WAIT(8)
855 RA=18:SL=8:S=9:V=4
860 GOSUB10000
865 PRINT&23,7", ,"
870 PRINT&24,3"Dostavame"
880 PRINT&25,14"v, , , v"
890 PRINT&26,5"rovnici prime umernosti."
900 WAIT(60)
910 A$="M"
920 GOSUB11000
930 GOTO140
1000 REM LIST G1
1005 PRINT&1,14",  ,"
1010 PRINT&2,3"Grafem linearni funkce je"
1015 PRINT&3,10","
1020 PRINT&4,3"pro jakekoliv hodnoty"
1030 PRINT&5,19"v,"
1040 PRINT&6,3"konstant a i b primka;"
1050 PRINT CHR$(15)&7,12;"QMMMQMQQQQQQ"
1060 PRINT&8,19"v"
1070 PRINT&9,2"konstanta a ovlivnuje sklon"
1080 PRINT&10,3"v,";&10,15",";CHR$(15)&10,12"Q"
1090 PRINT&11,2"primky a plati:"
1100 PRINT&12,13"v"
1110 PRINT&13,4"1) jestlize a>0"
1120 PRINT&14,26","
1130 PRINT&15,9"je funkce rostouci,"
1140 PRINT&16,13"v"
1150 PRINT&17,4"2) jestlize a=0"
1160 PRINT&18,28","
1170 PRINT&19,9"je funkce konstantni,"
1180 PRINT&20,21","
1190 PRINT&21,9"(viz vymezeni pojmu)"
1200 PRINT&22,13"v"
1210 PRINT&23,4"3) jestlize a<0"
1220 PRINT&24,25", ,"
1230 PRINT&25,9"je funkce klesajici,"
1240 A$="G"
1250 GOSUB11000
1255 REM LIST G2
1260 PRINT&1,22"v"
1270 PRINT&2,5"konstanta b ovlivnuje"
1280 PRINT&3,12",";&3,25"v";CHR$(15)&3,15"Q"
1290 PRINT&4,5"posunuti grafu ve smeru"
1300 PRINT&6,5"osy y."
1310 PRINT&9,2"ZAPAMATUJTE SI:"
1320 PRINT&11,11",  ,"
1330 PRINT&12,2"Graf linearni funkce y=ax+b"
1340 PRINT&13,6", ,";&13,21"v"
1350 PRINT&14,2"protina osu y v bode b."
1360 RA=10:SL=0:S=30:V=6
1370 GOSUB10000
1380 PRINT&18,3"v";&18,23","
1390 PRINT&19,2"Vsechna  tato  tvrzeni si"
1400 PRINT&20,3"ov          v       v"
1410 PRINT&21,2"muzete vyzkouset v rezimu"
1420 PRINT&22,9","
1430 PRINT&23,2"kresleni grafu."
1440 A$="M"
1450 GOSUB11000
1460 GOTO140
2000 REM KRESLENI GRAFU
2010 PRINT&10,3"D- dosadit konstanty"
2020 PRINT&12,3"P- plynule menit"
2030 PRINT&11,15"v"
2040 PRINT&14,3"H- pomoc"
2050 PRINT&16,3"M- menu"
2060 PRINT&23,14","
2070 PRINT&24,4"Stiskni klavesu"
2080 PRINT&27,8"D,P,H, nebo M";CHR$(7)
2090 I$=INKEY$
2100 IF I$="D" THEN CALLHEX(F973):CLS:GOTO2200
2110 IF I$="P" THEN CALLHEX(F973):CLS:GOTO2600
2120 IF I$="H" THEN CALLHEX(F973):CLS:GOTO2800
2130 IF I$="M" THEN CALLHEX(F973):CLS:GOTO140
2140 GOTO2090
2200 REM REZIM D
2205 GOSUB13000
2210 GOSUB14000
2220 GOSUB16000
2230 PRINT&10,2"zadej a"
2240 K=12:GOSUB17000
2250 AN=P
2260 PRINT&14,2"zadej b"
2270 K=16:GOSUB17000
2280 BN=P
2290 GOSUB13000
2300 IF CH=1 THEN GOSUB19000:GOTO2450
2320 GOSUB18000
2340 GOSUB15000
2350 GOSUB16000
2360 GOTO2430
2430 GOSUB18000
2450 PRINT&9,6"v";&10,2"chces"
2460 PRINT&11,5"v";&12,0"pokracovat?"
2470 PRINT&14,1"stiskni"
2480 PRINT&16,3"A/N"
2490 IF INKEY$="A" THEN CALLHEX(F973):GOSUB18000:GOTO2230
2500 IF INKEY$="N" THEN CALLHEX(F973):ERASE:CLS:GOTO2000
2510 GOTO2490
2600 GOSUB13000
2610 GOSUB14000
2620 GOSUB16000
2630 PRINT&10,1"Q- zvys a";&9,7"v"
2640 PRINT&12,1"A- sniz a";&11,7"v"
2650 PRINT&14,1"P- zvys b";&13,7"v"
2660 PRINT&16,1"L- sniz b";&15,7"v"
2670 PRINT&18,1"M- menu"
2680 I$=INKEY$
2690 IF I$="Q" THEN CALLHEX(F973):AN=AN+.5:GOTO2750
2700 IF I$="A" THEN CALLHEX(F973):AN=AN-.5:GOTO2750
2710 IF I$="P" THEN CALLHEX(F973):BN=BN+.5:GOTO2750
2720 IF I$="L" THEN CALLHEX(F973):BN=BN-.5:GOTO2750
2730 IF I$="M" THEN CALLHEX(F973):ERASE:CLS:GOTO2000
2740 GOTO2680
2750 GOSUB13000
2760 IF CH=1 THEN GOSUB19000:GOTO2630
2770 GOSUB15000
2780 GOSUB16000
2790 GOTO2680
2800 REM HELP K
2810 PRINT&1,5"v       v,";&1,26","
2820 PRINT&2,3"Rezim slouzi k zobrazeni"
2830 PRINT&3,7"o  o  ,       ,  ,"
2840 PRINT&4,3"grafu ruznych linearnich"
2850 PRINT&5,8",";&5,22"ov"
2860 PRINT&6,3"funkci. Konstanty muzeme"
2870 PRINT&7,15"v  v,      v"
2880 PRINT&8,3"dosazovat bud primo (rezim"
2890 PRINT&9,15"ov"
2900 PRINT&10,3"D) nebo je muzeme plynule"
2910 PRINT&11,4"v       v"
2920 PRINT&12,3"menit (rezim P)."
2930 PRINT&13,22",  , v"
2940 PRINT&14,3"M poskytuje zakladni vyber."
2950 A$="M"
2960 GOSUB11000
2970 GOTO2000
3000 REM TEST
3010 PRINT&1,5"v,  v  ,"
3020 PRINT&2,3"Pocitac vam bude kreslit"
3030 PRINT&3,11"o     ,  ,        ,"
3040 PRINT&4,3"osm grafu linearnich funkci."
3050 PRINT&5,5"v,  ,"
3060 PRINT&6,3"Vasim ukolem bude rozeznat"
3070 PRINT&8,3"velikost konstant a a b."
3080 PRINT&9,14",";&9,25"v"
3090 PRINT&10,3"Program nabidne pro kazdou"
3100 PRINT&11,14"v    v"
3110 PRINT&12,3"konstantu tri moznosti"
3120 PRINT&13,26","
3130 PRINT&14,3"(>0,<0,=0). Vyberte spravnou"
3140 PRINT&15,8"vv";&15,19"v    v,"
3150 PRINT&16,3"odpoved a stisknete pri-"
3160 PRINT&17,6"v ,    v,"
3170 PRINT&18,3"slusne tlacitko. Nakonec"
3180 PRINT&19,4",";&19,22","
3190 PRINT&20,3"vas program ohodnoti."
3210 FOR K=0TO2
3220 FOR I=0TO2
3230 P=I:GOSUB20000:A(1,I+3*K+1)=INT(100*P)/100
3240 P=K:GOSUB20000:A(2,I+3*K+1)=INT(100*P)/100
3250 NEXT I
3260 NEXT K
3270 FOR I=1TO8
3280 P=INT((9-I)*RND(0)+1)
3290 A(3,I)=A(1,P):A(4,I)=A(2,P)
3300 FORK=P TO8-I
3310 A(1,K)=A(1,K+1):A(2,K)=A(2,K+1)
3320 NEXT K
3330 NEXT I
3340 A$="T"
3350 GOSUB11000
3360 PRINT&1,13",";&1,24"vv"
3370 PRINT&2,4"Vyber spravnou odpoved a"
3380 PRINT&3,13","
3390 PRINT&4,3"stiskni klavesu 1,2 nebo 3"
3400 RA=0:SL=1:S=29:V=5
3410 GOSUB10000
3420 SP=0
3430 FORL=1TO8
3440 AN=A(3,L):BN=A(4,L)
3450 GOSUB13000
3460 IFL=1THEN GOSUB14000:GOTO3480
3470 GOSUB15000
3480 A$="a":P=A
3490 GOSUB21000
3500 A$="b":P=B
3510 GOSUB21000
3520 NEXT L
3530 ERASE:CLS
3540 PRINT&10,10"ZHODNOCENI";&9,19","
3550 RA=8:SL=8:S=13:V=4
3560 GOSUB10000
3570 SP=INT(SP/16*100+.5)
3580 PRINT&13,5"v  ,  vv"
3590 PRINT&14,3"vase uspesnost: ";SP;"%"
3600 A$="M"
3610 GOSUB11000
3620 GOTO140
4000 REM HELP
4010 PRINT&1,7",  ,     ,  ,"
4020 PRINT&2,1"V- poda zakladni vyklad o"
4030 PRINT&3,8",  ,        ,"
4040 PRINT&4,4"linearnich funkcich a pro-"
4050 PRINT&5,12",      ,v  ,  v,"
4060 PRINT&6,4"bere s vami zvlastni pri-"
4070 PRINT&7,10","
4080 PRINT&8,4"pady teto funkce."
4090 PRINT&9,7",  ,";&9,28","
4100 PRINT&10,1"G- poda vyklad o grafu linea-"
4110 PRINT&11,6",        ,"
4120 PRINT&12,4"rnich funkci."
4130 PRINT&13,23","
4140 PRINT&14,1"K- dovoluje zobrazit vami zvo-"
4150 PRINT&15,7",     ,  ,"
4160 PRINT&16,4"lene linearni funkce."
4170 PRINT&17,15"v"
4180 PRINT&18,1"T- otestuje vase znalosti."
4190 PRINT&19,9"v  ,"
4200 PRINT&20,1"E- zakonceni programu."
4210 A$="M"
4220 GOSUB11000
4230 GOTO140
5000 REM KONEC
5010 PRINT&10,4"N A S H L E D A N O U"
5020 PRINT&15,17"IQ 151"
5030 WAIT(30)
5040 CLS
5050 END
10000 REM RAMECEK
10010 PRINT CHR$(15)&RA,SL"P";&RA+V,SL+S"J";
10020 FOR I= 1TO S-1
10030 PRINT CHR$(15)&RA,SL+I"Q";&RA+V,SL+S-I"Q";
10040 NEXT I
10050 PRINT CHR$(15)&RA,SL+S"_";&RA+V,SL"K";
10060 FOR I= 1TO V-1
10070 PRINT CHR$(15)&RA+I,SL+S"T";&RA+V-I,SL"T";
10080 NEXT I
10090 PRINT""
10100 RETURN
11000 REM STISKNI
11010 PRINT&29,17",";
11020 PRINT&30,7"Stiskni klavesu ";A$;CHR$(7);
11030 IF INKEY$<>A$ THEN GOTO11030
11040 CALLHEX(F973):CLS
11050 RETURN
12000 REM ODVOZENI
12010 PRINT&8,10"v"
12020 PRINT&9,3B$;") necht konstanta   ";C$;" = 0"
12030 WAIT(55)
12040 RA=8:SL=22:S=8:V=2
12050 GOSUB10000
12060 WAIT(15)
12070 PRINT&11,12"v            ,"
12080 PRINT&12,6"jestlize toto dosadime do"
12090 PRINT&13,11",             ,  ,"
12100 PRINT&14,6"obecne rovnice linearni"
12110 PRINT&16,6"funkce:"
12115 WAIT(50)
12120 PRINT&20,10"y = ax + b"
12130 WAIT(15)
12140 FOR I=1TO3
12150 PRINT&20,K;C$;
12160 WAIT(3)
12170 PRINT&20,K"0";
12180 WAIT(3)
12190 NEXT I
12200 WAIT(8)
12210 PRINT&20,K"    "
12220 RETURN
13000 REM VYPOCET
13010 Y1=-10*AN+BN:Y2=10*AN+BN:CH=0
13020 IF Y1>=10 AND Y2>=10 OR Y1<=-10 AND Y2<=-10 THEN AN=A:BN=B:CH=1:GOTO13080
13030 IF Y1<=10 AND Y1>=-10 THEN X=-10:Y=Y1:GOTO13050
13040 X=(10*SGN(Y1)-BN)/AN:Y=10*SGN(Y1)
13050 IF Y2<=10 AND Y2>=-10 THEN Z=10:W=Y2:GOTO13070
13060 Z=(10*SGN(Y2)-BN)/AN:W=10*SGN(Y2)
13070 A=AN:B=BN
13080 RETURN
14000 REM KRIZ
14010 LIMIT190,511,0,205
14020 PEN2:FRAME
14030 SCALE-12,12,-12,12
14040 DRAW0,-11,-2:DRAW0,11,-1
14050 DRAW-11,0,-2:DRAW11,0,-1
14060 DRAW8.5,-1,-2:DRAW9.5,-1,-1
14070 RDRAW-.4,.2,-1:RDRAW0,0,-1:RDRAW-.4,-.2,-1
14080 DRAW-1,8.5,-2:DRAW-1,9.5,-1
14090 RDRAW-.2,-.4,-1:RDRAW0,0,-1:RDRAW.2,-.4,-1
14100 DRAW9,-.5,-2:LTYPE1.5,1.5:LREF4:LROT0:LABEL"X"
14110 DRAW-1.5,9,-2:LROT PI/2:LABEL"Y":LROT 0
14120 FOR I=-10 TO 10 STEP2
14130 IF I=0 THEN GOTO14160
14140 DRAW I,.2,-2:DRAW I,-.2,-1:DRAW I,-.5,-2:LABEL I
14150 DRAW-.2,I,-2:DRAW.2,I,-1:DRAW-.5,I,-2:LABEL I
14160 NEXT I
14165 DRAW-.5,-.5,-2:LABEL 0
14170 PEN0
14180 DRAWX,Y,-2:DRAWZ,W,-1
14190 XS=X:YS=Y:ZS=Z:WS=W
14200 RETURN
15000 REM KRESLI
15010 DRAW X,Y,-2:DRAW Z,W,-1
15020 DRAW XS,YS,-2:DRAW ZS,WS,-1
15030 XS=X:YS=Y:ZS=Z:WS=W
15040 RETURN
16000 REM NAPIS FCI
16010 IF A=0 THEN PRINT&0,8"y = ";B;:GOTO16080
16020 IF A=1 THEN PRINT&0,8"y = x";:GOTO16050
16030 IF A=-1 THEN PRINT&0,8"y =-x";:GOTO16050
16040 PRINT&0,8"y =";A;"x";
16050 IF B=0 THEN GOTO16080
16060 IF B>0 THEN PRINT" +";B;:GOTO16080
16070 PRINT" -";-B;
16080 PRINT"                  "
16085 P=1
16090 IF A=0 THEN PRINT&1,4"        ,";&2,3"konstantni funkce"
16100 IF A=0 AND B=0 THEN PRINT&3,8",    ";&4,3"shodna s osou x    ":GOTO16160
16110 IF A=0 AND B<>0 THEN PRINT&3,8" vv ,";&4,3"rovnobezna s osou x":GOTO16160
16120 IF B=0 THEN PRINT&1,4"v, , , v ";&2,3"prima umernost   ":P=3
16130 FOR I=P TO4
16140 PRINT&I,3"                    "
16150 NEXT I
16160 RETURN
17000 REM INPUT
17010 PRINTCHR$(15)&K,2"D";CHR$(14);CHR$(7);
17020 I=1:T=1:L=1:C$=""
17030 I$=INKEY$
17035 IF I$="" THEN GOTO17030
17040 IF ASC(I$)=13 AND L>1 THEN GOTO17120
17050 IF I$="-" AND I=1 THEN GOTO17095
17060 IF I$="." AND T=1 THEN T=0:GOTO17095
17070 IF ASC(I$)>47 AND ASC(I$)<58 THEN L=L+1:GOTO17095
17075 IF NOT(ASC(I$)=8 AND I>1) THEN GOTO17030
17080 I$=MID$(C$,I-1,I-1):C$=MID$(C$,1,I-2):I=I-1:PRINT&K,3C$;" ";&K,I+2;
17083 IF ASC(I$)>47 AND ASC(I$)<58 THEN L=L-1
17087 IF I$="." THEN T=1
17090 GOTO17100
17095 CALLHEX(F973):C$=C$+I$:PRINT&K,3C$:I=I+1
17100 IF L>3 THEN GOTO17120
17105 IF INKEY$="" THEN GOTO17030
17110 GOTO17100
17120 P=VAL(C$):CALLHEX(F973)
17130 RETURN
18000 REM SMAZ
18010 FOR I=9TO18
18020 PRINT&I,0"           "
18030 NEXT I
18040 RETURN
19000 REM NEVEJDE
19005 GOSUB18000
19010 PRINT&10,1"GRAF SE"
19020 PRINT&12,0"NEVEJDE DO "
19030 PRINT&14,1"OSOVEHO";&13,5","
19040 PRINT&16,2"KRIZE";&15,3"v,v"
19050 CALLHEX(F973):WAIT(30)
19060 GOSUB18000
19070 RETURN
20000 REM NAHODA
20010 IF P=0 THEN P=-(8*RND(0)+1):GOTO20040
20020 IF P=1 THEN P=8*RND(0)+1:GOTO20040
20030 P=0
20040 RETURN
21000 REM MOZNOSTI
21010 PRINT&10,2"1) "A$;"<0"
21020 PRINT&12,2"2) "A$;"=0"
21030 PRINT&14,2"3) "A$;">0"
21040 I$=INKEY$
21050 IF I$="1"OR I$="2"OR I$="3" THEN CALLHEX(F973):GOTO21070
21060 GOTO21040
21070 IF P<0AND I$="1"OR P=0AND I$="2"OR P>0AND I$="3" THEN GOTO21090
21080 PRINT&15,1"v    ,";&16,1"spatna":GOTO21100
21090 PRINT&15,4",  ,";&16,1"spravna":SP=SP+1
21100 PRINT&17,6"vv";&18,1"odpoved"
21110 WAIT(20)
21120 GOSUB18000
21130 RETURN