PKÁSlXñB–Hmimetypetext/x-wxmathmlPKÁSlXQdBV55 format.txt This file contains a wxMaxima session in the .wxmx format. .wxmx files are .xml-based files contained in a .zip container like .odt or .docx files. After changing their name to end in .zip the .xml and eventual bitmap files inside them can be extracted using any .zip file viewer. The reason why part of a .wxmx file still might still seem to make sense in a ordinary text viewer is that the text portion of .wxmx by default isn't compressed: The text is typically small and compressing it would mean that changing a single character would (with a high probability) change big parts of the whole contents of the compressed .zip archive. Even if version control tools like git and svn that remember all changes that were ever made to a file can handle binary files compression would make the changed part of the file bigger and therefore seriously reduce the efficiency of version control wxMaxima can be downloaded from https://github.com/wxMaxima-developers/wxmaxima. It also is part of the windows installer for maxima (https://wxmaxima-developers.github.io/wxmaxima/). If a .wxmx file is broken but the content.xml portion of the file can still be viewed using an text editor just save the xml's text as "content.xml" and try to open it using a recent version of wxMaxima. If it is valid XML (the XML header is intact, all opened tags are closed again, the text is saved with the text encoding "UTF8 without BOM" and the few special characters XML requires this for are properly escaped) chances are high that wxMaxima will be able to recover all code and text from the XML file. PKÁSlX›%”³ÅùÅù content.xml Kedvenc Matematikai Kísérleteim Alapok Halmazok Számok Valós számok Természetes, egész és racionális számok Megszámlálható halmazok Komplex számok Polinomok Jelölés Polinomok és racionális törtfüggvények kill(all); (%o0) done f:-15+3*x+5*x^2+7*x^5; (%o1) 7*x5+5*x2+3*x−15 subst(0,x,f); subst(1,x,f); (%o2) −15(%o3) 0 x^0; (%o4) 1 g:(x-4)+(x-4)^2+(x-4)^3; (%o5) x+

x−4

3
+

x−4

2
−4
ratsimp(%); (%o6) x3−11*x2+41*x−52 h:f/g; (%o7) 7*x5+5*x2+3*x−15x+

x−4

3
+

x−4

2
−4
subst(0,x,h); subst(4,x,h); (%o12) 1552expt: undefined: 0 to a negative exponent. -- an error. To debug this try: debugmode(true); ratnum(h); ratdenom(h); (%o14)/R/ 7*x5+5*x2+3*x−15(%o15)/R/ x3−11*x2+41*x−52 A maradédos osztás tétele polinomokra divide(f,g,x); (%o12) [7*x2+77*x+560,3372*x2−18953*x+29105] %[1]*g+%[2]; (%o13)

x+

x−4

3+

x−4

2
−4

*

7*x2+77*x+560

+3372*x2−18953*x+29105
expand(%); (%o14) 7*x5+5*x2+3*x−15 remainder(f,g,x); (%o15) 3372*x2−18953*x+29105 quotient(f,g,x); (%o16) 7*x2+77*x+560 Következmény: Horner-elrendezés horner(f); (%o17) x*

x*

7*x3+5

+3

−15
Következmény: gyöktényező leválasztása g:expand(g); (%o18) x3−11*x2+41*x−52 divide(g,x-4,x); (%o19) [x2−7*x+13,0] Következmény allroots(g); (%o20) [x=0.866025403784445*%i+3.499999999999998,x=3.499999999999998−0.866025403784445*%i,x=4.000000000000003] Következmény Polinomok egyértelmű felírása hipow(f,x); (%o21) 5 coeff(f,x,5); coeff(f,x,4); (%o22) 7(%o23) 0 A maradékos osztás egyértelműsége Többszörös gyökök Az algebra alaptétele allroots(f); (%o24) [x=1.0,x=0.6362775042581322*%i−0.9886660570244886,x=−0.6362775042581322*%i−0.9886660570244886,x=1.145166374451875*%i+0.4886660570244886,x=0.4886660570244886−1.145166374451875*%i] solve(f,x); (%o25) [x=−2252*7*252*

387521*%i98*3−14952646

23
−105*

387521*%i98*3−14952646

13
+604

387521*%i98*3−14952646

13
−

387521*%i98*3−14952646

13
−15163*

387521*%i98*3−14952646

13
−56
2
−252*

387521*%i98*3−14952646

23
−105*

387521*%i98*3−14952646

13
+604

387521*%i98*3−14952646

13
12*7
+−14,x=2252*7*252*

387521*%i98*3−14952646

23
−105*

387521*%i98*3−14952646

13
+604

387521*%i98*3−14952646

13
−

387521*%i98*3−14952646

13
−15163*

387521*%i98*3−14952646

13
−56
2
−252*

387521*%i98*3−14952646

23
−105*

387521*%i98*3−14952646

13
+604

387521*%i98*3−14952646

13
12*7
+−14,x=−−2252*7*252*

387521*%i98*3−14952646

23
−105*

387521*%i98*3−14952646

13
+604

387521*%i98*3−14952646

13
−

387521*%i98*3−14952646

13
−15163*

387521*%i98*3−14952646

13
−56
2
+252*

387521*%i98*3−14952646

23
−105*

387521*%i98*3−14952646

13
+604

387521*%i98*3−14952646

13
12*7
+−14,x=−2252*7*252*

387521*%i98*3−14952646

23
−105*

387521*%i98*3−14952646

13
+604

387521*%i98*3−14952646

13
−

387521*%i98*3−14952646

13
−15163*

387521*%i98*3−14952646

13
−56
2
+252*

387521*%i98*3−14952646

23
−105*

387521*%i98*3−14952646

13
+604

387521*%i98*3−14952646

13
12*7
+−14,x=1]
Gyöktényezős előállítás factor(f); (%o26)

x−1

*

7*x4+7*x3+7*x2+12*x+15

factor(g); (%o27)

x−4

*

x2−7*x+13

Lagrange-interpoláció load("interpol")$ lagrange([[2,4],[5,6],[9,3]]); (%o29) 3*

x−5

*

x−2

28
−

x−9

*

x−2

2
+4*

x−9

*

x−5

21
Többváltozós polinomok és racionális törtfüggvények f:(x+y)*(x-y)*(z^2-x^2); f:expand(f); (%o30)

x−y

*

y+x

*

z2−x2

(%o31) −y2*z2+x2*z2+x2*y2−x4
coeff(f,x,2); coeff(%,y,2); (%o32) z2+y2(%o33) 1 Feladat kill(all); (%o0) done 8*21; (%o1) 168 3*(-13)+5*6+(-11)*13+7*16; (%o2) −40 3*13; (%o3) 39 3*16; (%o4) 48 0; (%o5) 0 Feladat (1) divide(42*x^4-7*x^3+13*x^2+43*x-12, x^2-x-1); (%o6) [42*x2+35*x+90,168*x+78] (2) divide(x^3-3*x^2-x-1,3*x^2-2*x+1); (%o7) [3*x−79,−26*x+29] (3) divide(5*x^4+2*x-3,2*x^2-3*x+4); (%o8) [20*x2+30*x+58,−89*x+448] (4) divide(x^3,2*x+3); (%o9) [4*x2−6*x+98,−278] (5) divide(x^2+3*x-2,6*x^4+5*x^2-3*x+2); (%o10) [0,x2+3*x−2] (6) divide(x^3+x^2+3*x+2,2*x^2+4); (%o11) [x+12,x] Feladat kill(all); (%o0) done divide(x^4+3*x^2+a*x+b,x^2-2*a*x+2,x); (%o1) [x2+2*a*x+4*a2+1,

8*a3−a

*x+b−8*a2−2]
solve([8*a^3-a,b-8*a^2-2],[a,b]); (%o2) [[a=0,b=2],[a=−1232,b=3],[a=1232,b=3]] Feladat Feladat (1) remainder(x^4-3*x^3+6*x^2-10*x+16,x-4); (%o3) 136 (2) remainder(x^5+(1+%i)*x^4-(1+3*%i)*x^2+7, x+2+%i); (%o4) 23−37*%i (3) remainder(x^4-3*%i*x^3-4*x^2+5*%i*x-1, x-1-2*%i); (%o5) −2*%i−12 Feladat (1) g:x+1; (%o6) x+1 divide(x^4+2*x^3-3*x^2-4*x+1,g); (%o7) [x3+x2−4*x,1] divide(%[1],g); (%o8) [x2−4,4] divide(%[1],g); (%o9) [x−1,−3] divide(%[1],g); (%o10) [1,−2] 1*g^4-2*g^3-3*g^2+4*g+1; (%o11)

x+1

4
−2*

x+1

3
−3*

x+1

2
+4*

x+1

+1
expand(%); (%o12) x4+2*x3−3*x2−4*x+1 (2) g:x-1; (%o13) x−1 divide(x^5,g); (%o14) [x4+x3+x2+x+1,1] divide(%[1],g); (%o15) [x3+2*x2+3*x+4,5] divide(%[1],g); (%o16) [x2+3*x+6,10] divide(%[1],g); (%o17) [x+4,10] divide(%[1],g); (%o18) [1,5] 1*g^5+5*g^4+10*g^3+10*g^2+5*g+1; (%o19) 5*

x−1

+

x−1

5
+5*

x−1

4
+10*

x−1

3
+10*

x−1

2
+1
expand(%); (%o20) x5 Feladat kill(all); (%o0) done load("interpol")$ (1) n:2; makelist([k*%pi/2/n,sin(k*%pi/2/n)],k,-n,n); (%o2) 2(%o3) [[−%pi2,−1],[−%pi4,−12],[0,0],[%pi4,12],[%pi2,1]] L2:lagrange(%); (%o4) 32*x*

x−%pi4

*

x+%pi4

*

x+%pi2

3*%pi4
−2132*x*

x−%pi2

*

x+%pi4

*

x+%pi2

3*%pi4
+2132*x*

x−%pi2

*

x−%pi4

*

x+%pi2

3*%pi4
−32*x*

x−%pi2

*

x−%pi4

*

x+%pi4

3*%pi4
n:3; makelist([k*%pi/2/n,sin(k*%pi/2/n)],k,-n,n); (%o5) 3(%o6) [[−%pi2,−1],[−%pi3,−32],[−%pi6,−12],[0,0],[%pi6,12],[%pi3,32],[%pi2,1]] L3:lagrange(%); (%o7) 324*x*

x−%pi3

*

x−%pi6

*

x+%pi6

*

x+%pi3

*

x+%pi2

5*%pi6
−4*3112*x*

x−%pi2

*

x−%pi6

*

x+%pi6

*

x+%pi3

*

x+%pi2

5*%pi6
+486*x*

x−%pi2

*

x−%pi3

*

x+%pi6

*

x+%pi3

*

x+%pi2

%pi6
−486*x*

x−%pi2

*

x−%pi3

*

x−%pi6

*

x+%pi3

*

x+%pi2

%pi6
+4*3112*x*

x−%pi2

*

x−%pi3

*

x−%pi6

*

x+%pi6

*

x+%pi2

5*%pi6
−324*x*

x−%pi2

*

x−%pi3

*

x−%pi6

*

x+%pi6

*

x+%pi3

5*%pi6
n:4; makelist([k*%pi/2/n,sin(k*%pi/2/n)],k,-n,n); (%o8) 4(%o9) [[−%pi2,−1],[−3*%pi8,−sin

3*%pi8

],[−%pi4,−12],[−%pi8,−sin

%pi8

],[0,0],[%pi8,sin

%pi8

],[%pi4,12],[3*%pi8,sin

3*%pi8

],[%pi2,1]]
L4:lagrange(%); (%o10) 131072*x*

x−3*%pi8

*

x−%pi4

*

x−%pi8

*

x+%pi8

*

x+%pi4

*

x+3*%pi8

*

x+%pi2

315*%pi8
−1048576*sin

3*%pi8

*x*

x−%pi2

*

x−%pi4

*

x−%pi8

*

x+%pi8

*

x+%pi4

*

x+3*%pi8

*

x+%pi2

315*%pi8
+2372*x*

x−%pi2

*

x−3*%pi8

*

x−%pi8

*

x+%pi8

*

x+%pi4

*

x+3*%pi8

*

x+%pi2

45*%pi8
−1048576*sin

%pi8

*x*

x−%pi2

*

x−3*%pi8

*

x−%pi4

*

x+%pi8

*

x+%pi4

*

x+3*%pi8

*

x+%pi2

45*%pi8
+1048576*sin

%pi8

*x*

x−%pi2

*

x−3*%pi8

*

x−%pi4

*

x−%pi8

*

x+%pi4

*

x+3*%pi8

*

x+%pi2

45*%pi8
−2372*x*

x−%pi2

*

x−3*%pi8

*

x−%pi4

*

x−%pi8

*

x+%pi8

*

x+3*%pi8

*

x+%pi2

45*%pi8
+1048576*sin

3*%pi8

*x*

x−%pi2

*

x−3*%pi8

*

x−%pi4

*

x−%pi8

*

x+%pi8

*

x+%pi4

*

x+%pi2

315*%pi8
−131072*x*

x−%pi2

*

x−3*%pi8

*

x−%pi4

*

x−%pi8

*

x+%pi8

*

x+%pi4

*

x+3*%pi8

315*%pi8
plot2d([sin(x),L2,L3,L4],[x,-%pi/2,%pi/2])$ plot2d([L2-sin(x),L3-sin(x),L4-sin(x)], [x,-%pi/2,%pi/2])$ (2) n:2; makelist([k*%pi/2/n,sin(2*k*%pi/2/n)],k,-n,n); (%o13) 2(%o14) [[−%pi2,0],[−%pi4,−1],[0,0],[%pi4,1],[%pi2,0]] L2:lagrange(%); (%o15) 128*x*

x−%pi2

*

x−%pi4

*

x+%pi2

3*%pi4
−128*x*

x−%pi2

*

x+%pi4

*

x+%pi2

3*%pi4
n:3; makelist([k*%pi/2/n,sin(2*k*%pi/2/n)],k,-n,n); (%o16) 3(%o17) [[−%pi2,0],[−%pi3,−32],[−%pi6,−32],[0,0],[%pi6,32],[%pi3,32],[%pi2,0]] L3:lagrange(%); (%o18) −4*3112*x*

x−%pi2

*

x−%pi6

*

x+%pi6

*

x+%pi3

*

x+%pi2

5*%pi6
+2*3112*x*

x−%pi2

*

x−%pi3

*

x+%pi6

*

x+%pi3

*

x+%pi2

%pi6
−2*3112*x*

x−%pi2

*

x−%pi3

*

x−%pi6

*

x+%pi3

*

x+%pi2

%pi6
+4*3112*x*

x−%pi2

*

x−%pi3

*

x−%pi6

*

x+%pi6

*

x+%pi2

5*%pi6
n:4; makelist([k*%pi/2/n,sin(2*k*%pi/2/n)],k,-n,n); (%o19) 4(%o20) [[−%pi2,0],[−3*%pi8,−12],[−%pi4,−1],[−%pi8,−12],[0,0],[%pi8,12],[%pi4,1],[3*%pi8,12],[%pi2,0]] L4:lagrange(%); (%o21) −2392*x*

x−%pi2

*

x−%pi4

*

x−%pi8

*

x+%pi8

*

x+%pi4

*

x+3*%pi8

*

x+%pi2

315*%pi8
+524288*x*

x−%pi2

*

x−3*%pi8

*

x−%pi8

*

x+%pi8

*

x+%pi4

*

x+3*%pi8

*

x+%pi2

45*%pi8
−2392*x*

x−%pi2

*

x−3*%pi8

*

x−%pi4

*

x+%pi8

*

x+%pi4

*

x+3*%pi8

*

x+%pi2

45*%pi8
+2392*x*

x−%pi2

*

x−3*%pi8

*

x−%pi4

*

x−%pi8

*

x+%pi4

*

x+3*%pi8

*

x+%pi2

45*%pi8
−524288*x*

x−%pi2

*

x−3*%pi8

*

x−%pi4

*

x−%pi8

*

x+%pi8

*

x+3*%pi8

*

x+%pi2

45*%pi8
+2392*x*

x−%pi2

*

x−3*%pi8

*

x−%pi4

*

x−%pi8

*

x+%pi8

*

x+%pi4

*

x+%pi2

315*%pi8
plot2d([sin(2*x),L2,L3,L4],[x,-%pi/2,%pi/2])$ plot2d([L2-sin(2*x),L3-sin(2*x),L4-sin(2*x)], [x,-%pi/2,%pi/2])$ (3) n:2; makelist([k/n,abs(k/n)],k,-n,n); (%o24) 2(%o25) [[−1,1],[−12,12],[0,0],[12,12],[1,1]] L2:lagrange(%); (%o26) 2*

x−12

*x*

x+12

*

x+1

3
−4*

x−1

*x*

x+12

*

x+1

3
−4*

x−1

*

x−12

*x*

x+1

3
+2*

x−1

*

x−12

*x*

x+12

3
n:3; makelist([k/n,abs(k/n)],k,-n,n)$ (%o27) 3 L3:lagrange(%)$ n:4; makelist([k/n,abs(k/n)],k,-n,n)$ (%o30) 4 L4:lagrange(%)$ n:10; makelist([k/n,abs(k/n)],k,-n,n)$ (%o33) 10 L10:lagrange(%)$ plot2d([abs(x),L2,L3,L4],[x,-1,1])$ plot2d([abs(x),L10],[x,-1,1])$
PKÁSlXñB–HmimetypePKÁSlXQdBV55 5format.txtPKÁSlX›%”³ÅùÅù ’content.xmlPK§€