PKPlXBHmimetypetext/x-wxmathmlPKPlXQdBV55 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. PKPlX content.xml Kedvenc Matematikai Kísérleteim Alapok Halmazok Számok Valós számok Természetes, egész és racionális számok Természetes számok Rekurziótétel Tétel Sorozatok Feladat kill(all); (%o0) done load("simplify_sum")$ (1) sum(i,i,1,n); simplify_sum(%); (%o2) i=1ni(%o3) n2+n2 (2) sum(i^2,i,1,n); simplify_sum(%); (%o4) i=1ni2(%o5) 2*n3+3*n2+n6 (3) sum(i*(i+1),i,1,n); simplify_sum(%); (%o6) i=1ni*

i+1

(%o7) 2*n3+3*n2+n6+n2+n2 ratsimp(%); (%o8) n3+3*n2+2*n3 (5) sum(i^3,i,1,n); simplify_sum(%); (%o9) i=1ni3(%o10) n4+2*n3+n24 (6) sum(i*(3*i+1),i,1,n); simplify_sum(%); (%o11) i=1ni*

3*i+1

(%o12) 2*n3+3*n2+n2+n2+n2 ratsimp(%); (%o13) n3+2*n2+n (7) sum(1/i/(i+1),i,1,n-1); simplify_sum(%); (%o14) i=1n−11i*

i+1

(%o15) n−1n (10) sum(q^i,i,1,n); simplify_sum(%); (%o16) i=1nqi(%o17) qn+1−qq−1 Feladat Feladat Feladat Feladat Feladat Feladat Feladat (3) sum((2*i+1)^2,i,1,n); simplify_sum(%); (%o18) i=1n

2*i+1

2(%o19) 4*n3+6*n2+2*n3+2*n2+3*n ratsimp(%); (%o20) 4*n3+12*n2+11*n3 (4) sum(i*i!,i,1,n); simplify_sum(%); (%o21) i=1ni*i!(%o22)

n+1

!−1 (5) sum((i-1)*i^2,i,1,n); simplify_sum(%); (%o23) i=1n

i−1

*i2(%o24) n4+2*n3+n24−2*n3+3*n2+n6 ratsimp(%); (%o25) 3*n4+2*n3−3*n2−2*n12 simpproduct:true; (%o33) true (6) product(1-1/(i+1)^2,i,1,n); (%o34) i=1n1−1

i+1

2 Feladat (1) sum((2*i-1),i,1,n); simplify_sum(%); (%o35) i=1n2*i−1(%o36) n2 (2) sum((-1)^(i+1)*i^2,i,1,n); simplify_sum(%); (%o37) i=1ni2*

−1

i+1(%o38) −n*

n+1

*

−1

n2 Feladat (1) sum(1/(i-3)/(i+1),i,4,n); simplify_sum(%); (%o39) i=4n1

i−3

*

i+1

(%o40) −

3−n

*

25*n3−23*n2−22*n+8

48*

n−2

*

n−1

*n*

n+1

 factor(%); (%o41)

n−3

*

25*n3−23*n2−22*n+8

48*

n−2

*

n−1

*n*

n+1

 ratsimp(%); (%o42) 25*n4−98*n3+47*n2+74*n−2448*n4−96*n3−48*n2+96*n expand(%); (%o43) 25*n448*n4−96*n3−48*n2+96*n−98*n348*n4−96*n3−48*n2+96*n+47*n248*n4−96*n3−48*n2+96*n+74*n48*n4−96*n3−48*n2+96*n−2448*n4−96*n3−48*n2+96*n factor(%);floor; (%o44)

n−3

*

25*n3−23*n2−22*n+8

48*

n−2

*

n−1

*n*

n+1

(%o45) floor Teleszkopikus összeg. (2) sum(1/i/(i+1)/(i+2),i,1,n); simplify_sum(%); (%o46) i=1n1i*

i+1

*

i+2

(%o47) n*

n+3

4*

n+1

*

n+2

 (3) Feladat Feladat Feladat Feladat Feladat Feladat Feladat log(2)/log(10.); (%o48) log

2

log

10

 c:float(%), numer; (%o49) 0.3010299956639811 c*300; (%o50) 90.30899869919435 Feladat 60/c; (%o51) 199.3156856932418 Feladat Feladat Feladat Motiváció: további rekurzív definíciók Általános rekurziótétel Példa: Fibonacci-számok fib(10); (%o52) 55 fibo(n):=block([],if equal(n,0) then return(0) else if equal(n,1) then return(1) else fibo(n-1)+fibo(n-2)); (%o53) fibo

n

:=block

[],if equal

n,0

 then return

0

 else if equal

n,1

 then return

1

 else fibo

n−1

+fibo

n−2

 fibo(10); (%o54) 55 fundef(fibo); (%o55) fibo

n

:=block

[],if equal

n,0

 then return

0

 else if equal

n,1

 then return

1

 else fibo

n−1

+fibo

n−2

 Feladat Feladat Feladat Feladat %phi; (%o56) %phi float(%), numer; (%o57) 1.618033988749895 %phi^1000/5^(1/2); (%o58) %phi10005 float(%), numer; (%o59) 4.346655768693734*10208 Feladat Feladat Feladat Szorzatok és összegek Az általános disztributivitás tétele Faktoriális, binomiális együttható binomial(z,5); (%o60)

z−4

*

z−3

*

z−2

*

z−1

*z120 Binomiális tétel Következmény Egész számok Hatványozás egész kitevővel Racionális számok Arkhimédészi tulajdonság Állítás Egész rész, maradék entier(%pi); (%o61) 3 fix(%pi); (%o62) 3 floor(%pi); (%o63) 3 ceiling(%pi); (%o64) 4 round(%e); (%o65) 3 truncate(%pi); (%o66) 3 mod(1.4,1.2); (%o67) 0.1999999999999999 Tétel Tétel: gyökvonás Következmény Állítás Állítás Bővített valós számok inf; minf; (%o68) inf(%o69) −inf Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat (1) mod(100,3); (%o70) 1 (2) mod(100,7); (%o71) 2 (3) mod(-100,7); (%o72) 5 (4) mod(-100,0); (%o73) −100 (5) mod(5,-3); (%o74) −1 (6) mod(18,-3); (%o75) 0 (7) mod(-2,-3); (%o76) −2 (8) mod(1.1,1); (%o77) 0.1 (9) mod(.11,.1); (%o78) 0.00999999999999999 (10) mod(.11,-0.1); (%o79) −0.09000000000000001 Feladat Feladat Feladat Feladat: öröknaptár Feladat Feladat Feladat Feladat (1) 1,0,-,1 etc. Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat PKPlXBHmimetypePKPlXQdBV55 5format.txtPKPlX content.xmlPKi