Maxima

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1 Maxima dbzhang Maxima Maxima kill ev

......................................... 7 3.3 ev.......................................... 7 4 8 4.1........................................ 8 4.2.................................... 9 4.3................................... 10 4.

2 Maxima Maxima Windows Linux Mac OS X Maxima Maxima Computer Algebra System, CAS Mathematica Maple Maxima Maxima Maxima Maxima Maxima CAS Macsyma CAS Maple, Mathematica Macsyma Maxima Maple Mathematica Maxima

Linux........................................... 18 7.3 Mac OS X......................................... 19 8...... 19 8.1....................................... 19 8.2.

3 2 3 Mathematica Maple Matlab 2 Maxima 2.1 Maxima Maxima (%i1) 1+1; (%o1) 2 (%i2) 3*4*7; (%o2) 84 (%i3) 9/3; (%o3) 3 (%i4) 7/3; (%o4) 7 3 (%i5) 1/2+2/3; (%o5) 7 6 (%o4) 7/3 Maxima Maxima (CAS) (%o5) float (%i6) float(7/3); (%o6)

4 2 4 (%i7) 2^10; (%o7) 1024 (%i8) sqrt(9); (%o8) 3 (%i9) 5!; (%o9) Maxima ; Maxima (%i10) 2+3$ (%i11) 2+3; (%o11) 5 CAS Matehmatica Maxima 2.3 Maxima Maxima quit(); quit quit() 2.4 %

2 Maxima ; Maxima (%i10) 2+3$ (%i11) 2+3;

5 2 5 (%i12) 7/3; (%o12) 7 3 (%i13) float(%); (%o13) Maxima (%i14) myresult:34+(65*72)/119; (%o14) (%i15) float(myresult); (%o14) Maxima e π e %e π %pi 2.6 Maxima (%i16) a: 37; (%o16) 37 (%i17) a; (%o17) 37 (%i18) b: *( ); (%o18) (%i19) a+b; (%o19) 24759

float(myresult); (%o14) 73.32773109243698 2.5 Maxima e π e %e π %pi 2.

6 Maxima (%i20) f(x) := 3*x^2 + 5; (%o20) f(x) := 3x (%i21) f(2); (%o21) 17 (%i22) g(x,y) := sin(x)*cos(y); (%o22) g(x, y) := sin(x) cos(y); (%i23) g(2*%pi,4); (%o23) 0 := Maxima inf (%i1) integrate(%e^(-x^2),x,0,inf); π (%o1) 2 Maxima Maxima (%i2) integrate(%e^(-x^2),x,0,inf); 1 (%o2) dx e x2 0

7 kill kill kill(all) (%i3) f(x) := 3*x^2 + 5; (%o3) f(x) := 3x (%i4) f(x); (%o4) 3x (%i5) kill(all); (%o5) done (%i6) f(x); (%o6) f(x) 3.3 ev Maxima ev, ev : (%i7) f: integrate(x^2,x) (%o7) x 2 dx (%i8) ev(f,integrate) (%o8) x3 3,, : (%i9) f: a*x^2 + b*x + c; (%o9) ax 2 + bx + c a = 1, b = 2, c = 8,,, f x 2 2x 8, a, b, c,, ev,,, a, b, c f :

2 + 5 (%i5) kill(all); (%o5) done (%i6) f(x); (%o6) f(x) 3.

8 4 8 (%i10) g: ev(f, a=1, b=-2, c=-8); (%o10) x 2 2x 8 (%i11) a; (%o11) a Maxima (%i1) A:matrix([1,2,3],[-2,8,3],[1,4,9]); (%o1) (%i2) v: [2,3,5]; (%o2) [2, 3, 5] (%i3) v: transpose([2,3,5]); 2 (%o3) 3 5 (%i4) v: matrix([2],[3],[5]]; 2 (%o4) 3 5

1 Maxima (%i1) A:matrix([1,2,3],[-2,8,3],[1,4,9]); 1 2 3 (%o1) 2 8

9 4 9, Maxima,, Maxima :,,,, 4.2 entry Maxima CAS (%i5) A: matrix([a[1,1],a[1,2]],[a[2,1],a[2,2]]); ( ) a1,1 a 1,2 (%o5) a 2,1 a 2,2 (%i6) c*a; ( ) a1,1 c a 1,2 c (%o6) a 2,1 c a 2,2 c A A entry (%i7) A: matrix([1,2,3],[-2,8,3],[1,4,9]); (%o7) (%i8) row(a,1); ( ) (%o8) (%i9) col(a,2); 2 (%o9) 8 4 (%i10) A[2,3]; (%o10) 3

10 A v (%i11) A.v; 23 (%o11) A, B A.B A*B A*B (%i12) w: [2,3,5]; (%o12) [2, 3, 5] (%i13) w.w; (%o13) 38 Maxima * (%i14) 2*A; (%o14) A A A^2 A^2 A entry A A A^^2 4.4, Maxima A

11 4 11 (%i15) transpose(a); (%o15) (%i16) determinant(a); (%o16) 54 (%i17) rank(a); (%o17) 3 i, j (minor), A i, j, minor: : (%i18) minor(a,1,1); ( ) 8 3 (%o18) 4 9 (cofactor) Maxima, cofactor (%i19) cofactor(m,i,j):=(-1)^(i+j)*determinant(minor(m,i,j)); (%o19) cofactor(m, i, j) := ( 1) i+j determinant(minor(m, i, j)) (%i20) cofactor(a,1,1); (%o20) 60 (classical adjoint matrix) (%i21) adjoint(a); (%o21) Maxima (%i22) invert(a); (%o22)

cofactor(m,i,j):=(-1)^(i+j)*determinant(minor(m,i,j)); (%o19) cofactor(m, i, j) := ( 1) i+j determinant(minor(m, i, j)) (%i20)

12 4 12 : (%i23) A^^(-1); (%o23) (%i24) echelon(a); (%o24) Maxima trace Maxima trace Maxima trace ncharl mattrace trace (%i25) load("ncharl"); ncharl (%i26) A: matrix([1,2,3],[2,2,1],[3,3,1]); (%o26) (%i27) mattrace(a); (%o27) 4

5 Maxima trace Maxima trace Maxima trace ncharl mattrace trace (%i25)

13 A, : (%i1) A: matrix([4,0,1],[2,3,2],[1,0,4]); (%o1) (%i2) eigenvalues(a); (%o2) [[5, 3], [1, 2]]... list 5 3 list, eigenvectors eigenvectors eigenvalues eigenvectors eigenvalues (%i3) eigenvectors(a); (%o3) [[[5, 3], [1, 2]], [1, 2, 1], [1, 0, 1], [0, 1, 0]] eigenvectors 5 3 mutiplicities [1, 2, 1] 3 [1, 0, 1] [0, 1, 0] 5.2 Maxima Maxima

14 5 14 (%i4) A: matrix([4,0,1],[2,3,2],[1,0,4]); (%o4) A ti (%i5) f: charpoly(a,t); (%o5) f : t + (3 t)(4 t) 2 3, f : (%i6) expand(f); (%o6) t t 2 39t + 45 f, A, : (%i7) factor(f); (%o7) (t 5)(t 3) 2 A 5 3 f = 0 solve (%i8) solve(f=0, t); (%o8) [t = 5, t = 3] 5.3 solve Maxima x + 2y + 3z = 6 2x 3y + 2z = 14 3x + y z = 2 solve

15 5 15 (%i9) eq1: x + 2*y + 3*z = 6; (%o9) x + 2y + 3z = 6 (%i10) eq2: 2*x - 3*y + 2*z = 14; (%o10) 2x 3y + 2z = 14 (%i11) eq3: 3*x + y - z = -2; (%o11) 3x + y z = 2 (%i12) solve([eq1, eq2, eq3],[x,y,z]); (%o12) [[x = 1, y = 2, z = 3]] 5.4, eigenvectors : (%i13) A: matrix([4,0,1],[2,3,2],[1,0,4]); (%o13) A 5 3, 3, v, (A 3I)v = 0 ident n n : (%i14) I: ident(3); (%o14) (%i15) v:[x,y,z]; (%o15) [x, y, z] (%i16) u: (A-3*I).v; z + x (%o16) 2z + 2x z + x

4, eigenvectors : (%i13) A: matrix([4,0,1],[2,3,2],[1,0,4]); 4 0 1 (%o13) 2 3 2 1 0 4 A 5 3, 3, v, (A 3I)v = 0 ident n n

16 5 16 x, y, z u, Maxima : (%i17) eq1: u[1,1]=0; (%o17) z + x = 0 (%i18) eq2: u[2,1]=0; (%o18) 2z + 2x = 0 (%i19) eq3: u[3,1]=0; (%o19) z + x = 0 (%i20) solve([eq1,eq2,eq3],[x,y,z]); (%o20) [[x = %r1, y = %r2, z = %r1]] %r1 %r2?,, x = t, y = s, z = t,,, ans, (%r1, %r2) (1, 0), (0, 1) : (%i21) ans: %; (%o21) [[x = %r1, y = %r2, z = %r1]] (%i22) ev(ans, %r1=1, %r2=0); (%o22) [[x = 1, y = 0, z = 1]] (%i23) ev(ans, %r1=0, %r2=1); (%o23) [[x = 0, y = 1, z = 0]] : v 1, v 2, ev (%i24) v1: ev([x,y,z], %o22) (%o24) [ 1, 0, 1] (%i25) v2: ev([x,y,z], %o23) (%o25) [0, 1, 0]

,, x = t, y = s, z = t,,, ans, (%r1, %r2) (1, 0), (0, 1) : (%i21) ans: %; (%o21) [[x = %r1, y = %r2, z = %r1]] (%i22) ev(ans, %r1=1, %r2=0);

17 6 MAXIMA 17 6 Maxima 6.1 Maxima plot2d 4x 3 2x 2 x -5 5 (%i1) plot2d([4 * x^3-2 * x-2],[x,-5,5]); 6.2 plot3d (%i2) plot3d(cos(-x^2+y^3/4),[x,-4,4], [y,-4,4]); Geomview UNIX Maxima Geomview 3D Geomview (%i3) plot3d(cos(-x^2+y^3/4),[x,-4,4], [y,-4,4], [plot_format,geomview]); Geomview 3D Maxima Maxima 3D 2D Geomview 6.3 Maxima (5.9.2 ) 6.4 (%i4) plot2d([cos(x), sin(x), tan(x)], [x, -2*%pi, 2*%pi], [y,-2,2])$ cos(x), sin(x) tan(x) 6.5, Maxima (%i5) plot2d([parametric, cos(t), sin(t), [t,-2*%pi,2*%pi], [nicks,80]]);

plot3d(cos(-x^2+y^3/4),[x,-4,4], [y,-4,4], [plot_format,geomview]); Geomview 3D Maxima Maxima 3D 2D Geomview 6.3 Maxima 5.9.2 (5.9.2 ) 6.

18 7 MAXIMA 18 7 Maxima Maxima Maxima Windows, Mac, Linux TeXmacs 7.1 Windows Windows Maxima xmaxima Maxima Windows xmaxima PC Linux Maxima Linux Maxima LiveCD Linux LiveCD CD Linux TeXmacs Linux Maxima LiveCD download ftp://math.cgu.edu.tw/pub/knoppix/ TeXmacs.iso DVD Windows wxmaxima xmaxima WinTeXmacs Windows Maxima WinTeXmacs 7.2 Linux Linux Maxima Maxima Maxima TeXmacs Maxima Geomview Maxima 3D TeXmacs Maxima session Maxima

TeXmacs Linux Maxima LiveCD download ftp://math.cgu.edu.tw/pub/knoppix/ TeXmacs.

19 Mac OS X Mac OS X UNIX Linux Apple X11 UNIX X-Windows Mac OS X aqua UNIX X-Windows TeXmacs LaTeX i-installer Fink Maxima, TeXmacs, Geomview: Geomview unstable Maxima LaTeX2HTML, Version (1.71) Copyright c 1993, 1994, 1995, 1996, Nikos Drakos, Computer Based Learning Unit, University of Leeds. Copyright c 1997, 1998, 1999, Ross Moore, Mathematics Department, Macquarie University, Sydney. CJK CJK LaTeX2HTML taiwan.perl 8.2 Maxima dbzhang

..... 8.1 Maxima LaTeX2HTML, Version 2002-2-1 (1.

maxima report

maxima report 1. 安裝步驟 http://maxima.sourceforge.net/ Download Sourceforge download page Maxima-Windows 5.19.2-Windows Maxima-5.19.2.exe 2.Maxima 簡介 Maxima 是一個所謂的電腦代數系統 (Computer Algebra System, CAS),