Linux下的数学工具Maxima 简明教程（下）

三角运算
(%i1) trigexpand(sin(10*x+y)); (%o1) cos(10 x) sin(y) + sin(10 x) cos(y) (%i2) trigexpand(sin(2*x)); (%o2) 2 cos(x) sin(x) (%i3) trigsimp(2*cos(x)^2+sin(x)^2); 2 (%o3) cos (x) + 1 (%i4) trigreduce(-sin(x)^2+3*cos(x)^2+x); cos(2 x) cos(2 x) 1 1 (%o4) -------- + 3 (-------- + -) + x - - 2 2 2 2

代数推理
(%i1) assume(x>0,y<-1,z>=0); (%o1) [x > 0, y < - 1, z >= 0] (%i2) assume(a<b and b<c); (%o2) [b > a, c > b] (%i3) facts(); (%o3) [x > 0, - 1 > y, z >= 0, b > a, c > b] (%i4) is(a>c); (%o4) false (%i5) is(z-y>0); (%o5) true (%i6) is(z-x>0);

Maxima was unable to evaluate the predicate: z - x > 0 -- an error. Quitting. To debug this try debugmode(true); (%i7) prederror:false; (%o7) false (%i8) is(z-x>0); (%o8) unknown (%i9) forget(a<b); (%o9) [b > a] (%i10) is(a>c); (%o10) unknown

级数计算
(%i1) sum(i,i,1,5); (%o1) 15 (%i2) sum(i^2,i,1,5); (%o2) 55 (%i3) sum(1/2^i,i,1,inf); inf ==== 1 (%o3) > -- / i ==== 2 i = 1 (%i4) sum(1/2^i,i,1,inf),simpsum; (%o4) 1 (%i5) sum(1/i^2,i,1,inf),simpsum; 2 %pi (%o5) ---- 6 (%i6) sum(1/i,i,1,inf),simpsum; (%o6) inf

微积分
(%i1) limit(1/x,x,inf); (%o1) 0 (%i2) limit(sin(x)/x,x,0); (%o2) 1 (%i3) limit(sin(x),x,inf); (%o3) &n bsp; ind (%i4) diff(3*x^2+x+5/x,x); 5 (%o4) 6 x - -- + 1 2 x (%i5) diff(sin(x)*tan(x),x); 2 (%o5) cos(x) tan(x) + sec (x) sin(x) (%i6) diff(%e^(a*x),x); a x (%o6) a %e (%i7) integrate(sin(x)^3,x); 3 cos (x) (%o7) ------- - cos(x) 3 (%i8) integrate(x^3,x,1,3); (%o8) 20 (%i9) taylor(%e^x,x,0,3); 2 3 x x (%o9)/T/ 1 + x + -- + -- + . . . 2 6 (%i10) taylor(sin(x),x,0,5); 3 5 x x (%o10)/T/ x - -- + --- + . . . 6 120 (%i11) taylor(sqrt(x+1),x,1,3); 2 3 sqrt(2) (x - 1) sqrt(2) (x - 1) sqrt(2) (x - 1) (%o11)/T/ sqrt(2) + --------------- - ---------------- + ---------------- 4 32 128 + . . . (%i12) ratsimp(%); 3 2 sqrt(2) x - 7 sqrt(2) x + 43 sqrt(2) x + 91 sqrt(2) (%o12) ----------------------------------------------------- 128

矩阵运算
(%i1) f[i,j]:=i+j; (%o1) f := i + j i, j (%i2) genmatrix(f,3,3); [ 2 3 4 ] [ ] (%o2) &nbs p; [ 3 4 5 ] [ ] [ 4 5 6 ] (%i3) g[i,j]:=i-2^j; j (%o3) g := i - 2 i, j (%i4) genmatrix(g,3,3); [ - 1 - 3 - 7 ] [ ] (%o4) [ 0 - 2 - 6 ] [ ] [ 1 - 1 - 5 ] (%i5) %o2+%o4; [ 1 0 - 3 ] [ ] (%o5) [ 3 2 - 1 ] [ ] [ 5 4 1 ] (%i6) %o2.%o4; [ 2 - 16 - 52 ] [ ] (%o6) [ 2 - 22 - 70 ] [ ] [ 2 - 28 - 88 ] (%i7) %o2^^3; [ 360 474 588 ] [ ] (%o7) [ 474 624 774 ] [ ] [ 588 774 960 ] (%i8) x:matrix([17, 3],[-8, 11]); [ 17 3 ] (%o8) [ ] [ - 8 11 ] (%i9) x^^-1; [ 11 3 ] [ --- - --- ] [ 211 211 ] (%o9) [ ] [ 8 17 ] &n bsp; [ --- --- ] [ 211 211 ]