MaximaNotes

Maxima 笔记

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Cheat Sheet

http://www.math.harvard.edu/computing/maxima/

Number Theory

expand((x+y)^6);
factor(x^6-1);
factor(123412341231234);
factor(2^(2^5)+1);
100!;
bfloat(%pi);
block([fpprec:1000],bfloat(%pi));
cfdisrep([1,2,3,5,2]);
bfloat(%);

Programming

for a:-3 thru 26 step 7 do ldisplay(a);

s:0; for i:1 while i<=10 do s:s+i; done; s;

fib[0]:0; fib[1]:1; fib[n]:=fib[n-1]+fib[n-2];
fib[20];

Plotting

plot2d(sin(x)/x,[x,-5,5]);
plot3d(sin(sqrt(x^2+y^2))/sqrt(x^2+y^2),[x,-12,12],[y,-12,12]);
plot3d([cos(y)*(10.0+6*cos(x)),sin(y)*(10.0+6*cos(x)),-6*sin(x)],
       [x,0,2*%pi],[y,0,2*%pi],['grid,40,40]);
plot3d([5*cos(x)*(cos(x/2)*cos(y)+sin(x/2)*sin(2*y)+3.0)-10.0,
       -5*sin(x)*(cos(x/2)*cos(y)+sin(x/2)*sin(2*y)+3.0),
        5*(-sin(x/2)*cos(y)+cos(x/2)*sin(2*y))],
       [x,-%pi,%pi],[y,-%pi,%pi],['grid,40,40]);
plot2d(sec(x),[x,-2,2],[y,-20,20],[nticks,200]);
plot2d([parametric,cos(t),sin(t),[t,-%pi*2,%pi*2]]);
plot2d([x^3+2,[parametric,cos(t),sin(t),[t,-5,5]]], [x,-3,3]);

Differentiation and Integration

diff(sin(x^2));
'integrate(%E**sqrt(a*y),y,0,4);
integrate(%E**sqrt(a*y),y,0,4);
integrate(sin(x),x);
sum((1/2)^i,i,0,inf);
laplace(delta(T-A)*sin(B*T),T,S);

Limits

limit( (5*x+1)/(3*x-1),x,inf);

Ordinary Differential Equations

depends(y,x);
diff(y,x)=(4-2*x)/(3*y^2-5);
ode2(%,y,x);
latex(%);

Solving Linear Equations

linsolve( [3*x+4*y=7, 2*x+4*y=13], [x,y]);
eq1: x^2 + 3*x*y + y^2 = 0;
eq2: 3*x + y = 1;
solve([eq1, eq2]);

Working with Matrices

a: matrix([1,2],[3,4]);
b: matrix([2,2],[2,2]);
a.b;
h[i,j]:=1/(i+j);
a: genmatrix(h,3,3);
determinant(a);
b: matrix([2,3],[5,6]);
echelon(b);
invert(b);
eigenvectors(b);

Working with Files

load(file);

Interrupting computation

factor(2^(2^7)+1);
 c
MAXIMA>>:q

Quitting Maxima

quit();

Other Cheat Sheets

• http://www.hippasus.com/resources/symmath/maximasym.html

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