* solve two equations with two unknowns

  eq1: 1/x + 1/y = 1/1200;
  eq2: 1.8 * (x / (x + y)) = 0.45;

  ans : solve([eq1, eq2], [x, y]);

  *** Note : you could put this into a ".mac" file and then

      load("junk.mac");


* Normal Distribution

  f(x) := (1/(sqrt(2*%pi))) * exp(-x^2/2);

  F(x) := integrate(f(u), u, minf, x);

  ratsimp(F(x));


  F1(x) := (1 + erf(x/sqrt(2)))/2;


  ratsimp(F(x) - F1(x));




* numer : true;


* sinc(x) does not exist

  here are a few tips

  sinc(x) := sin(x) / x;

  sinc(%pi);
  sinc(%pi/2);
  limit(sinc(x), x, 0);
  limit(sinc(x), x, inf);





* Online Manual

  http://maxima.sourceforge.net/docs/manual/maxima_singlepage.html
  
  https://flex.phys.tohoku.ac.jp/texi/Maxima%205.38.1%20Manual.htm#SEC7

  http://maxima.sourceforge.net/docs/manual/maxima.html



* save stuff to file


  load("f90");

  f90_output_line_length_max : 200;

  with_stdout("crap.txt",
    f90('Gc=Gc),
    f90('Gd=Gd)
  );



* always start with "rmaxima" to get use of arrow keys
  (new versions of maxima don't have rmaxima, but already have commandline editing support)
  (it seems like rmaxima is something like rlwrap -c rmaxima)
  (in any case, rmaxima is no longer needed on new installations of maxima)


* useful functions

  /* numerator */
  num(expr);

  /* denominator */
  denom(expr);

  /* derivative */
  diff(f(x), x);


  /* extremely useful to generally simplify an expression */
  factor(expr);

  ratsimp(expr);

  subst([var1=expr1, var2=expr2], expr);

  linel : 200;

  grind(expr)


   


* ************************************************
* You can cause variable to be "rehashed" with ''
* ************************************************

  bob : gm1 + gm2;

  gm1 : 1/Rx;

  bob
    --> gm1 + gm2

  ''bob
                  1
    -->    gm2 + ---
                  R2
* ************************************************




* ***********************************
* plot a complex function
* ***********************************
h(x) := (1 - %e^(-%i*x*4)) / (1 - %e^(-%i*x));


plot2d(cabs(h(x)), [x, 0, 20]);

plot2d(carg(h(x)), [x, 0, 20]);


* ***********************************
* Solve a simple differential equation
* ***********************************

eq : 'diff(y, t, 1) + 3*y = 0;

sol : ode2(eq, y, t);

ans : ic1(sol, t=0, y = 6);



* ***********************************
* define some functions - put in funcdef.mac
* ***********************************
  if (t < -1) then
    0
  elseif (t < 1) then
    t
  elseif (t < 2) then
    1
  elseif (t < 3) then
    3 - t
  else 
    0
);


u(t) := block([],
  if (t < 0) then
    0
  else
    1
);



mkdir wwmax
cd wwmax

wget http://gregbox.org/funcdef.mac


maxima
load("funcdef.mac")


plot2d(x(t-2), [t, -2, 6], [y, -2, 2], [title, "1 a"]);

plot2d(x(-2*t-1), [t, -4, 2], [y, -2, 2], [title, "1 b"]);

plot2d((x(t)-x(-t))*u(t), [t, -4, 2], [y, -2, 2], [title, "1 d"]);




* ***********************************
* Simple flow to run
* ***********************************

  mkdir wwmax
  cd wwmax
  maxima

  plot2d(sin(x), [x, 0, 6.28]);



* ***********************************


* ***********************************
* To get help on something :
* ***********************************
    ? stringout;

  or

    ?? stringout;
* ***********************************



* **************************
* special constants
* **************************
  %i --> sqrt(-1)
  %e --> natural log base
  %pi --> pi
* **************************



* ***************************
* Useful functions
* ***************************
  realpart(%);
  imagpart(%);

  expand (%);

  ratsimp (%);

  factor (%);

  solve([%o6, %o7, %o8], [a, b, c]);

  trigexpand (%);

  trigreduce (%);

  diff (f, x);
  integrate (f, x);
  integrate (f, x, 1, inf);

  quit();
* ***************************



* ****************************************
* To give the numeric result of something

* ****************************************
  float(x)
* ****************************************



* ****************************************
* For extended numeric precision
* (not useful for outputing to other programs)
* ****************************************
  fpprec;

  fpprec : 100;

  bfloat(%);
* ****************************************



* ****************************************
* Small example of manipulating equations
* ****************************************
  (x + 1) / (x - 1);

  %, x=2/z;

  ratsimp(%);
* ****************************************



* ****************************************
* Basic 2D Plot
* ****************************************
  plot2d(sin(x), [x, 0, 4*%pi]);
* ****************************************