lehrkraefte:blc:math:maxima-cheatsheet [https://fginfo.ksbg.ch Fachgruppe Informatik der KSBG]

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====== Maxima Cheat Sheet ======

===== Solving exponential equations =====
Maximas solve cannot handle exponential equations. However, it converts them into a form which can be used further by taking the logarithm of both sides. Make sure to set 'logexpand' to 'all':
<code text>
f(x):=a*2^((x-2)/2)+2;
g(x):=b*3^((x-4)/5)+1;
solve(f(x)=g(x),x);
                                         x - 4
                              x - 2      -----
                              -----        5
                                2     b 3      - 1
(%o8)                       [2      = ------------]
                                           a

logexpand:all;
solve(log(solve(f(x)=g(x),x)),x);
                            x/5 - 4/5
                   2 log(b 3          - 1) - 2 log(a) + 2 log(2)
(%o11)        [x = ---------------------------------------------]
                                      log(2)

</code>
Und sonst halt mit ''find_root (expr, x, a, b)''
===== Output stuff like Maxima Input =====
<code txt>
(%i14) x^2/3;
                                       2
                                      x
(%o14)                                --
                                      3
(%i15) string(%);
(%o15)                               x^2/3
</code>

===== Derivative as a new function (force evaluating the differentiation) =====
<code txt>
f(x):=a*2^((x-2)/10)+2;
define(ff(x), diff(f(x),x));
</code>

===== Using results of solve for further computations =====
<code txt>
sol:solve(x^2-x-1=0,x);
x^2-x, sol[2];
expand(%);
val:x,sol[2];
/* Usable inside an expresseion: */
subst(sol[2],x);
</code>
Or even better:
<code text>
rhs(sol[2]);
map(rhs, sol);
</code>
===== Nummerically solve equations =====
[[https://maxima.sourceforge.io/docs/manual/maxima_116.html|Maxima doc]]
<code txt>
find_root(sin(2*x)=x,x,0.5,2);
</code>

===== Vector operations =====
<code maxima>
load("vect");
cross(u,v):=express(u ~ v);
norm(a):=sqrt(a.a);
area(a,b,c):=1/2*norm(cross(b-a,c-a));
vec2eq(eq):=makelist(rhs(eq)[i]=lhs(eq)[i], i, 1, length(rhs(eq)));
</code>

===== Binomial Distribution =====
<code maxima>
load("distrib");
pdf_binomial (25,500,0.03);   
cdf_binomial (25,500,0.03);
</code>