Observatorio-de-Matematica

/*
You can run this file with

maxima -b cosine-rule.mac

or maybe also using M-x quickrun
*/

/*

Observatorio-de-Matematica

(%i1) eq1: a = b + c /d;
                                       c
(%o1)                              a = - + b
                                       d
(%i2) eq2: e = b - c*d;
(%o2)                             e = b - c d
(%i3) eliminate([eq1, eq2], [b]);
                                              2
(%o3)                     [(- d (e - a)) - c d  - c]
(%i4) expand(%);

Observatorio-de-Matematica

(%i1) t: matrix([%t^3],[%t^2],[%t],[1])
;
                                                                              [   3 ]
                                                                              [ %t  ]
                                                                              [     ]
                                                                              [   2 ]
(%o1)                                                                         [ %t  ]
                                                                              [     ]
                                                                              [ %t  ]
                                                                              [     ]

Observatorio-de-Matematica

(%i1) eqn:I12 = I11*(((-d)+3)/(pp-4*m2))+I10*((d-2)/((2*m2)*pp-8*m2^2))
                              I10 (d - 2)     I11 (3 - d)
(%o1)                 I12 = --------------- + -----------
                                          2    pp - 4 m2
                            2 m2 pp - 8 m2
(%i2) sol:solve(eqn,[I10])
                                         2
                   2 I12 m2 pp - 8 I12 m2  + (2 I11 d - 6 I11) m2
(%o2)       [I10 = ----------------------------------------------]
                                       d - 2

Observatorio-de-Matematica

(%i1) eq1: a = b + c / d;
                                       c
(%o1)                              a = - + b
                                       d
(%i2) eq2: x = b - c*d;
(%o2)                             x = b - c d
(%i3) solve([eq1, eq2], [a,b,c,d, x]);
(%o3) [[a = %r1, b = %r2, c = (%r1 - %r2) %r3, d = %r3, 
                                                                      2
                                                   x = (%r2 - %r1) %r3  + %r2]]

Observatorio-de-Matematica

(%i1) integrate(x^2 * %e ^ (-x ^ 2), x);
                                                    2
                                                 - x
                          sqrt(%pi) erf(x)   x %e
(%o1)                     ---------------- - --------
                                 4              2
(%i2) plot2d(%o1, [x, -1.5, 1.5]);

Observatorio-de-Matematica

declare(bra, nonscalar);
declare(ket, nonscalar);
dotscrules:true;
matchdeclare(m,lambda([t],featurep(t,integer)));
matchdeclare(n,lambda([t],featurep(t,integer)));

tellsimp(bra(m).ket(n), kron_delta(m,n));

simp:false;
matchdeclare(aa, true);

Observatorio-de-Matematica

anyp(pred, seq) := lreduce(lambda([P, x], P or pred(x)), seq, false);
allp(pred, seq) := lreduce(lambda([P, x], P and pred(x)), seq, true);

walklength(seq) := (length(seq)-1)/2;
walkverts(seq) := makelist(seq[2*i-1], i, 1, walklength(seq)+1);
walkedges(seq) := makelist(seq[2*i], i, 1, walklength(seq));
closedp(seq) := is(first(seq) = last(seq));

vertexset(G) := first(G);
edgeset(G) := second(G);

Observatorio-de-Matematica

/*  Author Chung Chan
    Copyright (C) 2021 Chung Chan */
/* remove
load(descriptive);
load(draw);
*/

/****************
 helper functions 
 ****************/

Observatorio-de-Matematica

with_slider_draw(k,makelist(i,i,1,7),
	proportional_axes = xy,
	xrange = [-3,3],
	yrange = [-3,3],
	xaxis=true,
	yaxis=true,
	grid = true,
	title = "animation" ,
	label([sconcat("k=",k-4),-1,2]),
	point_type=7,