jsMath

# Demo

for l in permutations(range(8)): if all([ abs(l[i]-l[j]) != i-j or i == j for i in range(8) for j in range(8) ]): show(matrix_plot([[ l[i]!=j for i in range(8)] for j in range(8)])) break
var('x,a,b,c,d') show(solve(a*x^2+b*x+c==0,x))
 [x=−2ab+√−4ac+b2,x=−2ab−√−4ac+b2]
diff(tan(x),x)
 tan(x)^2 + 1
show(diff(tan(x),x,8))
 128(tan(x)2+1)tan(x)7+7680(tan(x)2+1)2tan(x)5+24576(tan(x)2+1)3tan(x)3+7936(tan(x)2+1)4tan(x)
integral(sin(6*x),x)
 -1/6*cos(6*x)
sum(1/x^2,x,1,infinity)
 1/6*pi^2
limit(sin(x)/x,x=0)
 1
plot(sin(x), x, 0, 2*pi)
animate([sin(x + float(k)) for k in [0,0.3,..,2*pi]], xmin=0, xmax=2*pi).show()
plot(sin(x), x, 0, 2*pi).save("sin.pdf")
var('x,y'); plot3d(sin(x-y)*y*cos(x),(x,-3,3),(y,-3,3))

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sum( [ point( [cos(t), sin(t), t]) for t in [0,0.1,..10] ])

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taylor(sin(x),x,1,3)
 -1/6*(x - 1)^3*cos(1) - 1/2*(x - 1)^2*sin(1) + (x - 1)*cos(1) + sin(1)
show(_)
 −61(x−1)3cos(1)−21(x−1)2sin(1)+(x−1)cos(1)+sin(1)
sum([ plot(taylor(sin(x),x,1,k),x,-2,2,rgbcolor=[k/10,0,0]) for k in [1..10]]) + plot(sin(x),x,-2,2)
factor(19753908033962706153880721511761)
 238749823749839 * 82738942897234399
M=matrix([[1,2,3],[4,5,6],[11,11,12]]) M.determinant()
 -3
M^-1
 [ 2 -3 1] [ -6 7 -2] [ 11/3 -11/3 1]
G=graphs.DodecahedralGraph() G
 Dodecahedron: Graph on 20 vertices
G.plot(partition=G.coloring())
G.show3d(vertex_colors=dict([((random(),random(),random()),i) for i in G.coloring()]))

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@interact def tangent_line(f = input_box(default=sin(x),label="f(x) ="), x0 = slider(-5, 5, 1/100, 7/4,label="x<sub>0</sub>")): xbegin = -5 xend = 5 var('x') df = diff(f,x) tanf = f(x=x0) + df(x=x0)*(x-x0) fplot = plot(f, xbegin, xend) html('Érintő egyenes: l(x) = $'+latex(f(x=x0))+' + '+latex(df(x=x0))+'\\cdot (x-'+latex(x0)+') '+'$') tanplot = plot(tanf, (x,xbegin, xend), rgbcolor = (1,0,0)) fmax = f.find_maximum_on_interval(xbegin, xend)[0] fmin = f.find_minimum_on_interval(xbegin, xend)[0] show(fplot + tanplot+point((x0,f(x=x0))), xmin = xbegin, xmax = xend, ymax = fmax, ymin = fmin)

f(x) =
x0
 7/4
 Érintő egyenes: l(x) = sin(47)+cos(47)·(x−47)  
%gap G := Group((1,2)(3,4),(1,2,3)); T := CharacterTable(G); Display(T);
 Group([ (1,2)(3,4), (1,2,3) ]) CharacterTable( Alt( [ 1 .. 4 ] ) ) CT1 2 2 2 . . 3 1 . 1 1 1a 2a 3a 3b 2P 1a 1a 3b 3a 3P 1a 2a 1a 1a X.1 1 1 1 1 X.2 1 1 A /A X.3 1 1 /A A X.4 3 -1 . . A = E(3)^2 = (-1-ER(-3))/2 = -1-b3
%latex \LaTeX\ képlet: $\int\limits_{-\infty}^{\infty} \frac{\sin(x)}x\, \mathrm{d}x$
t = Tachyon(camera_center=(8.5,5,5.5), look_at=(2,0,0), raydepth=6, xres=1500, yres=1500) t.light((10,3,4), 1, (1,1,1)) t.texture('mirror', ambient=0.05, diffuse=0.05, specular=.9, opacity=0.9, color=(.8,.8,.8)) t.texture('grey', color=(.8,.8,.8), texfunc=7) t.plane((0,0,0),(0,0,1),'grey') t.sphere((4,-1,1), 1, 'mirror') t.sphere((0,-1,1), 1, 'mirror') t.sphere((2,-1,1), 0.5, 'mirror') t.sphere((2,1,1), 0.5, 'mirror') show(t)
var("u,v") p1 = parametric_plot3d([cos(u)*v, sin(u)*v, 3/2-3*v/2], (u, 0, 2*pi), (v, 0, 1.5), opacity = 0.5, plot_points=[20,20]) p2 = parametric_plot3d([cos(u)/2, sin(u)/2, v-3/4], (u, 0, 2*pi), (v, 0, 3/2), plot_points=[20,20]) show(p1+p2)

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N=200 M1=200 M2=200 x0=0.509434 puntos=[] for t in range(N): mu=2.0+2.0*t/N x=x0 for i in range(M1): x=mu*x*(1-x) for i in range(M2): x=mu*x*(1-x) puntos.append((mu,x)) point(puntos,pointsize=1)
""" Draws Loretz butterfly using matplotlib (2d) or jmol (3d). Written by Matthew Miller and William Stein. """ g = Graphics() x1, y1 = 0, 0 from math import sin, cos, exp, pi for theta in srange( 0, 10*pi, 0.05 ): r = exp(cos(theta)) - 2*cos(4*theta) + sin(theta/12)^5 x = r * cos(theta) # Convert polar to rectangular coordinates y = r * sin(theta) xx = x*6 + 25 # Scale factors to enlarge and center the curve. yy = y*6 + 25 if theta != 0: l = line( [(x1, y1), (xx, yy)], rgbcolor=hue(theta/7 + 4) ) g = g + l x1, y1 = xx, yy g.show(dpi=100, axes=False)
r = RubiksCube().move("R U R'") r.show3d()

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