4824.sagews

var('x y')
a=x+x^2+y
show(a)

\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} + x + y

maxima("ode2('diff(y,x) =-y,y,x)")

y=%c*%e^-x

latex(maxima("ode2('diff(y,x) =-y,y,x)"))

y={\it c}\,e^ {- x }

show(maxima("ode2('diff(y,x) =-y,y,x)"))

\newcommand{\Bold}[1]{\mathbf{#1}}y={\it c}\,e^ {- x }

plot(sin(x),(x,-pi,pi),plot_points=3,marker='x')+plot(sin(x),(x,-pi,pi),color='red',linestyle='-.',fill = 'axis',axes_labels=['$x$','$y$'])

# example
fig_v=plot_vector_field((1,x*y),(x,-10,10),(y,-10,10))
fig_s=plot_slope_field(x*y,(x,-10,10),(y,-10,10))
fig_i=implicit_plot(y^2==0.05*exp(x^2),(x,-10,10),(y,-10,10),color='red')
show("y'=x*y")
show(fig_v+fig_s+fig_i)

\newcommand{\Bold}[1]{\mathbf{#1}}\verb|y'=x*y|

sage: u, v = var('u,v')
sage: fx = (3+sin(v)+cos(u))*cos(2*v)
sage: fy = (3+sin(v)+cos(u))*sin(2*v)
sage: fz = sin(u)+2*cos(v)
sage: parametric_plot3d([fx, fy, fz], (u, 0, 2*pi), (v, 0, 2*pi),
...   frame=False, color="red")

# other field plot
var('x y z')
plot_vector_field3d((x,sin(y),tanh(z)),(x,0,1),(y,-pi,pi),(z,-1,1))

t = Tachyon(xres=1000,yres=600, camera_center=(1,0,5), antialiasing=3)
t.light((4,3,2), 0.2, (1,1,1))
t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(1.0,1,1))
t.texture('t1', ambient=0.5, diffuse=0.5, specular=0.0, opacity=1.0, color=(0,0,0))
t.texture('t2', ambient=0.2, diffuse=0.7, specular=0, opacity=0.7, color=(.5,.5,.5))
t.texture('t3', ambient=.9, diffuse=5, specular=0,opacity=.1, color=(1,0,0))
t.sphere((1,0,0), 30, 't2')
k=0
for i in srange(-pi*10,0,.01):
  k += 1
  t.sphere((cos(i/10)-.1, sin(i/10)*cos(i), sin(i/10)*sin(i)), 0.1, 't0')
  t.sphere((cos(i/10) + 2.1, sin(i/10)*cos(i), sin(i/10)*sin(i)), 0.1, 't1')
t.show(verbose=1)

tachyon /sagenb/sagenbws/.sage/temp/mod.math.washington.edu/599//tmp_0.dat -format PNG -o sage0.png ; rm -f "/sagenb/sagenbws/.sage/temp/mod.math.washington.edu/599//tmp_0.dat" Tachyon Parallel/Multiprocessor Ray Tracer Version 0.98.9 Copyright 1994-2010, John E. Stone <[email protected]> ------------------------------------------------------------ Scene Parsing Time: 0.0155 seconds Scene contains 6286 objects. Preprocessing Time: 0.0100 seconds Rendering Progress: 0% complete Rendering Progress: 0% complete Rendering Progress: 8% complete Rendering Progress: 16% complete Rendering Progress: 24% complete Rendering Progress: 32% complete Rendering Progress: 40% complete Rendering Progress: 48% complete Rendering Progress: 56% complete Rendering Progress: 64% complete Rendering Progress: 72% complete Rendering Progress: 80% complete Rendering Progress: 88% complete Rendering Progress: 96% complete Rendering Progress: 100% complete Ray Tracing Time: 1.5551 seconds Image I/O Time: 0.1318 seconds