# complex-part-그림

## 2096 days 전, jhlee2chn 작성

var('u, v') z=u+i*v w=(exp(i*z)+exp(-i*z))/2 expand(sageobj(w._maxima_().demoivre()))
 1/2*cos(u)*e^(-v) + 1/2*cos(u)*e^v + 1/2*I*e^(-v)*sin(u) - 1/2*I*e^v*sin(u) 1/2*cos(u)*e^(-v) + 1/2*cos(u)*e^v + 1/2*I*e^(-v)*sin(u) - 1/2*I*e^v*sin(u)

## Coordinate Transformations

by Jason Grout

var('u v') from sage.ext.fast_eval import fast_float from functools import partial @interact def trans(x=input_box(u^2-v^2, label="x=",type=SR), \ y=input_box(u*v+cos(u*v), label="y=",type=SR), \ t_val=slider(0,10,0.2,6, label="Length of curves"), \ u_percent=slider(0,1,0.05,label="<font color='red'>u</font>", default=.4), v_percent=slider(0,1,0.05,label="<font color='blue'>v</font>", default=.4), u_range=input_box(range(-5,5,1), label="u lines"), v_range=input_box(range(-5,5,1), label="v lines")): thickness=4 u_val = min(u_range)+(max(u_range)-min(u_range))*u_percent v_val = min(v_range)+(max(v_range)-min(v_range))*v_percent t_min = -t_val t_max = t_val g1=sum([parametric_plot((i,v), (v,t_min,t_max), rgbcolor=(1,0,0)) for i in u_range]) g2=sum([parametric_plot((u,i), (u,t_min,t_max), rgbcolor=(0,0,1)) for i in v_range]) vline_straight=parametric_plot((u,v_val), (u,t_min,t_max), rgbcolor=(0,0,1), linestyle='-',thickness=thickness) uline_straight=parametric_plot((u_val, v), (v,t_min,t_max),rgbcolor=(1,0,0), linestyle='-',thickness=thickness) (g1+g2+vline_straight+uline_straight).save("uv_coord.png",aspect_ratio=1, figsize=[5,5], axes_labels=['$u$','$v$']) xuv = fast_float(x,'u','v') yuv = fast_float(y,'u','v') xvu = fast_float(x,'v','u') yvu = fast_float(y,'v','u') g3=sum([parametric_plot((partial(xuv,i),partial(yuv,i)), (v,t_min,t_max), rgbcolor=(1,0,0)) for i in u_range]) g4=sum([parametric_plot((partial(xvu,i),partial(yvu,i)), (u,t_min,t_max), rgbcolor=(0,0,1)) for i in v_range]) uline=parametric_plot((partial(xuv,u_val),partial(yuv,u_val)),(v,t_min,t_max),rgbcolor=(1,0,0), linestyle='-',thickness=thickness) vline=parametric_plot((partial(xvu,v_val),partial(yvu,v_val)), (u,t_min,t_max), rgbcolor=(0,0,1), linestyle='-',thickness=thickness) (g3+g4+vline+uline).save("xy_coord.png", aspect_ratio=1, figsize=[5,5], axes_labels=['$x$','$y$']) print "x=%s, \: y=%s"%(x, y) print "<html><table><tr><td><img src='cell://uv_coord.png'/></td><td><img src='cell://xy_coord.png'/></td></tr></table></html>"

x=
y=
Length of curves
u
v
u lines
v lines

## Click to the left again to hide and once more to show the dynamic interactive window