13.1

119 days ago by nathantoddstone

var('x,y,z,t') 
        
(x, y, z, t)
(x, y, z, t)
def par(_x,_y,_z,r): return parametric_plot3d([_x,_y,_z],(t,0,r), thickness=20) 
       
par(sin(t), cos(t),t,10) 
       
par((4+sin(20*t))*cos(t), (4+sin(20*t))*sin(t), cos(20*t), 6*pi) 
       
v = vector([e**(-3*t),t**2/sin(t)**2, cos(2*t)]) v 
        
(e^(-3*t), t^2/sin(t)^2, cos(2*t))
(e^(-3*t), t^2/sin(t)^2, cos(2*t))
[f.limit(t=0) for f in v] 
        
[1, 1, 1]
[1, 1, 1]
par(t**2,t**4,t**6,10) 
       
a,b = [0,0,0],[1,2,3] a,b = [vector(var) for var in a,b] f = (1-t)*a+t*(b-a) f 
        
(t, 2*t, 3*t)
(t, 2*t, 3*t)
a,b = [1,-1,2],[4,1,7] a,b = [vector(var) for var in a,b] f = a+t*(b-a) f 
        
(3*t + 1, 2*t - 1, 5*t + 2)
(3*t + 1, 2*t - 1, 5*t + 2)
point([a,b],size=30)+parametric_plot3d(f,(t,0,1),thickness=4, color='red') 
       
par(cos(t),sin(t),sin(6*t),2*pi) 
       
var('x,y,z') 
        
Traceback (click to the left of this block for traceback)
...
TypeError: 'list' object is not callable
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_14.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyKCd4LHkseicp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpLk3NVR/___code___.py", line 2, in <module>
    exec compile(u"var('x,y,z')" + '\n', '', 'single')
  File "", line 1, in <module>
    
TypeError: 'list' object is not callable
par(t*cos(t),t*sin(t),t,20)+plot3d(sqrt(x**2+y**2), (x,-20,20),(y,-20,20),color='red') 
       
par(t,0,2*t-t**2,2)+plot3d(x**2+y**2, (x,-3,3),(y,-2,2),color='red')+point([(0,0,0),(1,0,1)], size=30, color='green') 
       
solve(2*t-t**2==t**2,t) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}\left[t = 0, t = 1\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[t = 0, t = 1\right]
par(cos(t)*sin(2*t),sin(t)*sin(2*t),cos(2*t),2*pi) 
       
par(t,t*sin(t),t*cos(t),10*pi) 
       
def xyz(r): return [(var,-r,r) for var in x,y,z] 
       
plot3d(sqrt(x**2+y**2), *xyz(10))+plot3d(1+y,*xyz(10))+par(t,(t**2-1)/2,(t**2+1)/2,6) 
       
solve(-t**2+4*t-3,t) 
        
[t == 3, t == 1]
[t == 3, t == 1]
a = lambda q: [q**2,7*q-12,q**2] b = lambda q: [4*q-3,q**2,5*q-6] a(1), b(1),a(3), b(3) 
        
([1, -5, 1], [1, 1, -1], [9, 9, 9], [9, 9, 9])
([1, -5, 1], [1, 1, -1], [9, 9, 9], [9, 9, 9])
print 'collides at:', a(3), b(3) 
        
collides at: [9, 9, 9] [9, 9, 9]
collides at: [9, 9, 9] [9, 9, 9]