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The following code segment works well in sagenb.com until the @interact is put in to permit varying variables a and b. Then a long error is thrown, ending with

"self.loc = (float(center[0]), float(center[1]), float(center[2])) TypeError: 'sage.symbolic.expression.Expression' object does not support indexing"

The issue is the statement found near the end that says G+=point((x,y), color='red',pointsize=4) If that statement is commented out, then it runs again, although and of course the desired plot is not obtained. Why? What can i do about it?
Clearly you won't let me show you by uploading the file. I am posting what i can.

def Pxy(s,a,b): x=var('q') EQ1=s==(a(sqrt(1+b^2))e^(bq))/b theta=solve([EQ1],q) x=acos(theta[0].rhs())e^(btheta[0].rhs()) y=asin(theta[0].rhs())e^(btheta[0].rhs()) return theta,x,y def morestuff(a,b): L=[] t=var('t') G=parametric_plot((acos(t)e^(bt),asin(t)e^(bt)),(t,0,3pi),rgbcolor=hue(0.6),figsize=5,axes=True) for i in range(1,20): i=i/2 q,x,y=Pxy(7,a,b) L.append([x.n(),y.n(),q[0].rhs().n()]) #create a list of x,y,q pairs. G+=point((x,y), color='red',pointsize=4) G.show(figsize=4) @interact def putvariables(a = slider(range(1,200), default = 97),b = slider(range(100), default = 38) ): a=a/100 b=b/100 morestuff(a,b)

The following code segment works well in sagenb.com until the @interact is put in to permit varying variables a and b. Then a long error is thrown, ending with

"self.loc = (float(center[0]), float(center[1]), float(center[2]))
TypeError: 'sage.symbolic.expression.Expression' object does not support
indexing"
indexing"

def Pxy(s,a,b):  x=var('q') EQ1=s==(a(sqrt(1+b^2))e^(bq))/b 
   EQ1=s==(a*(sqrt(1+b^2))*e^(b*q))/b 
   theta=solve([EQ1],q) x=acos(theta[0].rhs())e^(btheta[0].rhs()) y=asin(theta[0].rhs())e^(btheta[0].rhs()) 
   x=a*cos(theta[0].rhs())*e^(b*theta[0].rhs()) 
   y=a*sin(theta[0].rhs())*e^(b*theta[0].rhs()) 
   return theta,x,y  def morestuff(a,b):  L=[] t=var('t') G=parametric_plot((acos(t)e^(bt),asin(t)e^(bt)),(t,0,3pi),rgbcolor=hue(0.6),figsize=5,axes=True) 
   G=parametric_plot((a*cos(t)*e^(b*t),a*sin(t)*e^(b*t)),(t,0,3*pi),rgbcolor=hue(0.6),figsize=5,axes=True) 
   for i in range(1,20):  i=i/2  q,x,y=Pxy(7,a,b)  L.append([x.n(),y.n(),q[0].rhs().n()])  #create a list of x,y,q pairs.  G+=point((x,y), color='red',pointsize=4)  G.show(figsize=4)  @interact  def putvariables(a = slider(range(1,200), default = 97),b = slider(range(100), default = 38) ):  a=a/100  b=b/100 morestuff(a,b) 

   morestuff(a,b)

The following code segment works well in sagenb.com until the @interact is put in to permit varying variables a and b. Then a long error is thrown, ending with

"self.loc = (float(center[0]), float(center[1]), float(center[2]))
TypeError: 'sage.symbolic.expression.Expression' object does not support
indexing"

The issue is the statement found near the end that says G+=point((x,y), color='red',pointsize=4) If that statement is commented out, then it runs again, although and of course the desired plot is not obtained. Why? What can i do about it?
Clearly you won't let me show you by uploading the file. I am posting what i can.

def Pxy(s,a,b): 
   x=var('q') 
   EQ1=s==(a*(sqrt(1+b^2))*e^(b*q))/b 
   theta=solve([EQ1],q) 
   x=a*cos(theta[0].rhs())*e^(b*theta[0].rhs()) 
   y=a*sin(theta[0].rhs())*e^(b*theta[0].rhs()) 
   return theta,x,y 

def morestuff(a,b): 
   L=[]  t=var('t') 
   G=parametric_plot((a*cos(t)*e^(b*t),a*sin(t)*e^(b*t)),(t,0,3*pi),rgbcolor=hue(0.6),figsize=5,axes=True) 
   for i in range(1,20): 
      i=i/2 
      q,x,y=Pxy(7,a,b) 
      L.append([x.n(),y.n(),q[0].rhs().n()]) 
      #create a list of x,y,q pairs. 
      G+=point((x,y), color='red',pointsize=4) 
   G.show(figsize=4) 

@interact 
def putvariables(a = slider(range(1,200), default = 97),b = slider(range(100), default = 38) ): 
   a=a/100 
   b=b/100 
   morestuff(a,b)