2021.11.17 MATH 3600 Fundamental Theorem of Arithmetic

192 days ago by calkin

def Preal(r,theta): return(cos(4*theta)*r^4 +7*cos(3*theta)*r^3 + 5* cos(2*theta)*r^2 +6*cos(theta)*r +13) Pimaginary(r,theta)=sin(4*theta)*r^4 +7*sin(3*theta)*r^3 + 5* sin(2*theta)*r^2 +6*sin(theta)*r +13 
       
Pimaginary(pi) 
       
13
13
plot(Preal(10,theta),theta,0,2*pi) 
       
plot(Pimaginary(10,theta),theta,0,2*pi) 
       
parametric_plot((Preal(.1,theta),Pimaginary(.1,theta)),theta,0,2*pi) 
       
/usr/local/sage-6.10/local/lib/python2.7/site-packages/sage/misc/decorat\
ors.py:550: DeprecationWarning: variable ranges to parametric_plot must
be given as tuples, like (2,4) or (t,2,3)
See http://trac.sagemath.org/7008 for details.
  return func(*args, **options)
/usr/local/sage-6.10/local/lib/python2.7/site-packages/sage/misc/decorators.py:550: DeprecationWarning: variable ranges to parametric_plot must be given as tuples, like (2,4) or (t,2,3)
See http://trac.sagemath.org/7008 for details.
  return func(*args, **options)
parametric_plot((Preal(1,theta),Pimaginary(1,theta)),theta,0,2*pi) 
       
parametric_plot((Preal(10,theta),Pimaginary(10,theta)),theta,0,2*pi) 
       
parametric_plot((Preal(5,theta),Pimaginary(5,theta)),theta,0,2*pi) 
       
parametric_plot((Preal(6.305,theta),Pimaginary(6.305,theta)),theta,.99*pi,pi) 
       
Preal(6.3,pi) 
       
-1.38289999999994
-1.38289999999994
Pimaginary(6.3,pi) 
       
13.0000000000000
13.0000000000000