Hello,
I'm trying to approximate a curve, here is my code:
a = 1 # x radius length
b = 1 # y radius length
cut = pi/4 # angle of plane
theta = var('theta')
phi = var('phi')
def getnumerical(i):
diffx = diff(a*cos(theta), theta)
diffy = diff(b*sin(theta), theta)
func = (diffx^2+diffy^2)^(1/2)
approx = numerical_integral(func, 0, i)
return approx[0]
parametric_plot((getnumerical(phi), b*sin(phi)*tan(cut)), (phi, 2*pi, 4*pi), aspect_ratio = 1)
The integral defining the x term in the parametric plot is elliptic, so it must be numerically approximated. So far, I have had little success getting any numerical integral methods to work, including nintegral, and am frustrated because I cannot discern the problem. This implementation gives the error:
Traceback (most recent call last):
File "", line 1, in <module>
File "/tmp/tmpDAHxNF/___code___.py", line 17, in <module>
exec compile(u'parametric_plot((getnumerical(phi), b*sin(phi)*tan(cut)), (phi, _sage_const_2 *pi, _sage_const_4 *pi), aspect_ratio = _sage_const_1 )
File "", line 1, in <module>
File "/tmp/tmpDAHxNF/___code___.py", line 14, in getnumerical
approx = numerical_integral(func, _sage_const_0 , i)
File "sage/gsl/integration.pyx", line 332, in sage.gsl.integration.numerical_integral (build/cythonized/sage/gsl/integration.c:3159)
File "sage/symbolic/expression.pyx", line 1177, in sage.symbolic.expression.Expression.__float__ (build/cythonized/sage/symbolic/expression.cpp:8897)
TypeError: unable to simplify to float approximation
Thank you for any help you provide.
