complex numbers and parametric curves

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sage: line([zeta(I + t) for t in srange(-2,2,0.1)])

http://www.sagemath.org/doc/reference...

http://www.sagemath.org/doc/construct...

http://www.sagemath.org/doc/reference...

I cannot say for sure because I haven't check that but using line is not equivalent to using parametric_plot as I would expect parametric_plot to use finer drawing techniques than just a collection of connected lines.

You could the 'lambda trick' use instead : parametric_plot ((lambda t : zeta (I + t) . real (), lambda t : zeta (I + t) . imag ()), (t, -2 , 2))

The drawback is that this computes the value of the function twice which isn't very elegant.

The lambda trick is necessary every time you need to use a complex function with drawing/solving equations with sage. This is possible that optimization techniques relying on formal expression expect these expressions to be real valued.