How to plot this

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As said in my previous comment to @slelievre's answer (see above or below according to this site's software whims), the D[0](real_part) expression has no obvious meaning. Assuming that :

• the author meant $\displaystyle{\frac{\partial}{\partial t}\Re\left(t\right)}$

• $t\in\mathbb{R}$

we can replace it by 1 :

sage: with assuming(t, "real"): real_part(t).diff(t)
1

We note also that this curious notation occurs only in the expression D[0](real_part)(1/4*pi). foo noting the original triplet, duly completed by its closing parenthesis, this replacement leads to :

sage: [u.subs(D[0](real_part)(1/4*pi)==1) for u in foo]
[-1/6*sqrt(6)*sqrt(3)*sqrt(2)*t + 1/2*sqrt(2)*e^(1/4*pi),
 1/2*sqrt(2)*e^(1/4*pi),
 e^(1/4*pi)]

It turns out that all the quantities involved are real :

sage: [[v[0].n() for v in u.subs(D[0](real_part)(1/4*pi)==1).coefficients(t)] for u in foo]
[[1.55088319691803, -1.00000000000000], [1.55088319691803], [2.19328005073802]]

The sought curve is therefore a straight line parallel to the $x$ axis, determined by $y=1.55\dots$ and $z=2.19\dots$. Materializing this graph is lazily left as an exercise to the reader which is incidentally incited to check his notations...

HTH,

It seems you want to plot a curve in 3d, parametrized by t.

The example provided in the question has problems:

• parentheses don't match
• the entries involve
  • non-real complex numbers, like e^(1/4*pi), e^(1/2*pi), e^(-1/2*pi)
  • the derivative of the real_part function

Here is an example of plotting a parametric curve in 3d:

sage: M(t) = (t + 1, 2 * t - 1, 3 * t)
sage: parametric_plot(M, (-2, 2), color="red")

It could be adapted to the example from the question, once fixed.