sage fails to plot a quarter circle when it should

[fmaltey]

I use sage 4.1.2alpha4. This plot is right with this version :

parametric_plot([real(exp(i*m)),imaginary(exp(i*m))],m,0,7)

I apply the patch 7122 by copy/paste in emacs and run sage -br. Now this plot is also right, it draw a half-circle :

parametric_plot([real(m+sqrt(m^2-1)),imaginary(m+sqrt(m^2-1))],m,-5,5)

I also get it by this function :

def solve2pplot (eq) : return [real(eq.rhs()),imaginary(eq.rhs())]
res = solve(z^2+2*m*z+1,z)
parametric_plot (solve2pplot (res[0]), m, -5,5)

Now I solve this 4 degree equation. The solve is right with sqrt at 2 levels.

But I get an error in the parametric_plot :

res = solve(z^4+2*m*z^2+1,z)
parametric_plot (solve2pplot (res[0]), m, -5,5)

The local solve2pplot(res[0]) generates a long formula.

real axe and imaginary axe are right.

But sage doesn't plot the quarter-circle between axes at position 1=(1,0) and i=(0,1) and claims failed to evaluate function at 40 points. So the plot is a line between the 2 axes.

[fmaltey]

I browse the two previous expressions real(...) and imaginary(...), and test real(sqrt(...)).

Theses calculus are right and remain real.

real(sqrt(m)) ; real(sqrt(I*m)) ; real(sqrt(I*m+1)) # are right 

But this one is the shorter that contains complex expressions :

real(sqrt(sqrt(m)+i+1))

The outer sqrt(...) assume that the inner sqrt is obvious ; so sqrt(m)+i+1 remains, even if it's a complex expression. Then plot fails with this internal complex computation.

plot (real(sqrt(m)+i+1),m,-3,3) # fails with a system error
plot (real(m+i+1),m,-3,3) # is a pretty line

[jason]

The plot (real(sqrt(m)+i+1),m,-3,3) now works, probably as a result of #7614. However, I don't think the original question is addressed.

[vdelecroix]

Now this does work

m = SR.var('m')
parametric_plot([real(exp(i*m)),imaginary(exp(i*m))], (m,0,7))

[chapoton]

This needs a doctest.