More importantly, the error also doesn't occur with

S = Curve(f).riemann_surface(integration_method="heuristic")

so it's indeed in the newer code. The fact that swapping x,z makes the 
error disappear is also unsurprising: entirely different path integrals are 
executed.

As an indication for what is likely happening, on line 2211:

delta_z and rho_z seem to be indistinguishable, forcing Delta and M to be 
+infinity. Path splitting should definitely happen here. I think delta_z 
should have been smaller than rho_z when you reach this point, so I think 
the code should have bailed before.
On Monday 22 January 2024 at 03:03:20 UTC-8 Linden Disney wrote:

> In Sage 9.8 I ran the following code:
>
>     R.<z,x> = QQ[]
>     f = x*(1^5+z^5) + (x*1*z)^2 - x^4*1*z - 2*1^3*z^3
>     S = Curve(f).riemann_surface()
>     S.riemann_matrix()
>
> and got a ValueError occurring inside rigorous_line_integral. This error 
> doesn't occur if instead for the first line I used "R.<x,z> = QQ[]" 
> (swapping the order of x and z). Can anyone replicate the error? If so 
> please let me know and I will open a ticket about this and have a look, as 
> I wrote the rigorous_line_integral code. 
>
>

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