As a note, I have now raised an 
issue https://github.com/sagemath/sage/issues/37438 about this on github. 

On Monday, January 22, 2024 at 5:57:50 PM UTC Nils Bruin wrote:

> 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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