Hi, I don't think it's normal in a computer algebra system that 1%((x^2-1)/(x-1)) equals zero. It is a mal-design, if not a bug. [email protected] 在 2025年10月6日 星期一晚上8:21:54 [UTC+2] 的信中寫道：
> Thas't normal. Corece it yourself. > > Le dim. 5 oct. 2025 à 14:12, Taylor Huang <[email protected]> a écrit > : > > > > Hi all, > > > > Cutting to the chase, I realized that the modulo operator "%" is > un-naturally defined to be constant-zero in the fraction field of > polynomials. This has caused the following issue. > > > > See the following minimal code on the online Sage server: Sage Cell > Server > > > > In this example, we are doing 1 modulo x+1, which supposedly should give > us 1 as output. However, since the datatype of x+1 is rational polynomial, > it produces 0 as output. > > > > I imagine there are two ways that may potentially solve this issue: > > (1) Disgard the modulo operator % for fraction field! In the > mathematical sense there is no interesting modulo (other than producing > zero) for fraction field anyway, so such an operator seems more confusing > than helpful. Removing % from fraction field should also cause the > triggering of coersion from rational polynomial to a polynomial in the > above example. > > (2) Perform the modulo only on the integral ideal. Upon each time we > compute f%g in a fraction field, we can derive its ring of integer O, and, > return a representative in the co-set f + g*O. In the above example, this > should also return the representative 1. > > > > Best, > > Yu-Hsuan (Taylor) > > > > -- > > You received this message because you are subscribed to the Google > Groups "sage-devel" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to [email protected]. > > To view this discussion visit > https://groups.google.com/d/msgid/sage-devel/56a6410d-3644-4b7a-9181-d0911d1dee17n%40googlegroups.com > . > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/sage-devel/7c32e18d-2e81-4c41-9d34-64cae8ad2ccbn%40googlegroups.com.
