Am Dienstag, 16. Juni 2020 19:03:40 UTC+2 schrieb Nils Bruin: > > That's quite a thread. One thing I'd like to highlight from there that > didn't seem to get so much traction is a point Marco Streng made about > possible notations for right actions: > > If G is a group acting on the right on a ring R, and a,b in R and s in G > then denoting right-action by right-multiplication has a problem: > > (a*b)*s would suggest it's equal to a*(b*s), which it is generally not. > Exponential notation (a*b)^s does not suffer from this problem. That > disqualifies right-multiplication as a general notation for right-actions > to me. >
I would also be in favor of using a different notation for actions. My suggestion would be to use the shift operator << to denote right actions and, similarly, the right shift operator >> for left actions. This makes it explicit what kind operation is intended; for example, `a*b << s*t` and `a*b << s << t` would do exactly what one expects. This notation can be thought of as a generalization of the bitwise << operation if one interprets it as a monoid action of (ℕ,+). The notation can be used for both multiplicative and additive groups. As the shift operators are not common mathematical operators, it is less likely to confuse them with actual mathematical operations like exponentiation or multiplication. This could also resolve otherwise ambiguous cases, such as the Weyl algebra acting on the polynomial ring, where multiplication already has a different meaning. If one wants, one could even define the action of permutations on permutations themselves and, thus, distinguish between left-to-right and right-to-left multiplication via << and >>. -- 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 sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/f2bda511-d8ce-416a-b0cd-fa5150023dbdo%40googlegroups.com.
