On Tuesday, April 18, 2023 at 4:19:45 PM UTC-6 Nils Bruin wrote:
The present default is to use "1.1" as a designation of a floating point literal, with in implied precision derived from the number of digits used to write down the mantissa. This is true in some context, but not others. In a physics or engineering context, everyone would see 1.1 as having only two significant figures. In a *math* context, no one would see it as having only two significant figures. Here's a hypothetical test you could do: Suppose someone scrawls "1.1" on the blackboard in the math common room, and a mathematician walks in and sees it, what does he think about its value? If you ask him to paraphrase the value of it, he would say "11/10", "1 plus 1/10", or something else equivalent to 11/10. It would not occur to him that it could also be a finite-precision floating point quantity, unless you told him that 11/10 was not the right interpretation. In other words, the mathematician's default semantics for "1.1" is 11/10. The physicist's default semantics is 1.1 * 10^0, only two significant figures. Which semantics should Sage use? I would say Sage is for math, so it should use the math semantics. In high-precision environments like RealField(1000), Sage should *definitely* use the math semantics, because physics people, or engineers, or any other applied type folks, have zero use for 1000 bits of precision in anything that they do. Only a math person, doing math, has a use for 1000 bits. So RealField and RealLazyField should use the math semantics. They should see 1.1 as 11/10. -aw -- 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/3ccd36cc-024d-460c-81d8-8ab8661ee889n%40googlegroups.com.
