Ok. Something to consider is rendering to Mathematica output. (And then doing the same thing for Sage.)
On Fri, Jul 10, 2020 at 1:37 PM Fredrik Johansson < fredrik.johans...@gmail.com> wrote: > I will just mention http://fungrim.org/grim/ which is somewhat related to > the present discussion. > > This is an attempt to design a symbolic formula language that is easy to > parse and has well-defined semantics. Key points: > > * Can be used within Python (and other languages) without special syntax > * Expressly designed to describe mathematical objects and not for > reflection (manipulation of symbolic expressions is meant to be done in the > environment, e.g. Python, not from within the symbolic expression language) > * Expressions are inert by default (there is no automatically-enforced > pseudo-canonical form, and any form of evaluation or rewriting must be > invoked explicitly by the user) > * Evaluation and simplification is subject to a rigorous assumptions system > * There is an explicit distinction between symbolic variables and > polynomial indeterminates > * Real numbers are mathematical real numbers > * Functions are mathematical functions, with well-defined and consistent > behavior at "exceptional points" > > The specification is still far from complete and the implementation still > has a long way to go, but I'm working on it :-) > > I'm using it with some success to build http://fungrim.org/. Thanks to > the strong semantics, it is possible to do automated randomized testing of > the formulas and their assumptions. To illustrate: > > >>> formula = Equal(Gamma(x+1), x*Gamma(x)) > >>> formula.test(variables=[x], assumptions=Element(x, CC)) > {x: -3} ... True > {x: 8} ... True > {x: 0} ... False > Traceback (most recent call last): > ... > ValueError > > (Gamma(0+1) = 0*Gamma(0) is not a true identity.) With correct > assumptions, excluding the poles: > > >>> formula.test(variables=[x], assumptions=Element(x, SetMinus(CC, > ZZLessEqual(0)))) > {x: Sqrt(2)} ... Unknown > {x: Mul(Mul(2, Pi), ConstI)} ... Unknown > {x: Div(Mul(3, Pi), 2)} ... Unknown > {x: Neg(Div(1, 2))} ... True > {x: Div(1, 2)} ... True > {x: Add(Sqrt(2), 1)} ... Unknown > {x: Add(1, ConstI)} ... Unknown > ... > {x: Sub(Pi, ConstI)} ... Unknown > {x: Sub(Sqrt(2), 1)} ... Unknown > {x: 64} ... True > {x: 255} ... Unknown > {x: 7} ... True > Passed 100 instances (25 True, 75 Unknown, 0 False) > {'True': 25, 'Unknown': 75, 'False': 0, 'Total': 100} > > Fredrik > > On Friday, July 10, 2020 at 5:21:07 PM UTC+2 rocky.b...@gmail.com wrote: > >> Ok. This is on my back-burner list of things to get to. >> >> It is something I would like to do, and think I could do reasonably well, >> but I never know if I'll have the free time. >> >> And if someone else wants to take the lead, I'll be happy to share what I >> know on the compiler/transpiler end and contribute. >> >> Also, if there is funding for this effort, then it will most likely get >> done. >> >> >> >> On Fri, Jul 10, 2020 at 10:52 AM kcrisman <kcri...@gmail.com> wrote: >> >>> >>> >>> >>> Clearly, adding the ability to parse some Mathematica code fits well >>>> into that goal. If nothing else, it could be a helpful step in converting >>>> existing Mathematica user code so that it can work in Sage, and that's >>>> part of being a viable alternative. >>>> >>> >>> This is an important point that I am sorry we did not mention earlier; >>> thanks, William. I have definitely had many requests for such an automated >>> tool in the past from colleagues with a lot of Mma stuff. >>> >>> -- >>> >> You received this message because you are subscribed to a topic in the >>> Google Groups "sage-devel" group. >>> To unsubscribe from this topic, visit >>> https://groups.google.com/d/topic/sage-devel/z3XBhQOCh9E/unsubscribe. >>> >> To unsubscribe from this group and all its topics, send an email to >>> sage-devel+...@googlegroups.com. >>> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/sage-devel/8dd1a617-6bcc-40e3-a1c7-89efb2927597o%40googlegroups.com >>> <https://groups.google.com/d/msgid/sage-devel/8dd1a617-6bcc-40e3-a1c7-89efb2927597o%40googlegroups.com?utm_medium=email&utm_source=footer> >>> . >>> >> -- > You received this message because you are subscribed to a topic in the > Google Groups "sage-devel" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sage-devel/z3XBhQOCh9E/unsubscribe. > To unsubscribe from this group and all its topics, 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/050a44ed-e31b-4ddb-8687-fc9dcd53e3c1n%40googlegroups.com > <https://groups.google.com/d/msgid/sage-devel/050a44ed-e31b-4ddb-8687-fc9dcd53e3c1n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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/CANCp2gY2DC%3DH0U6jKvdD-pWbkDABYc3FktR2okRJhSsu8BunGA%40mail.gmail.com.
