Is there a way to express any number in any number base using Maple?

Start with converting any positive real number (rational or irrational) into any positive real number base (rational or irrational), such as: what is "1/65536" in base "999" or what is "sqrt(2)" in base "exp(1)"?

But also for negative, imaginary, and complex numbers: for example, what is "(1/3)-sqrt(3)*I" in base "-Pi*I"?

Specifically, I would like to know what are the first 1024 digits of "exp(1)" in base 16777216, but a general function to convert any number into any base would be preferred.  Base 16777216 is a fun example since each digit can be expressed as a hexadecimal color (from #000000 to #ffffff) on a computer monitor.  Not sure how to get Maple to color the digits automatically though.

It's unfortunate that the "convert/base" feature on Maple only works for integers and bases that are positive integers.

https://en.wikipedia.org/wiki/golden_ratio_base

https://en.wikipedia.org/wiki/negative_base

https://en.wikipedia.org/wiki/quater-imaginary_base

How do I display Unicode characters in Maple 2023?  From the user manual, it seems like this should be supported, but all I see are tofu characters (empty white boxes) and/or question marks.  I have the correct Windows fonts installed for Unicode support and the characters display correctly in Microsoft Notepad.

For example, in sexagesimal (base-60) cuneiform, 1 = 𒐕 (𒐕), 2 = 𒐖 (𒐖), 3 = 𒐗 (𒐗), etc.  If the cuneiform characters display on your web browser, then you should have the correct fonts installed, but they don't display on Maple.  Using the special characters as numerical constants, then you should be able to say in Maple:

𒐕 := 1;
𒐖 := 2;
𒐗 := 3;
𒐕+𒐖;

I tried adding "with(XMLTools):" and "with(StringTools):" but that didn't help, nor did "DecodeEntities("𒐕");".

Even more problematic than simply not displaying the characters, but Maple does not seem to be able to save these characters as constants.  All three characters save as the value "3" instead of 1, 2, and 3, so that the sum of 𒐕 (1) and 𒐖 (2) equals 6 instead of 3.  Something else wrong is that I see two tofu boxes and/or two question marks for a single cuneiform character.  Not sure if this is a bug with Maple 2023.

I seem to have the same problem with က (က) and 𐀀 (𐀀) but not with Ā (Ā) so it looks like maybe there is not full Unicode support for Maple 2023?  𐀀 displays as two missing characters which somehow is already saved as the decimal value 3 whereas က displays as a single missing character with no defined value.

https://en.wikipedia.org/wiki/Babylonian_cuneiform_numerals

https://en.wikipedia.org/wiki/Cuneiform_Numbers_and_Punctuation#Block

I have been using WXMaxima for years and just upgraded to Maple 2023, but I am having a very difficult time adjusting from Maxima to Maple.  Is there a way to make Maple more Maxima-like?

The first problem that I encounter is that "Shift + Enter" and "Enter" should be reversed for people who are used to inputting with Maxima.  I would like to reconfigure Maple so that "Shift + Enter" will be for "Evaluate Expression" and "Enter" will be for "Soft New Line".  This makes inputting multi-line commands (using ":") much easier, so that you "Enter" to add the next line, and then "Shift + Enter" to evaluate.  I thought there was a way to switch these, but I can't find it in the manual.

The next problem is the syntax itself.  "MmaToMaple" will translate Mathematica syntax into Maple syntax, but why is there no equivalent for Maxima?  Maxima/Macsyma is the original computer algebra system (CAS) that inspired both Maple and Mathematica, and being free and open-source, has the widest possible user base (since anyone can use it for free).  Maple needs a way to translate to and from Maxima syntax.  For personal use, I already have a large body of Maxima worksheets saved as plaintext MAC files that I would like to use in Maple.  It will save me a lot of time and trouble if I can import Maxima worksheets directly into Maple.

Is there an easy way to save commonly used Maxima expressions that are not already reserved by Maple, such as "float" (for "evalf") and "%e" (for "exp(1)") so that some Maxima syntax can run directly in Maple?  The only major changes then would be replacing "$" with ":" and ":" with ":=" since ";" is the same in both Maxima and Maple.  Not sure what a "$" means in Maple....

Maple syntax is more similar to Maxima syntax than to Mathematica syntax.  Below is a sample problem that is un-solvable in Maxima (application will crash or run out of memory) but solvable in Maple, to show the differences in syntax.  Unfortunately, it seems that in many cases the Maple syntax is more verbose than the Maxima syntax, requiring more characters to type (such as when defining functions).

/* Maxima syntax */ $
c : 299792458 $
h : 6.62607015E-34 $
k : 1.380649E-23 $
n : exp(1) $
T : 25200 $
P (lmin,lmax) := integrate(2*(c^2)*h/(l^5*(n^(c*h/(k*l*T))-1)),l,lmin,lmax)/integrate(2*(c^2)*h/(l^5*(n^(c*h/(k*l*T))-1)),l,0,inf) $
float(P(380E-9,750E-9));

(* Maple syntax *) :
c := 299792458 :
h := 6.62607015E-34 :
k := 1.380649E-23 :
n := exp(1) :
T := 25200 :
P := (lmin,lmax) -> integrate(2*(c^2)*h/(l^5*(n^(c*h/(k*l*T))-1)),l=lmin..lmax)/integrate(2*(c^2)*h/(l^5*(n^(c*h/(k*l*T))-1)),l=0..infinity) :
evalf(P(380E-9,750E-9));

It seems like Maplesoft has gone to a lot of effort to create intercompatibility between Maple and Mathematica, but their real competition is getting customers to upgrade from Maxima (which is completely free and open-source) to Maple (which is non-free and closed-source like Mathematica is).  Making Maple more Maxima-friendly should increase the number of Maple customers by making it easier to upgrade from Maxima to Maple.