Extension can be install via Plugin Manager in SMath.

At first I had coded my own calculation algorithms which were slow, obviously.
Then I had implemented GNU Multiple Precision Library, which require a lot of work and extra download.
At last I have noticed there is a numerics library within visual studio if I use Net Framework 4.

So here is compiled DLL, which should be extracted to "%AppData%\SMath\extensions\plugins\".
Compiled dll should work out of box if there is Net Framework > 4 is installed on your system.
Source code to check and recompile, system.numerics file if you have not installed .Net4 framework.
If there is no Net4, just copy "system.numerics.dll" file under the folder of "BigIntegerArtihmetics.dll".

It also works under Linux with Mono if you copy files to "/home//.config/SMath".
If you use linux you would know where to copy extension.

Regards

biginteger_compiled.7z (4,4 KiB) scaricato 986 volta(e).
source_code.7z (6 KiB) scaricato 1025 volta(e).
System.Numerics.7z (43,65 KiB) scaricato 1001 volta(e).

Thanks to Andrey, I have uploaded plugin in to repository.
Now you don't have to manually install it.
Plugin can be added into SMath via plugins download page.
If you have this added into your SMath, please remove this plugin directory.
After removal, plugin can be available to download in SMath.

Regards

Hi. Arbitrary precission algebra, but with rationals, extending the big integers operations and introducing continued fractions expansions.



bigRationals.sm (212,6 KiB) scaricato 1769 volta(e).
bigRationals.pdf (378,28 KiB) scaricato 1109 volta(e).

Best regards.
Alvaro.

Wrote

Hi. Arbitrary precission algebra, but with rationals, extending the big integers operations and introducing continued fractions expansions.



bigRationals.sm (212,6 KiB) scaricato 1769 volta(e).
bigRationals.pdf (378,28 KiB) scaricato 1109 volta(e).

Best regards.
Alvaro.

This is very nice. Good job Alvaro.
Very beautiful, elegant and elaborated document.

I was writing some functions for this purpose too.
I think I will complete what I have started.
I am going to write a Big Number Plugin for SMath.
With mixed functions/ideas of yours and mine, it can be done.

Regards

Hi overlord. A plugin is definitely needed. This version also generates the rational approximation of any real with arbitrary precision without any plugin, but its efficiency is minimal.



ContFrac_Figures.sm (54,99 KiB) scaricato 1696 volta(e).
ContFrac_Figures.pdf (139,1 KiB) scaricato 1030 volta(e).

Best regards.
Alvaro.

Wrote

...but its efficiency is minimal.

When (If) I complete the Big Number plugin, it will be much faster.
I know this because I witnessed first hand while programming Big Integer plugin.
Same algorithms shall execute faster on C# than internal SMath programming.

Hi. Improved version. Newton-raphson method and row reduced echelon form were also added, both with arbitrary arithmetic precision.

bigRationals.sm (276,04 KiB) scaricato 1744 volta(e).
bigRationals.pdf (458,26 KiB) scaricato 1090 volta(e).

Best regards.
Alvaro.

Hola Alvaro,
Great piece of work.
For pi, you may want to check Simon Plouffe
to avoid continued fraction ... timing ?
Take care ... Jean.

Pi for Alvaro BigNumber.sm (4,54 KiB) scaricato 1714 volta(e).

Wrote

you may want to check Simon Plouffe

▲▲▲▲▲
Don't bother Alvaro, just a regular pi series calculation.
Not related with arbitrary precision results.

Well, promise is a promise.
I shall release the Big Rational Library when finished very soon.
Just a couple of essential functions remained.
Then I will try to add complex ones.

Big rationals has a niche and limited usage.
Though sometimes it is necessary for floating point precision.
Near none CAS including SMath is not capable such calculations.
It is due to electronic hardware and IEEE74 design.

Regards