Symja - Java computer algebra library - https://github.com/axkr/symja_android_library
https://en.wikipedia.org/wiki/Falling_and_rising_factorials "The rising factorial can be extended to real values of n using the gamma function provided x and x + n are real numbers that are not negative integers:" if I understood correct, x + n should be 0 or positive integers, in case x = 2, n = 0.9 x + n = 2.9 it is not integers. So, can we use these numbers
Hi axkr. Thank you for your time. With the information that I have, check("Gamma(2.0+1.0)/Gamma(2.0-0.9+1.0)", "1.91116"), is it valid case? x(n) = gamma(x + n)/ gamma(x), because, we have limitations for this equation: provided x and x + n are real numbers that are not negative integers => n can be real positive integers. You have other information?
you can check the numbers with method
IExpr#isInexactNumber() if they are floating-point real or complex numbers
With
EvalEngine#isDoubleMode() method you can check if the user runs a numeric evaluation:
@axkr we can use this formula Gamma(x+n)/Gamma(x-n+1) instead (x)n = x(x-1)(x-2)......(x-n+1) but in case if we have a step " for example h = 0.5, etc", we should think, if we can replace f(x) f(x-h) f(x-2h) .... f(x-(k-1)h) with Gamma(x+n)/Gamma(x-n+1) or another formula which depends on Gamma". Work (x)n = Gamma(x+n)/Gamma(x-n+1) or another formula which depends on Gamma in case when we have custom step.
Hi @axkr I did changes that I think you wanted to see. Please, let me know if I actually understood the requirements correct. In case if so, I do not understand the benefit
of those changes because of next:
of those changes because of next:
- It does not seem to be shorter.
- For me it makes logic more confusing and less generalized if to look the entire function logic (I mean where we use similar while loops in both cases, for second case we can't use gamma)
Maybe I am missing something, can you please help me to understand?
Also, based on the information I found (I posted the screenshort above) n can't be anything else but 0 or positive integer. Maybe I should add a verification for this case and throw an exception if it fails? Please let me what do you think.
Thanks in advance for your time. Stay safe.
Also, based on the information I found (I posted the screenshort above) n can't be anything else but 0 or positive integer. Maybe I should add a verification for this case and throw an exception if it fails? Please let me what do you think.
Thanks in advance for your time. Stay safe.
you can also use
ApfloatMath.gamma(arg1)
for apfloat floating point numbers which can have higher precision than Java double values.
to evaluate for a higher precision you can use the
N()function.
but the arguments of the function should be symbolic.
Hi Axel, I've been reading about SymJa. It's an amazing piece of work! I'm particularly impressed by the effort you've put into usability. Been reading through the source code and I'm not sure how it all fits together yet, but I was curious if you currently support or plan to implement Knuth–Bendix completion for general purpose term rewriting? Is there some documentation on how the different CAS's (e.g. JAS, Rubi) fit together? Can you describe your long-term goals for the project, i.e. do you plan to focus on the user-facing application and notebook support, or do you see Symja as becoming more of a library like Sympy? Thanks for your hard work on this project!
@breandan Yes general purpose term rewriting is the goal. JAS is supported by converting from Symja IExpr to JAS and backward:
https://github.com/axkr/symja_android_library/blob/master/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/convert/JASConvert.java.
The conversion of Rubi (Mathematica pattern matching rules) is described in this wiki page:
https://github.com/axkr/symja_android_library/wiki/Porting-Rubi-Integration-rules-to-Symja.
Symja is used currently in the Android and Apple Store NCalc programs by github user @tranleduy2000.
(Very) long term goal is to use Symja as a programming language (similar to Mathematica packages) and providing a JSON API interface (with NLP functions in the future?):
https://github.com/axkr/symja_android_library/wiki/API
https://github.com/axkr/symja_android_library/blob/master/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/convert/JASConvert.java.
The conversion of Rubi (Mathematica pattern matching rules) is described in this wiki page:
https://github.com/axkr/symja_android_library/wiki/Porting-Rubi-Integration-rules-to-Symja.
Symja is used currently in the Android and Apple Store NCalc programs by github user @tranleduy2000.
(Very) long term goal is to use Symja as a programming language (similar to Mathematica packages) and providing a JSON API interface (with NLP functions in the future?):
https://github.com/axkr/symja_android_library/wiki/API
The project is now splitted in more maven submodules:
<module>matheclipse-external</module>
<module>matheclipse-frontend</module>
<module>matheclipse-core</module>
<module>matheclipse-api</module>
<module>matheclipse-io</module>
There is the tutorial with the available functions in markdown: https://github.com/axkr/symja_android_library/tree/master/symja_android_library/doc
And there is the Wiki section https://github.com/axkr/symja_android_library/wiki
A feature "highlight" is the port of the RUBI integration engine: https://github.com/axkr/symja_android_library/wiki/Porting-Rubi-Integration-rules-to-Symja
Another is the "partial" Wolfram language package support: https://github.com/axkr/symja_android_library/wiki/Context
The
Compile function https://github.com/axkr/symja_android_library/blob/master/symja_android_library/doc/functions/Compile.md will be independent from the JDK in next version and will be realized with the Janino compiler: http://janino-compiler.github.io/janino/
The BooleanVariables() function use this internally https://github.com/axkr/symja_android_library/blob/master/symja_android_library/doc/functions/BooleanVariables.md
I want to write a formula with only "&&"s or only "||"s, and I think that's what my
deMorgan1/deMorgan2 replacements are doing