https://github.com/barton-willis/ordmexpt

new implementation of the Maxima function ordmexpt
https://github.com/barton-willis/ordmexpt

Last synced: 4 days ago
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new implementation of the Maxima function ordmexpt

• Host: GitHub
• URL: https://github.com/barton-willis/ordmexpt
• Owner: barton-willis
• License: gpl-3.0
• Created: 2024-11-01T13:23:52.000Z (14 days ago)
• Default Branch: main
• Last Pushed: 2024-11-09T20:31:56.000Z (6 days ago)
• Last Synced: 2024-11-09T20:32:13.040Z (6 days ago)
• Language: Common Lisp
• Size: 60.5 KB
• Stars: 2
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
## Maxima function `ordmexpt`

This project aims to develop a new version of the Maxima function `ordmexpt`, 

which is a subroutine for Maxima's ordering predicate `great`. This 

rewrite attempts to clarify the logic of the function and to fix [bug #4383: 

great not transitive (so simplifya not idempotent)](https://sourceforge.net/p/maxima/bugs/4383/). Specifically, bug #4383 causes the following expression to not simplify correctly

~~~

(%i1)	(declare(z,complex), domain : complex)$

(%i2)	exp(z) + sqrt(exp(z)) + exp(z);

(%o2)	%e^z+sqrt(%e^z)+%e^z

~~~

Maxima's ordering predicate `great` is closely linked to simplification, 

so tweaking `great` can cause syntactic testsuite failures. To help 

distinguish syntactic from semantic failures, this project includes a 

modified function `approx-alike` that applies several transformations 

to both the expected and actual outputs. This modified function is *not* 

intended as a replacement to `approx-alike`. 

The last I tried, my alternative `ordmexpt` function runs the testsuite, including

the share testsuite, with fifty-seven unexpected failures. Of these failures, the alternative `approx-alike` determines that twenty-three of these failures are syntactic. Of the remaining thirty-four failures, many are syntactic failures.

Here is a typical such failure:

~~~

********************** Problem 80 (line 736) ***************

Input:

         - v

         ───

          2

specint(t    bessel_j(v, 2 sqrt(a) sqrt(t)) exp(- p t), t)

Result:

 v - 1   - a/p                               a

p      %e      v gamma_incomplete_lower(v, - ─)

                                             p

───────────────────────────────────────────────

                v  v/2

           (- 1)  a    gamma(v + 1)

This differed from the expected result:

 v - 1   - a/p                             - a

p      %e      v gamma_incomplete_lower(v, ───)

                                            p

───────────────────────────────────────────────

            v/2      v

           a    (- 1)  gamma(v + 1)

~~~

The file `rtest_great` test the function `great`. Currently, with the new `ordmexpt` 

function several tests fail. Until these failures are sorted, this code is only 

experimental.

Running the testsuite calls `ordmexpt` about two million times, so we need to be

concerned with its efficiency. In addition to fixing bug #4383, the modified `ordmexpt` function fixes two testsuite failures-they are `rtest1`, #183 and `rtest_limit_extra` #259; the limit bug is  

~~~

Running tests in rtest_limit_extra:

********************** Problem 259 (line 909) ***************

Input:

                 - a

                 ───

              a   2

limit((%i + 1)  2   , a, inf)

Result:

ind

... Which was correct, but was expected to be wrong due to a known bug in Maxima or SBCL.

~~~

This bug fix is *not* related to the extra simplifications in `approx-alike`.