Long term goals: For your amusement :-)
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Tim Daly
May 26, 2026, 10:18:55 AMMay 26
to FriCAS - computer algebra system
The Hawaii Test. Ah, how dreams die.
If you haven't seen this you might find it amusing.
It would be interesting to know what are the Fricas long term goals.
If you raise your eyes to the horizon, where are you going? Why?
This is from (axiom/goals in git):
Computational Mathematics is not a competition, it is a field
of study. Do what you can to make it better for all.
Axiom has several goals.
1) Axiom needs to live.
Keeping Axiom alive is a primary goal. It is patently obvious that
open source projects tend to die when the lead maintainer stops
development for any reason. Github and Sourceforge have many
thousands of examples.
Commercial software dies when the company dies. Witness
Symbolics (Macsyma), Soft Warehouse (Derive), or MapleSoft
(Maple was sold to a Japanese company which currently
supports it). Companies die, on average, after 15 years.
Axiom is timeless in that it is computational mathematics. The
algorithms and results will always be correct. So unlike other
efforts, what we write can be used by later generations.
This goal influences every decision about direction and purpose,
in particular, driving some of the goals listed below.
2) Axiom needs to be better documented and better explained.
The decision to deeply explain and document Axiom is based on
the obvious need to make it possible for new people to maintain,
modify, and extend it.
Explanation needs structure so a new person can "linearly learn"
what is needed. It also needs structure so information can be found
easily through some search mechanism. It further needs structure to
incorporate what is already known.
Literate programming was chosen after a long search for possbile
solutions.
The book-like nature of a literate program focuses attention on
people, not machines. It is a linear format which provides a way
to communicate ideas using methods developed over history.
Books are structure we understand.
You can find information in the volume choice; there are currently
21; the table of contents, tables of figures and subjects, detailed
indexes, a new "rich form bibliography" which includes abstracts,
and the use of hyperlinks between volumes, to outside sources,
and to youtube videos and courses. Experiments are being done
to embed gifs to illustrate ideas.
Algorithms, Categories, and Domains now have hyperlinks to
published literature and there are some initial examples of deeper
documentation of the algorithms. Ideally every algorithm will provide
sufficient explanation of the implementation or links to explanations
so the implementation can be understood in context.
In additon, people have generously contributed material from other
sources which directly explain details of Axiom, sometimes even
written by the Axiom primary authors.
There is a structured bibliography based on various sub-topics as
well as a section on external references to Axiom (currently 636
have been found).
There is an automated regression test suite that is being expanded
and made uniform for testing all known functions. The Axiom code
is now using a uniform syntax and has per-function help text, as
well as automated generation of help files.
Finally there is a literate bug document that points at known
problems (with a plan for adding deeper explanations and possible
solutions).
3) Axiom is RESEARCH software.
It is exploring ways to push the boundaries of computational
mathematics.
3A) Proving Axiom Correct
Computational Mathematics IS Mathematics.
It needs proofs, not handwaving.
This effort involves adding proof technology to Axiom.
Propositions are types and can be incorporated into the Category
structure as "type signatures". Domains already have
representations which is known in logic as the "carrier". Proofs
of Propositions, using operations from the domain, will show that
the Domain is properly designed and implemented.
The three parts (signatures, representations, proofs) mirror the
logic structure of "typeclasses" which have (signatures, carriers,
proofs) so there is a solid formal basis in logic for Axiom's
Category/Domain structure.
Because Axiom uses Group Theory as a scaffold there is a solid
formal basis for inheriting propositions so a Domain knows what
it needs to prove and what operations are needed in the Domain
to support that proof.
Axiom currently can invoke Coq and ACL2 during the build process.
An example of automatically proving a lisp algorithm using ACL2
exists. A Coq example is being worked on. In addition, we are
looking in detail at a new system called LEAN.
3B) Number representations
There are two research efforts. One involves "formal numbers" so
that we can claim that the symbol 'x' is an 'Integer' without giving
it a value. This was work originally performed under grant at City
College of New York.
The second involves work by Gustafson on a new representation
of floats that can be dynamic in range and easier to reason about.
The goal is to push this through the numeric libraries in order to
eliminate some of the costly checking and arrive a reliable results.
Some of this work is being done on a FPGA (which is now
mainstream on some Intel chips).
3C) Provisos
Provisos are a long-standing research question. Some work has
been done, mostly using Cylindrical Algebraic Decomposition, to
derive new ways to constrain the boundaries of valid computations.
It is expected that this work will benefit greatly from the integration
with formal methods listed above.
4) Teaching
In order to keep Axiom alive we need to teach the next generation.
Axiom is developing the coursework necessary for teaching
computational mathematics. There are Universities planning to
teach using Axiom and every effort will be made to support those
efforts. In addition, there is a plan to teach at CMU.
The end result will be course outlines, a set of slides for standard
28 lecture courses, and published youtube videos collected under
a youtube channel for distance learning.
Besides computational mathematics, one of the courses will focus
on maintaining, modifying, and extending Axiom with new ideas.
5) Standards
5A) Axiom has done some work to automate the semantics of
NIST's Digital Library of Mathematical Functions (DLMF). Macros
translate the Latex sources to Axiom input based on additional
decorations.
5B) Axiom has a Computer Algebra Test Suite (CATS) which
uses published sources as test cases, finding bugs in Axiom
as well as the publications.
5C) Axiom is moving to full browser-based HTML5 documentation,
moving the Hypertex and Graphics packages to HTML and Canvas
code. Dynamic Axiom input/output in HTML exists and works.
6) New Algorithms
Research on new algorithms, such as a full implementation of Clifford
algebra, are "in-process". Gustafson Floats will eventually be
another Domain as a numeric category, useful for constructing
things like POLY(GUST), that is, Polynomials over Gustafson floats.
New algorithms are interesting but without proper explanation of the
idea and the implementation detail they are just "soon-to-be-dead-code".
Every effort is being made to ensure that new code provides the details
needed to understand the algorithm and the implementation, along with
proper testing, examples, help files, and associated external references.
7) The 30 Year Horizon
Axiom has a "30 Year Horizon" focus. We will arrive at our goal in 30
years, starting today. Which is, in mathematical fashion, true for every
given future day.
Computational Mathematics is a huge field and we are only at the very
beginning of this journey. Find an idea. Research the literature. Talk to
a lot of people. Push the envelope just a little bit. In other words, do the
equivalent of a PhD thesis. You already have a research platform. You
don't need the degree, you just need the ambition.
Collaborate, Cooperate, Contribute.
of study. Do what you can to make it better for all.
Axiom has several goals.
1) Axiom needs to live.
Keeping Axiom alive is a primary goal. It is patently obvious that
open source projects tend to die when the lead maintainer stops
development for any reason. Github and Sourceforge have many
thousands of examples.
Commercial software dies when the company dies. Witness
Symbolics (Macsyma), Soft Warehouse (Derive), or MapleSoft
(Maple was sold to a Japanese company which currently
supports it). Companies die, on average, after 15 years.
Axiom is timeless in that it is computational mathematics. The
algorithms and results will always be correct. So unlike other
efforts, what we write can be used by later generations.
This goal influences every decision about direction and purpose,
in particular, driving some of the goals listed below.
2) Axiom needs to be better documented and better explained.
The decision to deeply explain and document Axiom is based on
the obvious need to make it possible for new people to maintain,
modify, and extend it.
Explanation needs structure so a new person can "linearly learn"
what is needed. It also needs structure so information can be found
easily through some search mechanism. It further needs structure to
incorporate what is already known.
Literate programming was chosen after a long search for possbile
solutions.
The book-like nature of a literate program focuses attention on
people, not machines. It is a linear format which provides a way
to communicate ideas using methods developed over history.
Books are structure we understand.
You can find information in the volume choice; there are currently
21; the table of contents, tables of figures and subjects, detailed
indexes, a new "rich form bibliography" which includes abstracts,
and the use of hyperlinks between volumes, to outside sources,
and to youtube videos and courses. Experiments are being done
to embed gifs to illustrate ideas.
Algorithms, Categories, and Domains now have hyperlinks to
published literature and there are some initial examples of deeper
documentation of the algorithms. Ideally every algorithm will provide
sufficient explanation of the implementation or links to explanations
so the implementation can be understood in context.
In additon, people have generously contributed material from other
sources which directly explain details of Axiom, sometimes even
written by the Axiom primary authors.
There is a structured bibliography based on various sub-topics as
well as a section on external references to Axiom (currently 636
have been found).
There is an automated regression test suite that is being expanded
and made uniform for testing all known functions. The Axiom code
is now using a uniform syntax and has per-function help text, as
well as automated generation of help files.
Finally there is a literate bug document that points at known
problems (with a plan for adding deeper explanations and possible
solutions).
3) Axiom is RESEARCH software.
It is exploring ways to push the boundaries of computational
mathematics.
3A) Proving Axiom Correct
Computational Mathematics IS Mathematics.
It needs proofs, not handwaving.
This effort involves adding proof technology to Axiom.
Propositions are types and can be incorporated into the Category
structure as "type signatures". Domains already have
representations which is known in logic as the "carrier". Proofs
of Propositions, using operations from the domain, will show that
the Domain is properly designed and implemented.
The three parts (signatures, representations, proofs) mirror the
logic structure of "typeclasses" which have (signatures, carriers,
proofs) so there is a solid formal basis in logic for Axiom's
Category/Domain structure.
Because Axiom uses Group Theory as a scaffold there is a solid
formal basis for inheriting propositions so a Domain knows what
it needs to prove and what operations are needed in the Domain
to support that proof.
Axiom currently can invoke Coq and ACL2 during the build process.
An example of automatically proving a lisp algorithm using ACL2
exists. A Coq example is being worked on. In addition, we are
looking in detail at a new system called LEAN.
3B) Number representations
There are two research efforts. One involves "formal numbers" so
that we can claim that the symbol 'x' is an 'Integer' without giving
it a value. This was work originally performed under grant at City
College of New York.
The second involves work by Gustafson on a new representation
of floats that can be dynamic in range and easier to reason about.
The goal is to push this through the numeric libraries in order to
eliminate some of the costly checking and arrive a reliable results.
Some of this work is being done on a FPGA (which is now
mainstream on some Intel chips).
3C) Provisos
Provisos are a long-standing research question. Some work has
been done, mostly using Cylindrical Algebraic Decomposition, to
derive new ways to constrain the boundaries of valid computations.
It is expected that this work will benefit greatly from the integration
with formal methods listed above.
4) Teaching
In order to keep Axiom alive we need to teach the next generation.
Axiom is developing the coursework necessary for teaching
computational mathematics. There are Universities planning to
teach using Axiom and every effort will be made to support those
efforts. In addition, there is a plan to teach at CMU.
The end result will be course outlines, a set of slides for standard
28 lecture courses, and published youtube videos collected under
a youtube channel for distance learning.
Besides computational mathematics, one of the courses will focus
on maintaining, modifying, and extending Axiom with new ideas.
5) Standards
5A) Axiom has done some work to automate the semantics of
NIST's Digital Library of Mathematical Functions (DLMF). Macros
translate the Latex sources to Axiom input based on additional
decorations.
5B) Axiom has a Computer Algebra Test Suite (CATS) which
uses published sources as test cases, finding bugs in Axiom
as well as the publications.
5C) Axiom is moving to full browser-based HTML5 documentation,
moving the Hypertex and Graphics packages to HTML and Canvas
code. Dynamic Axiom input/output in HTML exists and works.
6) New Algorithms
Research on new algorithms, such as a full implementation of Clifford
algebra, are "in-process". Gustafson Floats will eventually be
another Domain as a numeric category, useful for constructing
things like POLY(GUST), that is, Polynomials over Gustafson floats.
New algorithms are interesting but without proper explanation of the
idea and the implementation detail they are just "soon-to-be-dead-code".
Every effort is being made to ensure that new code provides the details
needed to understand the algorithm and the implementation, along with
proper testing, examples, help files, and associated external references.
7) The 30 Year Horizon
Axiom has a "30 Year Horizon" focus. We will arrive at our goal in 30
years, starting today. Which is, in mathematical fashion, true for every
given future day.
Computational Mathematics is a huge field and we are only at the very
beginning of this journey. Find an idea. Research the literature. Talk to
a lot of people. Push the envelope just a little bit. In other words, do the
equivalent of a PhD thesis. You already have a research platform. You
don't need the degree, you just need the ambition.
Collaborate, Cooperate, Contribute.
Tim Daly
May 26, 2026, 11:01:28 AMMay 26
to fricas...@googlegroups.com
Even more amusing is that I have written several programs recently
using Claude Code. I haven't even looked at the generated source code.
Indeed one of the systems now just generates binary without code.
So clearly I have no idea what I'm talking about. History is harsh. :-)
The goal these days is to communicate from machine to machine
not human to human. The task is to create "skills", essentially
sets of prompts that focus the LLMs attention and indicate goals
for agents. For example,
Currently nobody actually understands how LLMs reach a conclusion
despite displaying "internal thoughts". Robots using VLA (vision language
action) perform actions that are so automatic they don't show up in the
internal thoughts trace.
I suspect that within a few years the hand-coded algorithm approach
will be pointless. Once the AI begins to deeply understand Trager's
Integration there is no need for code.
If you still write code by hand you're losing to history. The future arrived.
Write skills that "embody" computer algebra.
Tim
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Qian Yun
May 26, 2026, 7:26:10 PMMay 26
to fricas...@googlegroups.com
On 5/26/26 10:18 PM, Tim Daly wrote:
>
> It would be interesting to know what are the Fricas long term goals.
> If you raise your eyes to the horizon, where are you going? Why?
>
The README lists:
>
> It would be interesting to know what are the Fricas long term goals.
> If you raise your eyes to the horizon, where are you going? Why?
>
- continue structural improvements
(remove dead code, simplify code structure when possible)
- add new mathematical algorithms
(this goal will never be finished)
- develop better user interface
(needs better CLI, emacs interface, native GUI, web UI)
- develop improved Spad compiler
(hopefully Spad compiler is bootstrapped by Spad)
- make it easier for external programs to interface with FriCAS
(especially sagemath. The call-lisp-from-c interface seems brittle.)
- support for using external mathematical routines from Spad
(e.g. flint.)
From my side, goals/dreams:
fricas has fixed around 1000 bugs, maybe another few thousands
left to fix.
Some structural changes to avoid unsoundness.
Implement the missing pieces of Risch algorithm.
Once Spad compiler is bootstrapped, add backends to target
other languages.
Higher performance, multi-threading, SIMD, GPU even.
Make the architecture modular: core + extensions.
So that it is easier to understand, both by humans and AI.
- Qian
Qian Yun
May 26, 2026, 7:29:17 PMMay 26
to fricas...@googlegroups.com
On 5/26/26 11:00 PM, Tim Daly wrote:
> Even more amusing is that I have written several programs recently
> using Claude Code. I haven't even looked at the generated source code.
> Indeed one of the systems now just generates binary without code.
> So clearly I have no idea what I'm talking about. History is harsh. :-)
>
> The goal these days is to communicate from machine to machine
> not human to human. The task is to create "skills", essentially
> sets of prompts that focus the LLMs attention and indicate goals
> for agents. For example,
> https://github.com/human-avatar/skills-for-humanity <https://github.com/
> Even more amusing is that I have written several programs recently
> using Claude Code. I haven't even looked at the generated source code.
> Indeed one of the systems now just generates binary without code.
> So clearly I have no idea what I'm talking about. History is harsh. :-)
>
> The goal these days is to communicate from machine to machine
> not human to human. The task is to create "skills", essentially
> sets of prompts that focus the LLMs attention and indicate goals
> for agents. For example,
> human-avatar/skills-for-humanity>
>
What about machine to human?
Do you think LLMs can understand Axiom? Can it help people
to complete the goal of document Axiom in literature programming
style? So that humans can understand Axiom completely?
- Qian
Hill Strong
May 26, 2026, 8:39:22 PMMay 26
to fricas...@googlegroups.com
LLMs understand nothing and never can. At best, these systems are partial pattern recognisers and at worse the results are garbage.
What we see today is the same effect that occurred when database technology became common. People of all stripes including DBAs and other technical people had a trust of the technology which was unwarranted.
I have spent many many years having to analyse software systems and the vast majority are, how shall I put this, not doing what they are supposed to be designed for. The results obtained may appear to be correct. However, on deep analysis of the code base, one realises that the results obtained aren't real.
If one using any LLM has a detailed understanding of the code related to the specific LLM system, one can use that system somewhat effectively. Otherwise, one will face certain problems with whatever is produced.
I have found that subject matter experts are not necessarily au fait with the problems of the systems they use or build and trust those systems more than they should.
Mind you, most non-subject matter experts are worse in the trust they have for these systems.
One should trust these systems like you would a politician or a used car salesman or anyone trying to sell you a bridge in New York City.
I am not saying that one should never use these systems, but be very very very careful about trusting the results obtained. Check and recheck the results very very thoroughly before accepting those results.
- Qian
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Tim Daly
May 27, 2026, 12:45:58 AMMay 27
to fricas...@googlegroups.com
> Do you think LLMs can understand Axiom? Can it help people
> to complete the goal of document Axiom in literature programming
> to complete the goal of document Axiom in literature programming
> style? So that humans can understand Axiom completely?
Barry Trager sent me a copy of the book "Integration in Finite Terms:
Fundamental Sources"[0]. The book has a series of papers leading up
to his PhD thesis. Years ago I tried several times to read and understand
his PhD work in integration and failed completely. Now I am working
through the background material.
While working through the book I revisited the resultant algorithm.
I asked an LLM about it. The result was
"When integrating rational functions, finding the logarithmic part of the
integral requires determining the poles and their associated residues.
Computing these algebraically without finding the roots of large
denominator polynomials requires the Rothstein-Trager Resultant."
Pulling on that thread leads to Barry's Masters Thesis.
I asked an LLM to explain the resultant algorithm. The LLM not
only explained it in great detail (I'm a slow learner), it constructed
many examples until I could compute it by hand.
That leads to WHY you need the resultant algorithm which leads
to further LLM question-answer sessions.
Without LLMs I'm not sure I could fully understand Trager in any
reasonable amount of time.
The point is that the LLMs can already explain Trager. The question
then becomes "When can they use that understanding to compute
integration". My guess is it already can when given the correct series of
prompts.
I had advocated developing an MCP (Model Context Protocol) server
to give LLMs access to the computer algebra system, part of the goal
of making the algebra available to other systems. However I think the
time has passed when this is useful. The LLMs already "know" most
of the answers to computer algebra questions. Whether the answer is
correct or not is questionable at the moment but I think that will change.
It would be an interesting study to discover how much computer algebra
system output is already "known" to an LLM. The LLM output requires
careful prompt construction (known as "skills"). I suspect the likely path
going forward will be constructing "skills" that give the same or better
output than the current computer algebra systems. It has the added
feature of being able to explain the result (aka machine-to-human) in
any desired amount of detail.
So the forward-looking path is "skill development" rather than hand
written algorithms. I am trying hard to learn this new game.
As the Red Queen in Carroll's "Through the Looking-Glass" said:
"Now, here, you see, it takes all the running you can do, to keep in
the same place. If you want to get somewhere else, you must run
at least twice as fast as that!"
Tim, the trailing edge runner.
[0] Clemens G. Raab and Michael F. Singer (ed)
"Integration in Finite Terms: Fundamental Sources" (2022) ISBN 9783030978664
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Dima Pasechnik
May 27, 2026, 6:27:59 PMMay 27
to fricas...@googlegroups.com
On Tue, May 26, 2026 at 6:26 PM Qian Yun <oldk...@gmail.com> wrote:
>
> On 5/26/26 10:18 PM, Tim Daly wrote:
> >
> > It would be interesting to know what are the Fricas long term goals.
> > If you raise your eyes to the horizon, where are you going? Why?
> >
> The README lists:
>
> - continue structural improvements
>
> (remove dead code, simplify code structure when possible)
>
> - add new mathematical algorithms
>
> (this goal will never be finished)
>
> - develop better user interface
>
> (needs better CLI, emacs interface, native GUI, web UI)
>
> - develop improved Spad compiler
>
> (hopefully Spad compiler is bootstrapped by Spad)
>
> - make it easier for external programs to interface with FriCAS
>
> (especially sagemath. The call-lisp-from-c interface seems brittle.)
SageMath doesn't do call-lisp-from-c in the case of fricas (it uses
>
> On 5/26/26 10:18 PM, Tim Daly wrote:
> >
> > It would be interesting to know what are the Fricas long term goals.
> > If you raise your eyes to the horizon, where are you going? Why?
> >
> The README lists:
>
> - continue structural improvements
>
> (remove dead code, simplify code structure when possible)
>
> - add new mathematical algorithms
>
> (this goal will never be finished)
>
> - develop better user interface
>
> (needs better CLI, emacs interface, native GUI, web UI)
>
> - develop improved Spad compiler
>
> (hopefully Spad compiler is bootstrapped by Spad)
>
> - make it easier for external programs to interface with FriCAS
>
> (especially sagemath. The call-lisp-from-c interface seems brittle.)
pexpect, that's sockets/pipes, more or less),
and that's actually what makes it more brittle than SageMath's main
interface with maxima, which is call-lisp-from-c.
For the latter, fricas needs to be packaged as ecl .fas file, to be
loaded by ecl, among with other things on our side.
Dima
>
> - support for using external mathematical routines from Spad
>
> (e.g. flint.)
>
>
> From my side, goals/dreams:
>
> fricas has fixed around 1000 bugs, maybe another few thousands
> left to fix.
>
> Some structural changes to avoid unsoundness.
>
> Implement the missing pieces of Risch algorithm.
>
> Once Spad compiler is bootstrapped, add backends to target
> other languages.
>
> Higher performance, multi-threading, SIMD, GPU even.
>
> Make the architecture modular: core + extensions.
> So that it is easier to understand, both by humans and AI.
>
> - Qian
>
> --
> You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group.
> To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel...@googlegroups.com.
> To view this discussion visit https://groups.google.com/d/msgid/fricas-devel/4a60e5b6-9655-415c-8bd9-ce43fd0755a7%40gmail.com.
> You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group.
> To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel...@googlegroups.com.
Qian Yun
May 27, 2026, 7:22:20 PMMay 27
to fricas...@googlegroups.com
On 5/28/26 6:27 AM, Dima Pasechnik wrote:
>>
>> - make it easier for external programs to interface with FriCAS
>>
>> (especially sagemath. The call-lisp-from-c interface seems brittle.)
> SageMath doesn't do call-lisp-from-c in the case of fricas (it uses
> pexpect, that's sockets/pipes, more or less),
> and that's actually what makes it more brittle than SageMath's main
> interface with maxima, which is call-lisp-from-c.
>
> For the latter, fricas needs to be packaged as ecl .fas file, to be
> loaded by ecl, among with other things on our side.
>
> Dima
>
>
Yes, current fricas-sage interface is pexpect based.
>>
>> - make it easier for external programs to interface with FriCAS
>>
>> (especially sagemath. The call-lisp-from-c interface seems brittle.)
> SageMath doesn't do call-lisp-from-c in the case of fricas (it uses
> pexpect, that's sockets/pipes, more or less),
> and that's actually what makes it more brittle than SageMath's main
> interface with maxima, which is call-lisp-from-c.
>
> For the latter, fricas needs to be packaged as ecl .fas file, to be
> loaded by ecl, among with other things on our side.
>
> Dima
>
>
Each lisp has different call-lisp-from-c interface, which is
a bit messy, unlike call-c-from-lisp interfaces.
About ECL interface, my understanding is that it can only
load one .fas at a time, so that fricas and maxima can't coexist?
- Qian
Dima Pasechnik
May 27, 2026, 8:33:31 PMMay 27
to fricas...@googlegroups.com
(require 'maxima)
(require 'foobar)
loads maxima.fas and foobar.fas.
SageMath interface would need adjustments and a refactoring,
certainly, as it wasn't designed to handle FriCAS,
but I don't see real issues there.
Dima
>
> - Qian
>
> --
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Qian Yun
May 27, 2026, 8:37:50 PMMay 27
to fricas...@googlegroups.com
Only one instance of this interface can be instantiated,
so the user should not try to instantiate another one,
So there can be only one (ecl-python) interface working at a time?
- Qian
Waldek Hebisch
May 27, 2026, 8:41:55 PMMay 27
to fricas...@googlegroups.com
packages and probably could even use different threads, so this
is really not a limitation.
--
Waldek Hebisch
Dima Pasechnik
May 27, 2026, 8:48:50 PMMay 27
to fricas...@googlegroups.com
It's not designed to load multiple copies of maxima
(which would then need to live in different namespaces, etc)
>
> So there can be only one (ecl-python) interface working at a time?
one more Lisp-based
system with SageMath interface, Kenzo)
Dima
>
> - Qian
>
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Camm Maguire
May 28, 2026, 12:42:53 PMMay 28
to Tim Daly, ca...@maguirefamily.org, FriCAS - computer algebra system
Hi Tim!
Tim Daly <axio...@gmail.com> writes:
> The Hawaii Test. Ah, how dreams die.
> If you haven't seen this you might find it amusing.
> https://www.youtube.com/watch?v=Av0PQDVTP4A
>
Actually quite an inspiring talk, as the audience reaction readily
attested.
To me the struggle here has always been the mismatch between how the
human brain naturally works, and the precision and determinism we so
admire in the micproprocessors we construct.
We want the 'right answer' of mathematics, indeed it is one of the few
things in modern society we can 'trust'. For all the cacophony and
division among humans, mathematics is taught essentially the same way
everywhere throughout the world. Yet few, *very* few humans have the
patience and determination to follow the bit operations behind any
conclusion. We desperately need to shorten, abbreviate, generalize,
construct mnemonics and heuristics, and, sadly but importantly, *flush*
extraneous information. Even the compulsory sleep cycle of our biology
attests to the importance of this process.
So when humans look at code, it is to jog their memory as quickly as
possible to a greatly admired monument of precise logic just long enough
to spot a problem, or even simply wonder at its alien beauty. The code
itself should be mostly self explanatory for this purpose. Occasionally
we do have to consult a manpage or similar to explain in English what is
in reality a flow of mathematical logic, but in general the verbosity
and imprecision of human language limits the utility of this process.
One commits to memory a grab bag of useful tools to maximize the range
of our capability and ignores the rest. You are quite right that the
size of the documentation is not relevant as long as we have a good
indexing process, which we do -- today's internet in this sense is one
large 'book'.
So it is somewhat ironic but not all that surprising that the AI
movement of today has our beloved precise mathematical computers
spitting out vague, emotional dialogue suggestive of plausibility only
to supposedly facilitate our next advance in productivity. We have
reproduced all our human foibles in the new wave of computation -- the
comment about trusting 'it' like you would a used car salesman is quite
apropos. But you know, it works. One can retrieve an overlooked idea
or relevant notion much more quickly with this tool. And it is
constructed to never overtax our limited brains, providing only one page
at a time, spitting out verbatim tasks we would consider tedious and
uninteresting, and often flattering us to boot!
There are very few scholars, precious, who of course need a thorough
understanding of the algorithms to hopefully develop new ones. Then
there are a few more who want to use their work in scientific and
engineering applications, who basically need reliability. And there are
many more who like pretty graphics and get excited about fantastic
concepts related to technology. These, like most of us, need a "story"
or "narrative". One might look down on the narrative as a hopeless sign
of failure, but this would ignore its proven historical utility in
preserving "the book" for thousands of years. Indeed the people on this
list who have contributed countless hours maintaining and preserving the
thing of beauty that is AXIOM operate in part on principles of religion,
as any strictly utilitarian analysis would have us abandon anything
forsaken by the herd.
A "story" has to be concise, understandable even at a child's level,
inspiring, and motivating of service, cooperation, and reciprocity.
Please excuse the diatribe. On a practical matter, I would like to
cleanup the regression test failures in the Debian axiom package at some
point. A lot of work went into that suite, so I am not keen on
truncating it. Might you field some questions in this regard?
Take care,
--
Camm Maguire ca...@maguirefamily.org
==========================================================================
"The earth is but one country, and mankind its citizens." -- Baha'u'llah
Tim Daly <axio...@gmail.com> writes:
> The Hawaii Test. Ah, how dreams die.
> If you haven't seen this you might find it amusing.
> https://www.youtube.com/watch?v=Av0PQDVTP4A
>
attested.
To me the struggle here has always been the mismatch between how the
human brain naturally works, and the precision and determinism we so
admire in the micproprocessors we construct.
We want the 'right answer' of mathematics, indeed it is one of the few
things in modern society we can 'trust'. For all the cacophony and
division among humans, mathematics is taught essentially the same way
everywhere throughout the world. Yet few, *very* few humans have the
patience and determination to follow the bit operations behind any
conclusion. We desperately need to shorten, abbreviate, generalize,
construct mnemonics and heuristics, and, sadly but importantly, *flush*
extraneous information. Even the compulsory sleep cycle of our biology
attests to the importance of this process.
So when humans look at code, it is to jog their memory as quickly as
possible to a greatly admired monument of precise logic just long enough
to spot a problem, or even simply wonder at its alien beauty. The code
itself should be mostly self explanatory for this purpose. Occasionally
we do have to consult a manpage or similar to explain in English what is
in reality a flow of mathematical logic, but in general the verbosity
and imprecision of human language limits the utility of this process.
One commits to memory a grab bag of useful tools to maximize the range
of our capability and ignores the rest. You are quite right that the
size of the documentation is not relevant as long as we have a good
indexing process, which we do -- today's internet in this sense is one
large 'book'.
So it is somewhat ironic but not all that surprising that the AI
movement of today has our beloved precise mathematical computers
spitting out vague, emotional dialogue suggestive of plausibility only
to supposedly facilitate our next advance in productivity. We have
reproduced all our human foibles in the new wave of computation -- the
comment about trusting 'it' like you would a used car salesman is quite
apropos. But you know, it works. One can retrieve an overlooked idea
or relevant notion much more quickly with this tool. And it is
constructed to never overtax our limited brains, providing only one page
at a time, spitting out verbatim tasks we would consider tedious and
uninteresting, and often flattering us to boot!
There are very few scholars, precious, who of course need a thorough
understanding of the algorithms to hopefully develop new ones. Then
there are a few more who want to use their work in scientific and
engineering applications, who basically need reliability. And there are
many more who like pretty graphics and get excited about fantastic
concepts related to technology. These, like most of us, need a "story"
or "narrative". One might look down on the narrative as a hopeless sign
of failure, but this would ignore its proven historical utility in
preserving "the book" for thousands of years. Indeed the people on this
list who have contributed countless hours maintaining and preserving the
thing of beauty that is AXIOM operate in part on principles of religion,
as any strictly utilitarian analysis would have us abandon anything
forsaken by the herd.
A "story" has to be concise, understandable even at a child's level,
inspiring, and motivating of service, cooperation, and reciprocity.
Please excuse the diatribe. On a practical matter, I would like to
cleanup the regression test failures in the Debian axiom package at some
point. A lot of work went into that suite, so I am not keen on
truncating it. Might you field some questions in this regard?
Take care,
Camm Maguire ca...@maguirefamily.org
==========================================================================
"The earth is but one country, and mankind its citizens." -- Baha'u'llah
Grégory Vanuxem
May 28, 2026, 2:48:36 PMMay 28
to fricas...@googlegroups.com
Hello Tim,
> I had advocated developing an MCP (Model Context Protocol) server
> to give LLMs access to the computer algebra system, part of the goal
> of making the algebra available to other systems. However I think the
> time has passed when this is useful. The LLMs already "know" most
> of the answers to computer algebra questions. Whether the answer is
> correct or not is questionable at the moment but I think that will change.
>
> It would be an interesting study to discover how much computer algebra
> system output is already "known" to an LLM. The LLM output requires
> careful prompt construction (known as "skills"). I suspect the likely path
> going forward will be constructing "skills" that give the same or better
> output than the current computer algebra systems. It has the added
> feature of being able to explain the result (aka machine-to-human) in
> any desired amount of detail.
MCP is just a JSON protocol. A "server" is just for me a simpler way for LLMs or human interactions. It just defines something that was defined for AI relations at first.
Having something that helps AI having good insight without spending too a lot of tokens is for me a "must have". Of course AI has almost of the Internet and can be very good. But, the main point for me, and this happens now (very previsibe), is to make money. And one of the point of human in term of psychology/commercial things is to give you envy of the product. Facebook has used a very simple thing, behavioral conditioning, AI tries for me to first let "you can not do without". But their next step is you have to pay a lot (the cost of AI is pharamenous).
Skills is I think is very important too, I have to better work on it, but having a MCP for a particular system is to ameliorate this system, and accessorily the AI related.
Greg
Having something that helps AI having good insight without spending too a lot of tokens is for me a "must have". Of course AI has almost of the Internet and can be very good. But, the main point for me, and this happens now (very previsibe), is to make money. And one of the point of human in term of psychology/commercial things is to give you envy of the product. Facebook has used a very simple thing, behavioral conditioning, AI tries for me to first let "you can not do without". But their next step is you have to pay a lot (the cost of AI is pharamenous).
Skills is I think is very important too, I have to better work on it, but having a MCP for a particular system is to ameliorate this system, and accessorily the AI related.
Greg
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