I might perhaps represent a silent majority (?) of  the free CAS users!

As CSIRO research scientist (1968-2000) I used Reduce (since Reduce 2.0 !), 
Vaxima then later Macsyma, Mathematica and Maple. 

But I myself found Reduce and its PSL basis far more suited to my needs.
True the interactive use of Reduce could not be compared with the commercial 
products which offered more pleasant input & output. Besides their note books 
were invaluable for presentations and perhaps more importantly to convince the 
holders of the purse strings of their value for money! 

In that respect I had some difficulty even to justify the small fee required for the
 ZIB distribution of Reduce when the budgets became much tighter! 

I had none whatever for Mathematica!

Whereas I could only convince few of my colleagues that Reduce was an essential
 research tool Mathematica received universal support. I believe that no other CAS 
was supported after I retired.
The problem I found myself with the commercial CAS software is the impossibility 
to develop anything really creative because the inner machinery is sealed from the 
user and if something is not readily available as per the User's guide it can be done 
by the developers but at very high costs and under contract conditions unbearable 
in a public research context or even a private one for that matter. 

So use it as such and pay or leave it!

As Arthur says with Reduce all the software is there for you to do whatever you can.

But the most important part is that you can find support with very generous people!
Well Arthur cannot mention that since he is one of the most active support in the
matter. So I feel an obligation to do that for him!
This is a support one could never get from the commercial support even with access 
to unlimited finances!

Now when I retired I could not really justify (to my wife!) in my home budget even 
the modest ZIB fee but I discovered that Maxima --- originally a DOE project--- 
remained in public domain at least in the state left by William Schelter (I believe) 
before it became the commercial product I knew as Vaxima and then Macsyma.
Commercial Macsyma compared well with Mathematica as for its GUI and note books. 
Based on Common Lisp it was very attractive to me because PSL was a bit too restrictive 
(precisely in its input/output facilities). 

However I was soon disappointed because the inner workings were just as tightly sealed
--- in spite of the glossy publicity leaflets! --- as with Mathematica and, at least in my case, 
support remained totally unhelpful.

Maxima (the free SourceForge distributiuon) is even harder than Reduce in its interaction 
with the user. Constantly new users complain that it is very hard to read the output even 
of relative modest size. 

However there is a nice interactive version wxMaxima which is distributed with maxima itself. 

Maxima is based on Common Lisp and has more possibilities than PSL or CSL 
based Reduce --- I guess that CSL can use the possibilities of the C language 
but I for one would not venture on this mine field. 

I found simplification rules in maxima --- the core of any CAS --- far more complex
to deal with than is the case with Reduce and even the more obvious ones, automatically 
performed by Reduce, must be made explicitly, something a Reduce user like myself 
too often forgets.

Conclusion: there is no way in my opinion one could compare commercial CAS software 
with the two non-commercial ones I am most familiar with: Reduce and Maxima, 
both now freely available with all their code at SourceForge. 

Both in fact have a very high level of active and amazingly generous support from real experts. 

In my own experience this goes together with the free access of the code.
Commercial software cannot attract the same level of expertise because the support
here is from people not doing it for money but real dedication to a life long project.

To name just a single name for each, Reduce has Arthur Norman 
--- I cannot imagine how he can find the time to react so promptly 
and so extensively to even the silliest request (often mine!) --- 
whereas maxima has the (often stern) advice of Richard Fateman (equally generous 
but less tolerant of foolishness). 
Of course there are many others and perhaps Maxima has more of them than Reduce.

My apologies to be so verbose but both on the Reduce and Maxima forums the 
same queries and --- strangely --- even quite bitter complains regularly appear. 

IMHO mere queries are of course legitimate but hardly so the complains. 

Dr R J-M Grognard

On Sat, Jun 22, 2013 at 7:34 AM, Arthur Norman <acn1@cam.ac.uk> wrote:
On Fri, 21 Jun 2013, Peng Yu wrote:
> Hi,
> My question is not a developer question. But the forum on sf is just
> inconvenience to use.

OK! I am afraid that I can not change how sourceforge arranges its forums
etc, but discussion here can be of interest to developers so you are

> Reduce-algebra is very capable and free
Thank you!

(but the gui is bad, it fa.
Sorry you do not like that. There are a range of ways you can help there!
The most extreme would be by working on a new GUI that you liked better -
the fact that Reduce is open source means you have access to pretty much
all you need to do that! Less extreme would be if there were MODEST
changes to what there is now that you believe might make a useful move in
the right direction. I say "modest" changes because I very definitely know
how much time and effort it takes to do anything in that direction. I have
a re-implementation of the GUI code for the CSL version of Reduce as one
of my projects that is at present stalled but when/if I ever get back to
it or if somebody else joins in and moves things forward it would be good
to know what users would like. Please note that explaining things in terms
that could relate to actually implementing something is liable to be a lot
more liable to influence things that high level statements of what is
desirable that do not map neatly onto implementation projects, and
stepwise ways to move from where we are to a better world may be easier to
digest than a "throw it all away and do something different"!

> There are recent papers using it. But it is Mathematica is more used.
> Has anybody compared the pros and cons of reduce-algebra vs
> Mathematica? (I don't find a comparison.) Thanks.

I think that different people are motivated by very different aspects of
the two systems. Here is my start at a few thoughts, but note very well
that somebody employed by Mathematica or Maple, or working on Axiom, or
who had used Maxima for years and years would put things differently (and
could still be right!). You specifically ask about Mathematica but I may
raise points that put Reduce in a broader context of other systems too...

(1) If you are employed in some companies or work in some universities you
may not personally have to pay for your software. You may choose only to
collaborate with others who do not have budget constraints. But some
algebra systems cost money and others do not. If a student starts using
Reduce while studying they do not suddenly have to pay once they graduate.
This issue is irrelevant to some users but matters a lot to others!

(2) If you pay for your algebra system you hope that the supplier will
provide support in all sorts of ways. If you fetch something that is open
source then the help from the developers is not something you can count on
100%. But if you find a bug then with a commercial offering you can report
it but then may need to wait until a patch or a new version is released.
With open source at least in principle you can inspect the source code and
track down issues for yourself and fix then. An extreme stance taken by
some is that they will not trust a result where they can not see all the
steps to it (hence they will view any results from a closed source system
as unverifiable and hence scientifically indefensible). Others will not
feel happy unless they are using something with paid for support (even if
they do not do a careful assessment of the frequency with which things are
fixed for them).

(3) Mathematica (in particular) emphasises a use-interface with graphing
and a load of other stuff fully integrated. If you need that sort of stuff
then you need something other than Reduce. Some people do and others just
want to compute algebraic results - and for them the notebook stuff and
graphing capability of Mathematica (or Maple... etc) is not central to
what they need of an ALGEBRA system.

(4) Some users need an algebra system for what I will describe as "general
algebra". Eg almost any use in high-school or at undergraduate level is
liable to be like that. Any of the full systems is liable to do what they
need (maybe)???? Others have special needs and so some particular systems
might thus suit them best. Let me list some things I think are strengths
of and then weaknesses of Reduce so you can see that for SOME people these
may be special reasons to go one way or the other:
   (a) Maybe all of the "redlog" parts of Reduce are respectably
       cutting edge tools for solving the sorts of problem that they
       address? If you need that then you should probably take Reduce
       jolly seriously!
   (b) If you want to embed an algebra system within your existing
       or future product then Reduce is a sane candidate to look at
       rather carefully, and has been evaluated or adopted by a number
       of people in the past.
   (c) It may be that the Reduce origin in high energy physics makes it
       a useful tool for those keen on non-commutating algebra. Each of
       the various "loadable packages" in Reduce can represent a unique
       selling point for some users!
   (d) If you develop a new package for Reduce it can go out to the world
       free of charge. Do you like that or do you view that as a problem?
There are things that some other systems do better that Reduce!
   (a) Integration involving special functions is done better elsewhere.
       There are plans for a big upgrade to Reduce on that front but no
   (b) Branch cuts and multi-values functions are a menace - and in general
       Reduce is not at the forefront of getting them right. Some other
       systems are better at letting the user note that some values should
       be positive or negative or non-zero or whatever.
   (c) Mathematica will explain that it can do EVERYTHING. Graph theory,
       number theory, group theory and probability (etc etc), and if you
       count the number of built-in or library capabilities it has then it
       beats Reduce easily. If you ever need any of those things!
   (d) As we mentioned before, the Reduce interface to the user is
       such as to try to get the job done. It has not benefitted from
       hundreds of man-years of refinement to make it beautiful. That
       really matters to some people.
   (e) If you are working in some special domain then there may be
       specialist software that will serve you much better than any of the
       general purpose packages!

You can find comparisons of systems based on just what coverage of
capabilities they have. Eg the 1999 paper
is something to chew on if you have not found it already. Of course ANY
such report gets out of date after a few years, and for any particular
user there is a BIG issue of what capabilities they need, since my belief
is that most people have their own limited range of uses.

Mathematica makes a pitch for itself on its web-site, eg
which naturally explains how good it is and how it will solve all your

I then look at what Wikipedia reports, which is

"Mathematica is proprietary software restricted by both copyright law and
trade secret.
A regular single-user license for Mathematica used in a commercial
environment costs $2495 although new customers can purchase the "Starter
Edition" for $995. They include eight additional kernels for parallel
computations and one year of service that includes updates, technical
support, a home use license, a webMathematica Amateur license, a
Wolfram Workbench license and three Mathematica Player Pro licenses.
Discounts are available for government, charity, educational,
pre-college, school, student, home use and retiree use and depend on
geographical region. Student licenses cost $140. A general "home use"
license ("Mathematica Home Edition") is also available to the public and
is priced at $295. Educational site licenses allow use by students at
home. A license manager similar to FLEXnet is available to provide
sharing of licenses within a group."

and if they could NOT make a compelling argument that they had a bunch of
features makiing them better that Reduce (which you can download for free
and see all the source code for) then something would be seriously amiss.
The only two questions for an individual or which of the rungs of the
Mathematica pricing ladder might apply to them and whether one of the
(many) extra features Mathematica offers is important enough to them to
justify the cost (remembering that in some cases the license you buy will
expire after a while). Some people will jump one way some the other!

I hope that some who favour Reduce will join us in trying to keep its
existing capabilities up to date and in adding new refinements!

> --
> Regards,
> Peng

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