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From: Peng Yu <pengyu.ut@gm...>  20130621 20:21:23

Hi, My question is not a developer question. But the forum on sf is just inconvenience to use. Reducealgebra is very capable and free (but the gui is bad, it fa. There are recent papers using it. But it is Mathematica is more used. Has anybody compared the pros and cons of reducealgebra vs Mathematica? (I don't find a comparison.) Thanks.  Regards, Peng 
From: Peng Yu <pengyu.ut@gm...>  20130621 20:21:23

Hi, My question is not a developer question. But the forum on sf is just inconvenience to use. Reducealgebra is very capable and free (but the gui is bad, it fa. There are recent papers using it. But it is Mathematica is more used. Has anybody compared the pros and cons of reducealgebra vs Mathematica? (I don't find a comparison.) Thanks.  Regards, Peng 
From: Arthur Norman <acn1@ca...>  20130621 21:34:28

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 welcome! > > Reducealgebra 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 reimplementation 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 reducealgebra 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 useinterface 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 highschool 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 noncommutating 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 timetable. (b) Branch cuts and multivalues 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 nonzero 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 builtin 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 manyears 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 http://math.unm.edu/~wester/cas_review.html 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 website, eg http://www.wolfram.com/products/mathematica/analysis/content/ComputerAlgebraSystems.html which naturally explains how good it is and how it will solve all your problems. I then look at what Wikipedia reports, which is "Mathematica is proprietary software restricted by both copyright law and trade secret. A regular singleuser 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, precollege, 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 > Arthur 
From: Peng Yu <pengyu.ut@gm...>  20130621 22:17:01

Hi Arthur, First. I want to thank you for your long and detailed reply. Here are some of my thoughts, which others may or may not agree. But that is OK. > 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 > welcome! My impression is that github is much better than sourceforge (faster, easier for collaboration, more people are using it, I've seen a number of projects migrate from sf to github but the other way around). Therefore, github is a better repository than sf for the purpose of attracting more developers and make the > > (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 > reimplementation 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 reducealgebra 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 useinterface 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 highschool 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 noncommutating 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 > timetable. > (b) Branch cuts and multivalues 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 nonzero 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 builtin 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 manyears 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 > http://math.unm.edu/~wester/cas_review.html > 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 website, eg > http://www.wolfram.com/products/mathematica/analysis/content/ComputerAlgebraSystems.html > which naturally explains how good it is and how it will solve all your > problems. > > I then look at what Wikipedia reports, which is > > "Mathematica is proprietary software restricted by both copyright law and > trade secret. > A regular singleuser 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, precollege, 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 >> > Arthur  Regards, Peng 
From: RenĂ© Grognard <dositheus41@gm...>  20130621 23:34:03
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I might perhaps represent a silent majority (?) of the free CAS users! As CSIRO research scientist (19682000) 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 noncommercial 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 JM Grognard On Sat, Jun 22, 2013 at 7:34 AM, Arthur Norman <acn1@...> 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 > welcome! > > > > > Reducealgebra 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 reimplementation 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 reducealgebra 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 useinterface 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 highschool 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 noncommutating 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 > timetable. > (b) Branch cuts and multivalues 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 nonzero 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 builtin 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 manyears 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 > http://math.unm.edu/~wester/cas_review.html > 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 website, eg > > http://www.wolfram.com/products/mathematica/analysis/content/ComputerAlgebraSystems.html > which naturally explains how good it is and how it will solve all your > problems. > > I then look at what Wikipedia reports, which is > > "Mathematica is proprietary software restricted by both copyright law and > trade secret. > A regular singleuser 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, > precollege, 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 > > > Arthur > > >  > This SF.net email is sponsored by Windows: > > Build for Windows Store. > > http://p.sf.net/sfu/windowsdev2dev > _______________________________________________ > Reducealgebradevelopers mailing list > Reducealgebradevelopers@... > https://lists.sourceforge.net/lists/listinfo/reducealgebradevelopers > 
From: Raffaele Vitolo <raffaele.vitolo@un...>  20130623 21:56:10

Dear All, I started to use Reduce a few years ago for computations on PDEs ("integrable systems"). First of all I'd like to say that GUI is completely useless for intensive scientific computation; however, it might be comfortable for beginners or for occasional users. >> There are recent papers using it. But it is Mathematica is more used. >> Has anybody compared the pros and cons of reducealgebra vs >> Mathematica? (I don't find a comparison.) Thanks. As an example, in my computations I had to deal with rational functions of many variables and denominators of degree ~20. Together with a colleague we tried the same computation on Mathematica and Reduce, it was the sum of two rational functions as above; it was impossible to finish it it Mathematica, while Reduce produced a correct result in a reasonable time. Another feature that I like so much in Reduce is the fact that expressions are always evaluated keeping into account all existing rules. I do not think that this behaviour is so easy to reproduce in Mathematica. If you work with a lot of algebraic constraints this is an essential feature. I also think that the Reduce user base is much wider than what is shown by the activity on this mailing list, I know a lot of users who are not active here. > 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... I think that the economic aspect is important but it is minor with respect to: 1  having the possibility to learn from source code; 2  having an almost immediate reaction from the community about bug fixing. In particular I was always strongly and timely helped by Arthur Norman who fixed several problems in Reduce that I noticed in quite complicated computations, using many GB of ram. I think that also commercial programs like Mathematica suffer from the presence of lots of bugs; I do not think that the support of Mathematica would be as fast as the support from the free software community. I'm not fond of ideologies, but I do not think that there is anything better than free software for learning/teaching/scientific purposes. Raffaele. 
From: Tony Roberts <anthony.roberts@ad...>  20130622 00:50:39

BEGIN PGP SIGNED MESSAGE Hash: SHA1 Hi all, I had a student who was keen on Mathematica, so I set him the side challenge of comparing it with Reduce on the class of problems we were doing. The following is our conclusion (finally due to be published soon in the J. Engrg Maths) Tony Reduce was much faster Computational experiments found that the computer algebra package Reduce was at least an order of magnitude faster than Mathematica. Table 3 lists the computational time for the Reduce and the Mathematica implementation for constructing O???4,?2?? holistic models of the one dimensional Ginzburg?Landau equation with subgrid resolutions of 2, 4, 8 and 16 subgrid intervals. These times were observed on a Pentium III, 750MHz processor, with 256 Mb ram, running Reduce 3.7, under Windows XP. Table 3 shows the Reduce implementation was 20?70 times faster than the Mathematica implementation (even with the repeated help of the Mathematica news group). Thus we use the free package Reduce [18]. Table 3: Reduce and Mathematica computational times for numerical construction of O???4,?2?? holistic models of the one dimensional Ginzburg?Landau equation for various subgrid scale resolutions, n. n Reduce Mathematica 2 1.1s 70.2s 4 3.1s 215.4s 8 8.3s 367.6s 16 23.7s 517.7 s On 22/06/13 5:51 AM, Peng Yu wrote: > Hi, > > My question is not a developer question. But the forum on sf is > just inconvenience to use. > > Reducealgebra is very capable and free (but the gui is bad, it > fa. There are recent papers using it. But it is Mathematica is more > used. Has anybody compared the pros and cons of reducealgebra vs > Mathematica? (I don't find a comparison.) Thanks. >     Professor A.J. Roberts School of Mathematical Sciences phone: +61 8 8313 3035 University of Adelaide fax: +61 8 8313 3696 South Australia 5005. mailto:anthony.roberts@... http://www.maths.adelaide.edu.au/anthony.roberts/ ==.0000001000000100000110001000011010001111110010111011101000010000== BEGIN PGP SIGNATURE Version: GnuPG v1.4.10 (Darwin) Comment: Using GnuPG with Mozilla  http://enigmail.mozdev.org/ iEYEARECAAYFAlHE9NQACgkQ7TX8dTbro1vlawCfSbqwDmooT4wlivCai2hqjmWh 07UAnRMuwc4lXVHPoEtnGeWj5hk/Npfs =vh2h END PGP SIGNATURE 