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Thread: Computer Algebra System

  1. #1 Computer Algebra System 
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    Hi everybody

    I'm currently working on a open source computer algebra system. I want the system to be able to handle a very broad spectrum of mathematics.
    The first thing I'm going to implement are: equation solving, integration, derivation and function plotting. furthermore the system should be able to handle distributed computing.
    I now have 2 questions:
    1) What other features need to be implemented or would be a nice addition
    2) I'll need to find algorithm to implement all these things so if anybody happens to know about an algorithm please post it.

    Thanks very much


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  3. #2 Re: Computer Algebra System 
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    Quote Originally Posted by jan-pieterv
    Hi everybody

    I'm currently working on a open source computer algebra system. I want the system to be able to handle a very broad spectrum of mathematics.
    The first thing I'm going to implement are: equation solving, integration, derivation and function plotting. furthermore the system should be able to handle distributed computing.
    I now have 2 questions:
    1) What other features need to be implemented or would be a nice addition
    2) I'll need to find algorithm to implement all these things so if anybody happens to know about an algorithm please post it.

    Thanks very much
    An automated proof of the Riemann Hypothesis would be nice.


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  4. #3  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Differentiation and integration, AFAIK, can only be done as a list of rules. Numerical solvers are simple enough, but I'm not sure how symbolic solvers work.
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  5. #4 Re: Computer Algebra System 
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    Quote Originally Posted by DrRocket

    An automated proof of the Riemann Hypothesis would be nice.
    hmm I don't see why a CAS would need that functionality


    Quote Originally Posted by MagiMaster

    Differentiation and integration, AFAIK, can only be done as a list of rules. Numerical solvers are simple enough, but I'm not sure how symbolic solvers work.
    Differentiation is rather straight forward I think? It shouldn't be to hard to implement. Integration is a lot harder and I'll have a lot of trouble implementing it. I'm not really looking forward to that piece of the code :s But a CAS wouldn't be a CAS without integration
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  6. #5  
    Forum Radioactive Isotope MagiMaster's Avatar
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    About the only thing you can do for integration is the same as what you do for derivatives, apply a set of rules. It's just that for integration, the rules won't be able to cover all the possibilities.
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  7. #6  
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    Dr. Rocket,
    I assume you were the type of professor that would consistently make physics and math jokes throughout the lecture.

    Jan,
    Why are you adding the operations of differentiation and integration into a program that's designed for algebra?
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  8. #7  
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    I agree it's not really algebra. But it is a feature of most computer algebra systems.
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  9. #8  
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    Quote Originally Posted by jan-pieterv
    I agree it's not really algebra. But it is a feature of most computer algebra systems.
    Is there a point to this.

    Professionals already use MathCad and Mathematica. They use them because they have a lot more capability than just algebra and simple rules of differentiation and integration. mThere are relatively inexpensive student versions available to legitimate students for legitimate applications.

    Amateurs ought to learn to do these things without computer help.

    About the only application that I see is for students to have a tool that doesn't cost a lot of money to do things that they should be doing without computer help anyway. I think this is called "cheating".
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  10. #9  
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    Yes there is a point. A few actually

    Firstly I want to test my capabilities. I wanted a challenge to see how far I could go with my knowledge of mathematics and programming. Within a few months I'll know what I'm capable of.
    Secondly I'm interested in all kinds of science. I like maths, physics, computer science, engineering,... I think I can improve my knowledge of these thing by at least attempting to do this.
    Thirdly I want a CAS that is free, open source and is capable of doing parallel computing in maths.

    This isn't done to help student cheat. But I see you're point here. I could easily be used by students to cheat. But that's their problem. If thy don't want to be capable of doing there maths thy will have problems later on.
    I'm a student to you know. In February I'll start uni to study civil and construction engineering and I'll certainly use my system but only after I solved the problem first. I'll then use my system to check if it produces the correct result.

    I also know you're probably skeptical about my changes to succeed. I know this myself but as I already said I want to try
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  11. #10  
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    Quote Originally Posted by jan-pieterv
    Yes there is a point. A few actually

    Firstly I want to test my capabilities. I wanted a challenge to see how far I could go with my knowledge of mathematics and programming. Within a few months I'll know what I'm capable of.
    Secondly I'm interested in all kinds of science. I like maths, physics, computer science, engineering,... I think I can improve my knowledge of these thing by at least attempting to do this.
    Thirdly I want a CAS that is free, open source and is capable of doing parallel computing in maths.

    This isn't done to help student cheat. But I see you're point here. I could easily be used by students to cheat. But that's their problem. If thy don't want to be capable of doing there maths thy will have problems later on.
    I'm a student to you know. In February I'll start uni to study civil and construction engineering and I'll certainly use my system but only after I solved the problem first. I'll then use my system to check if it produces the correct result.

    I also know you're probably skeptical about my changes to succeed. I know this myself but as I already said I want to try
    You personally would probably learn a lot just by the attempt. It doesn't matter whether you succeed or not.

    But anyone else using a program like that could be doing themselves harm, as you recognize. You are also correct in your assessment that that is their problem.

    There is one problem that you probably cannot overcome. It is that simple differentiation and integration problems are just that, simple, and it is probably easier to do them in your head or with pencil and paper. Complicated problems can have solutions that are the same but that look quite different. A computer will find only one of them. Complicated integration problems are really complicated, and the methods used to solve them go well beyond the simple "rules" that you learned in an introductory calculus class -- some pretty tricky methods from the theory of complex variables and contour integrals come up. That is where big thick detailed integration tables show their value.

    The above difficulties nothwistanding you will probably learn a lot from the attempt, so I think it is a good idea. Just don't get too discouraged at the difficulty involved.
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  12. #11  
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    I wont get to discouraged easily. In year 10 we had to chose which course to follow. My maths teacher said I wasn't capable of doing science-maths (8) (They 8 says it's a course with 8 periods of maths a week, the maximum in Belgium) I didn't listen to here and I passed my last exams with 70%. The first I only got 40%, but I didn't give up.

    There will also be more than just integration and differentiation. But those will be the first thing I try to do. After that I want to do differential equations, Taylor series, function plotting and a few matrix things.
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  13. #12  
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    Quote Originally Posted by jan-pieterv View Post
    Hi everybody

    I'm currently working on a open source computer algebra system. I want the system to be able to handle a very broad spectrum of mathematics.
    The first thing I'm going to implement are: equation solving, integration, derivation and function plotting. furthermore the system should be able to handle distributed computing.
    I now have 2 questions:
    1) What other features need to be implemented or would be a nice addition
    2) I'll need to find algorithm to implement all these things so if anybody happens to know about an algorithm please post it.

    Thanks very much
    You may try this online CAS:

    [Omega . A Computer Algebra System Explorer]

    click on calculator image to access. no download/install needed. works on iPad, smartphne too.
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  14. #13  
    Moderator Moderator Markus Hanke's Avatar
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    Wow, you've taken on quite a project with this. Now, six months down the line, how are you getting on with it ??
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  15. #14  
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    Hello Folks ,
    Differentiation and integration may be the one way but VIII Grade Algebra can't be done through all these .
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