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# Computer Algebra - Science topic

Explore the latest questions and answers in Computer Algebra, and find Computer Algebra experts.
Questions related to Computer Algebra
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With 2 indices it's Aij=(Aij+Aji)/2+(Aij-Aji)/2 for GL(N).
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Hello everyone
I am working on the plankton diversity of freshwater. Other than the research articles, we can make monograph. Recently I knew about database management system (DBMS) and I can make database using my excel data and photograph but i do not how to make database management system? is anybody know about DBMS and how to make online to get everybody access. please share your knowledge.
Since you can store your data in excel file already, it means you are dealing with structured data which makes your problem even simpler. You may use the following guide:
1. Database: I recomend the use of MySQL to store your data and use Structure Query Language (SQL) to save and retreive data from it. MySQL can work with Linux & Windows servers. Also, it’s very light and open source.
...and since you want to make you system accessible online, then you need the following to make a complete system:
2. Serverside language: you may choose php, python or pearl etc. Any of this programming languages will help your web pages communicate with the server and your developed database.
3. Client-side: If your target is just the basic view, just use basic HTML or XHTML to design your page. Here, you may need to add some few things such as javascript, css etc. to get an advance user viewing experience (which you may not need at this stage).
To make your application accessible online after development, you need to communicate with a hosting company to subscribe and also get your own domain if at all you need to have your’s.
Hope this helps, good luck.
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I am trying to write a program in Java that uses Friedman Test. How can I write the algorithm? Is there any Java library for that?
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Given a tree or a graph are there automatic techniques or automatic models that can assign weights to nodes in a tree or a graph other than NN?
In the case of Euclidean graphs you can use the Euclidean distance between nodes. You can also use random weights. Depending on the application you can use appropriate weights...
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Are there techniques to automatically assign weights on weighted graphs or weights on links in concept hierarchy? Assuming the scenario depicted here : https://cs.stackexchange.com/questions/90751/weight-assignment-in-graph-theory
is a form of a weighted graph. Are there ways weights can be assigned to each edges?
Hi Jesujoba,
AFAIK, this should be accomplished based on previous knowledge (a.k.a background) such as ranking the content using certain aspect; otherwise, there is no meaning or logic behind such process.
HTH.
Samer Sarsam, PhD.
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Starting in polynomial extents, computational commutative algebra, branched into applications via Gröbner basis theory and the generalized concept of approximate commutative algebra. But what is next? Do you believe the computation extends to non-commutative algebra?
Some questions can be solved in a non-commutative graded case:
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As it is easily known, min-times and max-time algebra in the domain of real positive numbers is isomorphic to the max-plus algebra on real numbers. I have looked all papers in the references of this research project but could not find in the titles any explicit reference on the min-times or max-times algebra. I want to know if there is anybody who is working in min-times or max-times algebra.
I have found that min-times and max-times algebras and convex geometry based on these algebras are very good tool to know the structure of the maximal frontier of production possibility set for international trade economy of Ricardian type. See two of my papers below. This study is rather isolated from other idempotent semi-ring analysis, but it is possible that we can find many other fields in which we can use max-times or min-times algebra. Does anyone have information for me?
• International trade theory and exotic algebra
• Subtropical Convex Geometry as the Ricardian Theory of International Trade
N.B. Contents of two papers are not very different. The first one is much shorter but explanations are more concise.
Regarding your question, loose relation of max-plus with min- and max-times is often mentioned in the papers of the max-plus working group. Stéphane Gaubert and Marianne Akian are still active in this field, often making incursions into neighbouring topics.  I attach a link below.
Our own research deals with an abstraction of max-min-plus and max-min-times which is called idempotent semifields. We have a project in Researchgate that deals with idempotent semifields to generalize Formal Concept Analysis to matrices with entries in said semifields. Perhaps more to your liking, our IPMU 2016 paper explains how to obtain max-min-times (the dual completion of either max-times or min-times) using Pap's g-calculus from the positive reals.  I also attach a link below.
Enjoy!
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In which case a Grobner basis is stable under scalars extension ?
If you mean that given a Gröbner basis of an ideal I \cap K[X1,..,Xn] then it is a Gröbner basis for I \cap K'[X1,..,Xn] where K' is a field extension then this is (obviously) true.
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I develop CoCoA (an open source Computer Algebra System in C++) with a textual interface. It was relatively easy to write a nice Emacs interface for this textual binary: we defined the syntax for our programming language, and how to send commands from a text file to another window with the running binary.
We also have a dedicated opern source Qt interface, but it is too hard for us (mathematicians!) to develop and maintain it.
Personally I like and use the Emacs interface, but I see from our download logs that users prefer to download the GUI even though it actually does less and is not documented!!!
It would be nice to have an "empty graphical interface" (in Qt? or a "subset" of Emacs?) allowing basic editing and running a process, but I cannot find one.
Hi Anna,
Have a look at Jupyter. This is a notebook-based GUI running in the web browser. It is originally designed for Python but provided an API for connecting other "languages." Maxima already have linked to Jupyter, and I am considering this for Reduce.
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When I have two equations f=0 and g=0 over the reals, I can equivalently rewrite them as one equation f2+g2=0. Are there any alternative such encodings known? I am specifically interested in (multivariate) polynomial equations.
Are there any interesting options when more generally not considering equivalence but only equi-satisfiability?
Thomas, for univariate polynomials as in your example the trivial answer is gcd(f,g) which in this case is equivalent to computing the reduced Gröbner basis. I doubt that for the multivariate case (which is what you are really interested in) a simpler answer than f2+g2 exists for the simple reason that the complex number are a field extension of degree 2 over the reals. Of course, one could start computing a reduced Gröbner basis for the ideal generated by f and g, but I do not see that generally you will find a single polynomial expressing the solvability of f and g. Furthermore, this is of course a rather expensive approach...
Regards Werner
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The equation was given as follows:
1/ \sqrt (1+β)= \sqrt(1+β)/β
0<=β<=1 is a real number, originally defined as β=v/c.
The equation obviously has no solution.
Now lets multiply both sides with \sqrt(1-β). This is legal for real numbers in general. As β was defined to range <=1 this does not change the range of β at all.
Hurra! Physics got a solution.
You might think that x=x+1 has no solution, but multiply by x-1, simplify, and you get x=1 which has the solution x=1. Amazing!
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I have triangle mesh and calculate normal of triangles then calculate vertex normal and do some calculations on it and want to calculate vertex coordinates from this vertex normal after do calculations.
Look at this doc it may be helpful for your topic. Good luck.
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There are two surfaces in one figure, I wanted to use the legend option to distinguish the two surfaces, but this option is not available in plot3d. Thank you!!
Pro. Waldemar Koczkodaj
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A MuPAD notebook is a convenient environment for performing computations symbolically using the MuPAD language and documenting the results
There are many different computer algebra packages available, with different strengths, costs, etc. Maple, Mathematica and Matlab are among the best known commercial packages.  Sage builds (among other things) upon Maxima, and has the distinct advantage of being open source (and free as in thought, and free as in beer).  Personally, I am trying to work largely with Sage (check out sagemath.org), although I know others who prefer one of the commercial packages.
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Magma is a wonderful computer package for codes over rings but my favorite functions are missing like the Frobenius, the trace, the p-adic expansion...
Dear Christian, thanks for your answer. I am not sure that p-adic rings are the same thing as Galois rings. At least at the type level they are not. Typing is very important in Magma.
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1)Asymptotically the cost of finite field multiplication is same as field squaring. How to measure their ratio accurately on a machine?
2)Similarly, the asymptotic cost of finite field multiplication is same as field inversion. So how to measure their ratio accurately on a machine?
By Asymptotic I mean the Asymptotic complexity or Theta notation, tight bound, for the rate of growth of the function.
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Has anyone actually compared them on a specific problem?
One should also add CoCoA (see lin below) to the list of the freely available computer algebra systems specifically dedicated to commutative algebra (and non-free one could also add Magma). As written in the thread mentioned by Artur, there is not real point in asking which of the three is the "best" one, as this depends where much on what is important for you: breadth of the library, speed of computation, ease of programming. The next question is whether you have some specific problem in mind (for which perhaps only one of the three has some code available) or whether you are asking generally. But even for a very specific problem there is usually no simple answer. We developed recently a new algorithm for computing resolutions and implemented it in CoCoa. Then we run a lot of benchmarks comparing it with Singular and Macaulay2: each system had some examples where it was faster than the other one. Computational commutative algebra is a very complex field and there is usually not a "best" solution to a particular class of problems.
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Let there be a ring r of polynomials in six indeterminates t,u,v,w,x,y with complex numbers as coefficients. Take then a quadratic extension (if this is the right word) R of r by adding a new letter z which is the square root of a polynomial p in our six indeterminates (these latter are, of course, transcendental over C). Polynomial p is homogeneous of 14th degree, if this matters. The question is: where can I read about (algorithms of) factorizing elements in R? Answer for only homogeneous elements will suffice (assuming z has degree 7), but if a factorization is not unique, I want all of them!
Remark. Straightforward attempts using primary decomposition algorithm in Singular proved to be beyond the capabilities of my computer.
Here is an article that discusses the type of factorization you mention. (For what it's worth, I regard this as a very good article in this particular area.)
On Factorization of Multivariate Polynomials over Algebraic Number and Function Fields.
Proceedings of ISSAC '09, 199–206, ACM Press, 2009.
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The command I used is plot(plot::Implicit3d(x*1000-3.14*2^2*(1+y/1000)^2*544*(ln(5/z))^0.23*5/z, x=15..25, y=-15..10, z=0.5..4.5), Scaling = Constrained).
I'm sure that the value of the function falls into the ranges of x, y and z
Thanks for your answer, Andrew, unfortunately I failed both in MATLAB  2010b and version 2012a. I wonder if this error is caused by an older version, maybe I should try it in the latest version as your suggestion.
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A colleague told me that recently it was presented a specific method that reduces the numerical errors due to the presence of very large and very small eigenvalues. But the reference is missed.
Can somebody help to find the reference of this work?
Many thanks.
Dear Luis
1) Is your matrix real ?
2) Do you assume that it has only complex eigenvalues ? (No real eigenvals ? )
3)Does your matrix has some special properties i.e is it sparse, is it very large etc..
4) Are you interested on some iterative algorithm? Or would you be satisfied/looking for say more theoretical answer ?
A good book hint for iterative methods would probably be "Numerical Linear Algebra"
By Lloyd N. Trefethen. It provides several algorithmic approaches for investigation
of the spectrum of a matrix.
best regards
Samuli Piipponen
UN of Eastern Finland
Samuli Piipponen
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Using Mathematica software is it possible to plot real and imaginary part of an equation with variable coefficients for ex. x^4+2ax^3+4x^2+ax+1=0, where a varies from 0 to 2 with 0,.2 interval using mathematica. Here I need to plot each set of roots for the same interval of that is {{0,xi},{0,2,xi},{0.4,xi}...{2,xi}} where i is 1,2,3,4 that is four roots of the polynomial.
For those that do not have Mathematica I have attached a PDF which includes snapshots of the Manipulate function in action for this problem
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