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# Computer Algebra - Science topic

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Questions related to Computer Algebra

With 2 indices it's A

_{ij}=(A_{ij}+A_{ji})/2+(A_{ij}-A_{ji})/2 for GL(N).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.

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?

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?

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?

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?

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.

In which case a Grobner basis is stable under scalars extension ?

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.

When I have two equations f=0 and g=0 over the reals, I can equivalently rewrite them as one equation f

^{2}+g^{2}=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?

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.

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.

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!!

A MuPAD notebook is a convenient environment for performing computations symbolically using the MuPAD language and documenting the results

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...

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?

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.

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

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.

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.

I am a computer engineer and don't know much about advanced computer algebra concepts therefore I need your help in it. I would like someone to explain in general terms what grobner bases is. I have read about it but not understood it fully so need help of mathematics guys.

Suppose I have a set of equations in POS form

(x1 + 0) (x2 + 1) (y1 + 0) = 0

(x1 + 1) (x2 + 0) (y1 + 1) = 0

etc

How this is reduced to gobner of form y1 = function(x1,x2)? I heard of library risa/asir for computing these but I want to know how it works, I mean how POS form set of equations are solved to gobner form (in theory and also with the tool if someone knows)?