It would be good I hope to present symbolic-numeric CAE system for framed structures analysis.

It will be available soon as Preview version for enthusiasts

The main features are:

• One calculation act - all analytical dependencies.
• Fast designing process for structural systems in industry, consulting and design companies;
• Fastest parametric analysis of construction. New quality of designing in optimization tasks,...

   This is a promissory Maple package, which is rarely used (I found nothing  in MaplePrimes and in Application Center.). Let us see the ?padic package. It is well known that the field of rational numbers Q is not complete. For example, there does not exist a rational number k/n such that k^2/n^2=2. There are only two ways to complete Q ( http://en.wikipedia.org/wiki/Ostrowski's_theorem ) .  The first way is to create the field of real numbers R including Q. Every real number can be treated as a decimal fraction sum over [k in K] of a[k]*10^(k) with a[k] in {0,1,2,3,4,5,6,7,8,9}, finite or infinite. For example, the numbers 0.3+O(0.1), 0.33+O(0.01), 0.333+O(0.001), 0.3333+O(0.0001), ...  approximate the number  1/3.
   The second way is as follows (see http://en.wikipedia.org/wiki/P-adic_number  for more details). We choose a prime number p and consider the valuation v[p] of a rational number k/m=p^n*a/b <>0 where integers are supposed to be irreducible :v[p](k/m):=p^(-n) , v[p](0):=0. The completion of Q up to this valuation is the field of p-adic numbers Q[p] (also including Q).  Every p-adic number can be treated as a p-adic fraction sum over[k in K]of a[k]* p^(k) with a[k] in {0, 1, 2, 3, p-1}. For example, the numbers 2, 2+O(5),2+3*5+O(5^2),2+3*5+5^2+O(5^3) approximate the number 1/3 in Q[5]. These can be obtained with Maple as follows.
> with(padic);
> evalp(1/3, 5, 1);
                           2
> evalp(1/3, 5, 2);
                        2+O(5)
> evalp(1/3, 5, 3);
                          2+3*5+O(5^2)
> evalp(1/3, 5, 4);
                         2+3*5+5^2+O(5^3)
    The field Q[p] is a very strange object. For example, the set of integers is bounded in Q[p] because v[p](k) <= 1 for every integer k. Another striking statement: the sequence p^n tends to 0 in Q[p] as n approaches infinity. The functions expp(x), logp(x), sqrtp(x) and the others are defined in the usual way as the sums of power series (see ?padic,functions for more details). For example,
> Digitsp := 12;
> logp(2+3*5+5^2, 5);

               5+5^2+4*5^3+5^4+3*5^6+4*5^8+3*5^9+5^10+3*5^11+O(5^12)
> cosp(x, p, 2);

                            padic:-cosp(x, p, 2)
> eval(subs(x = 0, p = 5, padic:-cosp(x, p, 2)));

                             1
> eval(subs(x = 3*5, p = 5, padic:-cosp(x, p, 2)));

                             1                            
    The definition of the limit of a sequence in Q[p] is identical to the one in R (of course,  abs(x[n]-a)<epsilon should be replaced by v[p](x[n]-a)<epsilon for every rational epsilon) and the same with the derivative. But every continuous function is picewise-constant. There also exists a non-injective function on Q[p] having the  derivative 1 at every point of  Q[p] . It should also be noticed that the radius of convergence of the expp(x):=sum(x^n/n!,n=0..infinity) series equals p^(-1) if p >2 and 2^(-2) if p=2. Next, there exists a Haar measure d[p](x)=:dx on Q[p] such that d[p](Z)=1. The definite integral of a real-valued function f(x) over a subset D of Q[p] with respect to  dx is defined in certain cases. For example, the definite integral of 1 over
the ball B(0,p^n):={x in Q[p]: v[p](x)<=p^n} with respect to dx equals p^n, ie. the radius of B(0,p^n). It is clear that there does not exist any analog of the Newton-Leibniz formula in the p-adic case. Because of this reason every calculation of every definite p-adic integral is a hard problem.

        There are a lot of good and diffent books on p-adic analysis. In particular, see http://www.google.com/search?tbm=bks&tbo=1&q=p-adic&btnG= ,  http://books.google.com/books?id=H6sq_x2-DgoC&printsec=frontcover&dq=p-adic&hl=uk&ei=IgFuToupO8SL4gTE-tDOBA&sa=X&oi=book_result&ct=result&resnum=6&ved=
0CEYQ6AEwBQ#v=onepage&q&f=false
, and http://books.google.com/books?id=2gTwcJ55QyMC&printsec=frontcover&dq=p-adic&hl=ru&ei=UAxqTuabD5HGtAamhryxBA&sa=
X&oi=book_result&ct=result&resnum=4&ved=0CDkQ6AEwAw#v=onepage&q&f=false as a good introduction to the topic.
     Why  is it so important? Which are applications? There are indications that the space  we live in has not  the Archimedean property (see http://en.wikipedia.org/wiki/Archimedean_property) on a very small scale. To verify this hypothesis is  a dozen times more expensive than  the large hadron collider
 (see http://en.wikipedia.org/wiki/Large_Hadron_Collider ). However, the mathematicians already develop the necessary mathematical tools, in particular, p-adic analysis.  Concerning other applications, see the answer by Anatoly Kochubei in
 http://mathoverflow.net/questions/62866/recent-applications-of-mathematics.

Edit. The vanishing text and some typos.

restart; interface(version); # Maple 15
Digits:=40;

# symbolic expression
t:=1/292/(-77796+62196*I*3^(1/2))^(1/3)*73^(1/2)*
  ((-77796+62196*I*3^(1/2))^(1/3)*
  (-3*(-77796+62196*I*3^(1/2))^(2/3)-
  7812+688*(-77796+62196*I*3^(1/2))^(1/3)+
  3*I*3^(1/2)*(-77796+62196*I*3^(1/2))^(2/3)-7812*I*3^(1/2)))^(1/2)
  -0.3; # <--- does that give the trouble ?

simplify(t); # makes it a float ...

  0...

3D Paper Physical Model

We are looking for a Maple Wizard to join our team, based in California. US citizenship is an absolute requirement. Please send me a message if you are interested or know someone who might be.

thanks

A list of small graphs with associated pictures and tables of
values of various graph invariants.

The graph invariants were made using Maple programs which uses
the networks and GraphTheory packages.

A picture presents some inequality conjectures between the graph invariants.

http://www.msci.memphis.edu/~speeds/

Sam Speed   August 29, 2011

And so with this provocative title, "pushing dsolve to its limits" I want to share some difficulties I've been having in doing just that. I'm looking at a dynamic system of 3 ODEs. The system has a continuum of stationary points along a line. For each point on the line, there exist a stable (center) manifold, also a line, such that the point may be approached from both directions. However, simulating the converging trajectory has proven difficult.

I have simulated as...

Russian content for Maple T.A.
http://webmath.exponenta.ru/bsd/mapler_test.html

Tests are learning, not just inspectors.

I saw a fun blog post today from someone who plotted the Batman symbol within Maple. Enjoy!

All 19 chapters updated Mapler in elementary mathematics will be posted on this site:
http://webmath.exponenta.ru/bsd/mapler_01.html
...
http://webmath.exponenta.ru/bsd/mapler_19.html
Russian teachers have met the workshop with enthusiasm. Even during the holidays.
For me, the enthusiasm - it's thousands of visitors.

Since the collection began

07_eng.mw

A collection from 20 problems for students.
12 variants for each problem.
Adequate solution.
Programs are built into the buttons.
Kit has been used successfully for 12 years.

HTML & full archive

A collection from 43 problems for students. 12 variants for each problem. Adequate solution. Programs are built into the buttons. Kit has been used successfully for 12 years.

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