According to this site,"It is known that every even number can be written as a sum of at most six primes". 

http://www.theage.com.au/national/education/christians-goldbachs-magic-sum-20140903-3es2t.html

i wanted to test this using maple.

restart:
> PF := proc (a::integer)

> local cst,obj,res;
> cst := add(x[i], i = 1 .. numtheory:-pi(prevprime(a))) <= 6;
> obj := add(x[i]*ithprime(i), i = 1 .. numtheory:-pi(prevprime(a)))-a;
> res := Optimization:-LPSolve(obj, {cst ,obj>=0}, assume={nonnegative,integer}); end proc:
> PF(30);
[0, [x[1] = 0, x[2] = 0, x[3] = 6, x[4] = 0, x[5] = 0, x[6] = 0,x[7] = 0, x[8] = 0, x[9] = 0, x[10] = 0]]

the third prime is 5 and 6 of them make 30. as an aside, it would be nice to know how to get maple to output "30 = 6x5".

this is obviously pretty limited, because 30 can be written as the sum of two primes (7+23 and 11+19) [GOLDBACH], but using DS's GlobalSearch for all solutions takes a long time to compute. also I have to nominate the highest prime.

any suggestions?

I have an indexed equation that contains serval definite integrals in it. I want maple to evaluate the equation for different indices. But when I set the parameter "N=100" in the code, it takes maple lots of time for the evaluation. I am looking for some tricks to make the code numerically more efficient. I will be so thankful for any opinion and help.
you can find my code below. The code is so simple and just contains few lines. I will appreciate any help.

Numerical_Performance.mw

Thanks in advance.

Download ak_BER_9sep.mw

need to plot these values for various values of i.

any help??

For two angles a and b, and functions  and , I have a system of two equations,

 and .

The actual equations (i.e. not in terms of  and ) are known but are ommitted because they are very long.

I need not the solutions but simply the time  at which . While I have inputted the full equations into Maple, I do not know how to ask it to find an expression for  in terms of the constants of the equation.

How would I ask Maple to find this time?

Hi all

I have written the following code in maple to approximate arbitrary functions by hybrid of block-pulse and bernstein functions but it doesn't work properly especially for f(t)=1.0, so what is the matter?

bb1.mws

best wishes

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

I have written a code that computes the fourier-bessel series of a function over the period [a,b].
When I wanted to get some numerical results, I noticed that it takes lots of time for maple to numerically compute the coefficients of the series. Each coefficient of the series is expressed in terms of some integrals that I was expecting maple to compute them in few seconds, however, when  I want to compute "N=100" terms of the series, it takes lots of time.

I was wondering if there is any way to boost up the numerical computation time. I will appreciate any help.

Below you can find my code.

Example_2.mw

Many many thanks for your attentions! :)

can maple 17 make serial communication with arduino such as i wan to get data from accelerometer then the data will display in maple 17

Hi,

I need to transfer an array of size (M,N) from maple to matlab. But i dont know how to make it. Please help me for this. Thanx in advance.

Regards

Sunit

In using the Maple 17 VectorCalculus package I was suprised to find that the Norm of a free vector is not the same as the Norm of a "corresponding" RootedVector, i.e.the same vector with a different root. Am I missing something ? Thanks for an explanation.

restart;
with(VectorCalculus):

P:=<1,2,3>; # free vector
PP:=RootedVector(root=[-1,2,-3],P)

Norm(P);
Norm(PP);

Hi all,

I have a problem when creating package by using 'read' function to concatenate package's elements

Case1: Create package normally, Proc1 and Proc2 are exported

restart;
###################################
# Define package Test contains 2 proc: Proc1 and Proc2
##################################
Test := module()
    option package;
    export Proc1, Proc2;

    Proc1 := proc()
        description "Proc1() is an element of package Test";
        printf("In Proc1\n");
    end proc;
    Proc2 := proc()
        description "Proc2 is an element of package Test";
        printf("In Proc2\n");
        Proc1();
    end proc;
end module;

#################################
# Try to call Proc1 from Proc2
#################################
Test:-Proc2();

Console output:

> Test:-Proc2();
In Proc2
In Proc1

==> The result looks OK

Case2: Split Proc1 into another file and include it into master file by using 'read' function, Proc1 and Proc2 are exported

restart;
###################################
# Define package Test contains 2 proc: Proc1 and Proc2
##################################
Test:= module()
    option package;
    export Proc1, Proc2;

    ###########################
    # Code to concatenate "Proc1.maple" here
    ###########################

    read "Test/Proc1.maple";

    Proc2 := proc()
        description "Proc2 is an element of package Test1";
        printf("In Proc2\n");
        Proc1();
    end proc;


end module;


#################################
# Try to call Proc1 from Proc2
#################################
Test:-Proc2();

Console output:

> Test:-Proc2();
In Proc2
                                    Proc1()

==> The Proc1 seem does not execute or evaluate

Case3: Split Proc1 into another file and include it into master file by using 'read' function, just export Proc2, not export Proc1

restart;

###################################
# Define package Test contains 2 proc: Proc1 and Proc2
##################################
Test:= module()
    option package;
    export Proc2;

    ###########################
    # Code to concatenate "Proc1.maple" here
    ###########################

    read "Test/Proc1.maple";

    Proc2 := proc()
        description "Proc2 is an element of package Test1";
        printf("In Proc2\n");
        Proc1();
    end proc;


end module;


#################################
# Try to call Proc1 from Proc2
#################################
Test:-Proc1();

Console output:

> Test:-Proc2();
In Proc2

In Proc1

==> The result looks good

Please help to explain the problem from case 2 and case 3. If I want to split package proc into many files, how can I do?

Hi! I'm trying to solve a system of four non-linear equations in Maple 17 but it doesn't work.

Equations are: F, Fw, Ft, Fk and varibles are T,w,k,ki.

Parametars are Mn=10, Ms=2, alfa=0.2 and Tf=(k*T^(alfa)/Mn)^(1/alfa).

Solutions must be positive. 

This is maple script:

restart;
> assume (w>0):
> assume (T>0):
> assume (k>0):
> assume (ki>0):
> assume (Mn>0):
> assume (Ms>0):
> assume (Tf>0):
> assume (alfa>0):

> Gp:=1/exp(sqrt(w*I));

> Cf:=((T*w*I+1)/(Tf*w*I+1));

> Cpi:=(k*w*I+ki)/(w*I);

> L:=Cf*Cpi*Gp;
> L:=evalc(L):
> F:=subs(Ms=2,Tf=(k*T^(alfa)/Mn)^(1/alfa),evalc(abs(1+L)^2-1/Ms^2));
> F:=subs(Mn=10,alfa=0.2,evalc(F));

> Fw:=diff(F,w):
> Fk:=diff(F,k):
> Ft:=diff(F,T):
> fsolve({F,Fw,Fk,Ft},{w,k,ki,T});

Thanks in advance for any help. Dragoslav

Hi there

I've got an 18*18 matrix which almost all of its elements are in parametric form. I Need to export this matrix to MATLAB to do some numerical alnalysis on that But when I click on  " export as MATLAB", the following error appears:

"can not convert matrix elements to float[8] datatype"

I wonder if thre's a solution to that or anyother way to move the matrix(as it is) to MATLAB.

I'll be appreciated your help

I am sure that with this vector file with embedded components will learn how it works the vector operations. The code is free and can be modified to be improved. Forward engineers.

Vectores_con_Components_Embedded.mw     (in spanish)      

Lenin Araujo Castillo

This seems such a simple/basic question I'm almost too embarassed to ask.

Anyway. this is causing me some headaches

> A := <0|0>;

         A:= [0 0 ]

> B := A:

> A(1,1) := 2 ;

         A:= [2 0 ]

> B;

         B:= [2 0 ]

What do I do to prevent the elements of B changing if A changes, after using the assignment B:=A (or should I not be using this assignment?)  I mean, I would like the same behaviour as 

> a := 0;

         a:=0

> b := a;

         b:=0

> a := 2;

         a:=2

> b;

         b:=0

which seems to work as I "expect"...

I'm used to Mathcad, and I am very new to Maple. Something I cannot figure out right now is how to define multiple elments of a matrix using a function.

Input Data

Define system dimensions as n:=2;

i:=1..n;

j:=1..n;

lambda:=Matrix(n);

Lambda:=Matrix(n);

upsilon:=vector(n); 

Minor side note: I originaly had upsilon defined using the syntax "Vector[row](ncomp)", but this was giving me an 'exponentiation' operation error, so I changed it to what it is now (basically a list/array, which I guess has different type definitions that no longer cause the error?).

lambda[1,2]:=471.0433;

lambda[2,1]:=883.7530;

upsilon[1]:=58.69;

upsilon[2]:=18.07;

The Problem I'm Having

Now I just want to define Lambda using a function to define all elements (like I would in Mathcad).

Lambda[i,j]:= (upsilon[j]/upsilon[i]) * exp (-lambda[i,j]/2853);

which gives me an extremely long error message:

Error, invalid input: exp expects its 1st argument, x, to be of type algebraic, but received Matrix(2, 2, {(1, 1) = -0.3504976272e-3, (1, 2) = -.16509955895845776, (2, 1) = -.30975332953088164, (2, 2) = -0.3504976272e-3}, datatype = float[8]

As far as I can tell (keep in mind that this is my very first Maple project) that it doesn't like lambda as a matrix? But shouldn't it just evaluate to the element? and why is (2,2) and (1,1) giving values, because it should intialize to zero, so exp(0) = 1 in these cases??

I tried to simplify further by just trying

Lambda[i,j]:=(upsilon[j]/upsilon[i]);

but then it just gives me 1, and when I look into Lambda all the elements are now 1 when only the diagnol elements should be 1 (the rest some fractional amount)??

I am at a complete loss. I thought about doing something like For i = 1 to n etc. but then it just looks like coding, which defeats the purpose of trying to make a calculation sheet documenting the procedure...

Any help and/or insights into what I am doing wrong here would be most welcomed :)

P.S. I've just noticed that there is an upload option :/ Wilson_Equation.mw.