Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

 

[[p__jb = (Typesetting[delayDotProduct](c__a . ((rho*(-1+alpha)*t__a-alpha*t__b)/(t__b*t__a)), t__b, true)*t__a+((c__b+`p__-jb`)*alpha-c__b-t__b-`p__-jb`)*t__a-alpha*t__b*(c__b+`p__-jb`))/((2*alpha-2)*t__a-2*alpha*t__b)]]

I cannot seem to set up this integral correctly:

Gradshteyn 3.529

I think maple should do it.

`assuming`([int(((cosh(a*x)-1)/sinh(b*x))(1/x), x = 0 .. infinity)], [b > abs(a)])

I wonder where I'm going wrong here? Thank you in advance.

hi

I'm working on my thesis,to solve a particular problem,I created a 84*84 matrix in Matlab.

I want to calculate the determinat of that matrix in maple,so from tools>assistance>import date added this matrix in maple.

every thing seems to be ok but when i want to caculate the determinant this error apears :

 Error, (in LinearAlgebra:-Determinant) matrix must be square

does anybody know what is the problem here?

Also sorry for my weak English 

and it's worth mentioning that I'm a beginner in maple programming 

thank you

 

 

Since I've updated maple to version 2019 it's has become very slow. Erverytime I enter something it seems to reload all the side buttons just like when a new worksheet is started. This is very annoying because during this loading time you cannot enter anything. Has anyone any suggestions? btw I've bought my pc in march 2020 and it has enough CPU and GPU.

 

 

i have a nonlinear inequality which is plotted using plots:-inequl
can i find an algebric solution for this inequality? for example sth like this : 0.08<t<10 
thnx in advance

 

restart:with(plots):with(Optimization):

with(SolveTools[Inequality]):

k := 1; c := 5; sigma := .85;N=10;

1

 

5

 

.85

 

N = 10

(1)

x:=t->4*exp(-t);

proc (t) options operator, arrow; 4*exp(-t) end proc

(2)

t0:=0.0065:

inequal(sigma*k/(2*c+k)*abs(x(t))<abs(x(t)-x(t0)),t=0..10,x=0..4)

 

 

 

NULL


 

Download inequality.mw

Hello, Everyone. can anyone help me to find the solution of the transcendental equation by using the newton raphson method ( want to calculate the valve of lambda by putting p=0) by assuming the valve of k=0.1,beta=0.2 in the attached maple file?

help.mw

Hi, 

 

Let S(N) the set of all N by N matrices defined this way:

  • each element of a matrix M in S(N) is an integer number between 1 and included N^2
  • all the elements of M are different

For instance the matrix M = < <1, 2>|<3, 4> > belongs to S(2).

I'm interesting in finding the number of singular matrices of S(N), and more reasonnably of S(N <=3).
It's easy to verify that no matrix in S(2) is singular.
For S(3) now: as S(3) contains only 9! = 362880 elements a brute force approach can still be used. It showed that 2736 matrices were singular (about 0.75%).
But I wonderded if a more elegant approach could be used?
In the attached file I wrote all the relations elements of S(2) (and next S(3)) must verify and solved these equations for integer solutions (I only accounted for singular matrices . The case S(2) is tractable, but not S(3) (at least on my computer).

So my question: do you have any idea of some method to tackle this problem, or are you aware of any theoritical results about this issue?

PS: of course a statistical approach in which elements of S(N) would be generated using random permutations of [$1..N^2] is still possible to get a crude approximation of the number of singular matrices, but I'm not interested in this kind of approach.

Thanks in advance


 

restart:

alias(det = LinearAlgebra[Determinant])

det

(1)

 

Brute Force

 

S    := 0:
p    := 3:
PERM := combinat:-permute(p^2):
for perm in PERM do
  M := Matrix(p, p, perm):
  if det(M)=0 then S := S+1; end if:
end do:
S;
evalf(S/9!);

2736

 

0.7539682540e-2

(2)

 

A non systematic approach

Case of S(2)

 

M := Matrix(2, 2, symbol=m):
iM := {indices(M)}:

# set of all relations that define the elements of S(2)

rels :=
  {
    det(M) = 0,

    # each term is equal to an integer between 1 and 4 included

    mul((M[1, 1]-k), k=1..4)=0,
    mul((M[1, 2]-k), k=1..4)=0,
    mul((M[2, 1]-k), k=1..4)=0,
    mul((M[2, 2]-k), k=1..4)=0,

    # the sum of all the terms is equal to 10

    # M[1, 1]+M[1, 2]+M[2, 1]+M[2, 2]=10,

    # all the terms are different

    seq( mul(seq((M[op(im)]-M[op(ij)]), ij in iM minus {im})) <> 0, im in iM)
  }

{(m[1, 1]-1)*(m[1, 1]-2)*(m[1, 1]-3)*(m[1, 1]-4) = 0, (m[1, 2]-1)*(m[1, 2]-2)*(m[1, 2]-3)*(m[1, 2]-4) = 0, (m[2, 1]-1)*(m[2, 1]-2)*(m[2, 1]-3)*(m[2, 1]-4) = 0, (m[2, 2]-1)*(m[2, 2]-2)*(m[2, 2]-3)*(m[2, 2]-4) = 0, m[1, 1]*m[2, 2]-m[1, 2]*m[2, 1] = 0, (m[1, 1]-m[1, 2])*(m[1, 1]-m[2, 1])*(m[1, 1]-m[2, 2]) <> 0, (m[1, 2]-m[1, 1])*(m[1, 2]-m[2, 1])*(m[1, 2]-m[2, 2]) <> 0, (m[2, 1]-m[1, 1])*(m[2, 1]-m[1, 2])*(m[2, 1]-m[2, 2]) <> 0, (m[2, 2]-m[1, 1])*(m[2, 2]-m[1, 2])*(m[2, 2]-m[2, 1]) <> 0}

(3)

isolve(rels);  # no solution founds

 

A non systematic approach

Case of S(3)

 

 

M := Matrix(3, 3, symbol=m):
iM := {indices(M)}:

rels :=
  {
    det(M) = 0,

    # each term is equal to an integer between 1 and 9 included

    mul((M[1, 1]-k), k=1..9)=0,
    mul((M[1, 2]-k), k=1..9)=0,
    mul((M[1, 3]-k), k=1..9)=0,
    mul((M[2, 1]-k), k=1..9)=0,
    mul((M[2, 2]-k), k=1..9)=0,
    mul((M[2, 3]-k), k=1..9)=0,
    mul((M[3, 1]-k), k=1..9)=0,
    mul((M[3, 2]-k), k=1..9)=0,
    mul((M[3, 3]-k), k=1..9)=0,

    # the sum of all the terms is equal to 10*9/2 = 45

    M[1, 1]+M[1, 2]+M[1, 3]+M[2, 1]+M[2, 2]+M[2, 3]+M[3, 1]+M[3, 2]+M[3, 3]=45,

    # all the terms are different

    seq( mul(seq((M[op(im)]-M[op(ij)]), ij in iM minus {im})) <> 0, im in iM)
  }:

numelems(rels);

20

(4)

run_this := false:
if run_this then
  isolve(rels);  # requires a huge amount of memory and computational time
end if;

 


 

Download HowManyMatricesAreSingular.mw

Is there a pallette that contains the symbol for a contour integral both clockwise and anticlockwise?

doubt5.mw

Hi I want to run the following algorithm in code edit region:

for m in set_m do
    for n in set_n do
      solve for N solving ODE11 and ODE12 simultaneously
      solve for t_2 solving ODE11 and ODE12 simultaneouly
      find t__3 and t__4
      if (N<=t_4 and M>=t_3) then
        d1= TCS__1 using n,m,t__2 and N
          if (d1< d2)
            d2=d1
            print(d2,m,n,N,t_2)
    end do
end do
 

But I am struck for to how to extract N and t__2 from SOL1 in code edit region

SOL1 := fsolve({ODE11, ODE12}, {N, t__2});

Thanks in advance

How do I convert the expression

y = (sqrt(x) + 10)^(1/3) - (sqrt(x) - 10)^(1/3);

into

y^3 = 20 - 3*(x - 100)^(2/3);

A post on the Maxima mailing list said this was done by cubing both sides.  I can not seem to be able to get there.  A suggestion that the process involved recognizing the product (a+b)*(a-b)

Hello!

Could you help me plesase, I have a matrix like this:

And I want to get determinant of this matrix as function f(w1,w2) but when I use Determinant I always get something like this:

doubt4.mw

Hi, As shown in the figure(red color). I am not able to understand why Exp(0) is not showing as 1. As evaluating rules of maple says that it evaluates everything till it gets unassigned variables.

Do I am doing something wrong? There is a link to the file. 

Thanks in advance

Dear friends, please I would like to ask for your help with the following problem: 

I have a remember table generated by a recursive procedure

x:= proc(n)
option remember; 
....
end proc:

It helps compute x(1), x(2), x(3), x(4). 

After several additional steps I have a new x(2), say 

x(2):= 3; 

With this new x(2) I need to recompute x(3), x(4). I've tried 

forget( x, [ x(3), x(4) ], subfunctions = false ); 

x(3); 

x(4); 

However, I do not get the new values of x(3) and x(4) but the old ones. What could it be wrong? 

Many thanks for your help.  

Hello!

I have a matrix and all elements has two indexes. For example 3x3 case:

1,1 1,2 1,3

2,1 2,2 2,3

3,1 3,2 3,3

So if I want to travers this matrix in zig-zag way and fill it with increasing numbers I will get this matrix:

1 2 6

3 5 7

4 8 9

From 1 to 2,3 and 4,5,6 ...

We have 9 elemets in this order:

1 - (1,1); 2 - (1,2); 3 - (2,1); 4 - (3,1); 5 - (2,2); 6 - (1,3); 7 - (2,3); 8 - (3,2); 9 - (3,3).

The question is - do we have a way to convert two indexes in one digit like (3,1) -> 4 or (2,3) -> 7

Thank you!

Could you help me please if there is a way to convert to

I am not able to get the proper integration results

Question_integration_eqn18.mw
 

Dm(A, p, i(t)) := A^gamma*(a-b*p+c*i(t))

A^gamma*(a-b*p+c*i(t))

(1)

NULL

NULL

Lsc := cl*(int(Dm(A, p, i(t))*(1-1/(1+delta(T-t))), t = t2 .. T))

cl*(int(A^gamma*(a-b*p+c*i(t))*(1-1/(1+delta(T-t))), t = t2 .. T))

(2)

simplify(Lsc)

cl*A^gamma*(int((a-b*p+c*i(t))*delta(T-t)/(1+delta(T-t)), t = t2 .. T))

(3)

``

subs(i(t) = (A^gamma*(-b*p+a)*ln(1+delta*(T-t))-R*delta)/delta, Lsc)

cl*(int(A^gamma*(a-b*p+c*(A^gamma*(-b*p+a)*ln(1+delta*(T-t))-R*delta)/delta)*(1-1/(1+delta(T-t))), t = t2 .. T))

(4)

simplify(%)

cl*(int(-(-A^(2*gamma)*c*(-b*p+a)*ln(1+delta*(T-t))+A^gamma*delta*(R*c+b*p-a))*delta(T-t)/(1+delta(T-t)), t = t2 .. T))/delta

(5)

``

``


 

Download Question_integration_eqn18.mw

 

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