untit.mw

This is a new question came up from a follow up to https://www.mapleprimes.com/questions/225083-Maple-Command-To-Find-Domain-Of-Function

Does Maple have support for removing points from an interval automatically? An example will make this clear. This is all on the real line. No complex domain.

Given one interval,. say real_domain :=  x>-infinity and x<infinity: and now I want to remove from this interval, another interval. This second interval can be defined as single point(s) or as interval(s) itself. 

I will give an example of both.

when the singularity interval to remove is defined as one or more single points, here is an example using one point:

real_domain :=  x>-infinity and x<infinity:
singlarity_pt := 1/2:

So I want Maple to give me automatically the new interval as   {x>-infinity and x<1/2} , {x>1/2 and x<infinity}:

Becuase the singularity point was "removed" from the real domain. I tried solve, but it did not work

solve(x<>singlarity_pt and real_domain,{x})
                         

I know I could probably code this by hand, and add logic to figure it if the singularities are points. But this can get complicated if the real domain itself has many sub intervals itself. I thought Maple should be able to do this. fyi, In Mathematica, this is done as follows

singularity = 1/2;
realDomain = -Infinity < x < Infinity;
Reduce[x != singularity && realDomain , x, Reals]

Here is second example where now the singulartiy interval to remove, is not single point, but an interval itself. I found that in this case, solve did the right thing

real_domain :=  x>-infinity and x<infinity:
singlarity_domain := x>-1/2 and x<1/2:

Now the final domain should be   -infinity<x<-1/2 , 1/2<x<infinity, 

solve( not(singlarity_domain) and real_domain,{x})

The question is, why it worked when the singulaity is an interval, but it did not work when it is a specific point? And how can one make it work for single points? Is there a different command to use other than solve for this?

In general, singularities can contain single points and also intervals, but single points is more commin. So I need it to work for both cases.

This has to be done non-interactivally and without plotting or such, as it will be part of a script. 

Thanks for any hints

In the following problem at two example are given. For Z=2 the sum is converging whereas at Z=4 it is not converging. Thank you

PROBLEM.mw

I have a polynomial in the variables ya[i] and yd[i] where i are integers. I want to divide each of the coefficients by the 'shortest' coeficient. What i mean by that is the coefficient that is going to cause me the least trouble when i later do things with groebner bases of on the coefficients - I expect a good proxy for that is the one that has the smallest number of terms.

For example, for the polynomial:

2*yd[0]*k[a1]*k[d1]*ya[1]+(alpha*C[T]*k[a1]*k[m]-alpha*R[b]*k[a1]*k[d1]-alpha*R[m]*k[a1]*k[d1]-alpha*k[d1]*k[m])*ya[1]-2*k[a1]*k[d1]*yd[1]*yd[0]+(-alpha*C[T]*k[a1]*k[m]+alpha*R[b]*k[a1]*k[d1]+alpha*R[m]*k[a1]*k[d1]+alpha*k[d1]*k[m])*yd[1]

2*k[a1]*k[d1] is the shortest monomial coefficient

 

I have a program that produces lists of polynomails in multiple variables; I want to remove any polynomials that have the variable x[i] where i is a number.

An example list would be:
[
y[a0]-y[d0],
k[d1]*y[a1]-k[d2]*y[d2],
k[d1]*y[a1]*x[1]-k[d2]*y[d2]*x[2],
]
 

int(int(x,y^4..16),y=0..2);

yields the output $\int_0^2\int_{y^4}^{16} x(x) dx dy$.

any one can help me to get the output of the plot in 3 rows and 2 columns here is my codes. thanks in advance.

 restart;
  h:=z->1-(delta2/2)*(1 + cos(2*(Pi/L1)*(z - d1 - L1))):
  K1:=((4/h(z)^4)-(sin(alpha)/Gamma2)-h(z)^2+Nb*h(z)^4):
  lambda:=unapply(Int(K1,z=0..1), Gamma2):
  L1:=0.2:
  d1:=0.2:
  alpha:=Pi/6:
  with(plots):
  display
  ( Vector[row]
    ( [ seq
        ( plot
          ( [ seq
              ( eval(lambda(Gamma2), Nb=j),
                j in [0.1,0.2,0.3]
              )
            ],
            delta2=0.02..0.1,
            legend=[Nb=0.1,Nb=0.2,Nb=0.3],
            labels=[typeset(`&delta;1`), typeset(conjugate(`&Delta;p`))],
            title=typeset("Effect of ", ''alpha'', " when ", Gamma,"2=", Gamma2)
          ),
          Gamma2 in [10,20,30,40,50,-10]
        )
      ]
    )
  );
 

After run a batch to cmaple to run a prettyprint=0 and screenwidth=500

it use lprint in window

i set prettyprint=2 

still can not set back to original print for matrix

Excel tool import can not be used in cmaple.exe

Plot the first 20 Fibonacci numbers.

I have this so far..

restart;

nums := [seq(i, i = 1 .. 20)]*with(combinat, fibonacci);

fibnums;

  here my loop; after  8 iteration maple couldnt solve the equations and give me this error .
Is there any method to garentee that fsolve could work intire the 1000 iteration 
 

I am calling a function (GTS2) multiple times with varying inputs, using the curry function, and i want to record how long/how much RAM the function takes with each input, and put those in seperate matrices that i can plot later
 

Sols3 := proc (H::algebraic, F::(list(algebraic)), i::posint, j::posint) options operator, arrow; GTS2(H, F, i, j) end proc;
n, m := 5, 4;
M=Matrix(n, m, curry(Sols3, H, F))

You can find all the functions required in this worksheet. The curried call to this function is in section 4.

MHD_cchf_2.mw
 

Download MHD_cchf_2.mw

Respected sir, I try to plot graphs using two parameters once. But it showing the error as

Error, invalid input: nops expects 1 argument, but received 2
Error, invalid input: nops expects 1 argument, but received 2
Error, invalid input: nops expects 1 argument, but received 2

can anybody do help in this regard?

I have a problem writing a program for the numerical solution of nonlinear volterra integral equation using the method of reproducing kernel space. I have my algorithm as well as the program I tried to write, though they are full of error messages. Please could anyone give me a clue on how to go about my challenges. The algorithm is as follows:

Step 1. Fix 𝑎 ≤ 𝑥 and 𝑡 ≤ 𝑏.
If 𝑡 ≤ 𝑥, set 𝑅𝑥(𝑡) = 1 − 𝑎 + 𝑡.
Else set 𝑅𝑥(𝑡) = 1 − 𝑎 + 𝑥.
Step 2. For 𝑖 = 1, 2, . . . , 𝑚 set 𝑥_i = (𝑖 − 1)/(𝑚 − 1).

Set 𝜓_i(𝑥) = 𝐿_t𝑅𝑥(𝑡)|𝑡=𝑥_i .
Step 3. Set 𝑢₀(𝑥₁) = 𝑢(𝑥₁).
Step 4. For 𝑖 = 1, 2, . . . , 𝑚 set 𝛾_ij = [𝜓^-1]_ij.
Step 5. 𝑛 = 1.
Step 6. Set S_n = Σ𝑛
𝑘=1 𝛾_nk𝑢_k-1(𝑥_k).
Step 7. Set 𝑢_n(𝑥) = Σ𝑛
𝑖=1 S_i𝜓_i(𝑥).
Step 8. If 𝑛 < 𝑚then set 𝑛 = 𝑛 + 1 and go to step 6.
Else stop.