Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

how do i Import part or all  PDF files into maple 

I believe this was easier in older versions of maple or worked partially.

This is very strange problem, and it seems to happen at random times.

From my worksheet, I call a function in a local fille maple_proc.mpl. This function ends up calling int() command with a timeout.

I Have the int() call wrapped by try...catch:.. end try in order to catch timeout and any other error.

Yet, when I run my worksheet, looping over hundreds of integrals, for each one, calling the function in maple_proc to integrate it, and after running for many many integrals, then sometimes, the worksheet terminates with error, at some iteration with error

Error, (in OrProp) too many levels of recursion |maple_proc.mpl:45|
 

So the try/catch I have in place are not catching the above error, wherever it is coming from.  

line 44 in maple_proc.mpl, just does this (it is the line with cpu_time := .... below

try
print(`before calling int`); 
cpu_time := timelimit(180,CodeTools[Usage](assign('result_of_int',int(lst[i,1],lst[i,2])),output='realtime')):   
print(`after calling int`); 
catch "time expired":
   #...
catch: 
   #...
end try;

Again, this works for sometimes for hundreds of iterations, and then on some entry, it gives this error.

I do not use recursion myself at all. i.e. I have no place where the function calls itself. Worksheet does a loop, and in each interation calls this function in maple_proc.mpl.

Sometimes, when I run the worksheet again, the error do not show up again. I have print statements in the catch above, and these do not show up at all, which means this error is not cought.

What should I do to find why this happens? This did not happen in Maple 2019.2. Is there any other way to trap this error so my loop does not terminate like this and I have to restart it again each time? 

I am using Physics 642 and Maple 2020 on windows 10.

Update

I was able to strip all the code and make a MWE. There is a zip file attached.

one worksheet, which calls a maple_proc() function now in the same worksheet. 

This function reads a plain text file in same folder, which contains list of integrals. The function maple_proc() does a "read" which reads all problems into a variable called lst

Now it simply does a LOOP over all entries in lst calling int() on each integral (one integral per line) with a timeout. You see there is catch() there.

I get the erorr 

At iteration number 188 each time.

I will attach a ZIP file now, which contains one folder which contains the worksheet and the input plain textfile. All what you need to do to reproduce this is open the worksheet and evaluate the call there. You might want to edit the hardcoded folder in the worksheet to your own folder where you unzipped the zip file.
 

currentdirName :="C:/MAPLE_BUG";
currentdir(currentdirName);

I hope someone will be able to repoduce this. It looks like a real bug in Maple 2020.

The problem is not in the integral 188 itself. Because if the loop starts at say 100 or 120, instead from 1, the integral now is processed OK and no error is generated.

MAPLE_BUG.zip

How I can pdsolve these equations in toroidal coordinates?

Initial conditions are arbitrary.

Please see attached pdf .

Thanks

Where.pdf

Weston1958

Can old maple version saved .m files in window be readable in maple 2015 Linux version?

Hello (again)

I thought I won't need help with that type of question but I came across an example that says otherwise.  Here it is

vars:=[x,y,z];

model7 := [x*(-RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)-5/4)+y*alpha[1, 2]-33/(32*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)), x*z*alpha[2, 6]+y*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561), x^2*(17*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)+17)/(alpha[1, 2]*alpha[2, 6])-17*x*y/alpha[2, 6]+2*z*x-z-(163/32+RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)^2+5*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)*(1/4))/(alpha[1, 2]*alpha[2, 6])]

then I issued the command 

map(w->coeffs(w,vars),model7);

to get 

 

[-33/(32*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)), -RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)-5/4, alpha[1, 2], RootOf(64*_Z^3+80*_Z^2+1104*_Z+561), alpha[2, 6], -(163/32+RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)^2+5*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)*(1/4))/(alpha[1, 2]*alpha[2, 6]), -1, (17*RootOf(64*_Z^3+80*_Z^2+1104*_Z+561)+17)/(alpha[1, 2]*alpha[2, 6]), -17/alpha[2, 6], 2]

clearly the order does not follow model7's.  

I have also tried

[seq(coeffs(expand(model7[i]), indets(model7[i], suffixed({vars[]}))),i=1..nops(model7))];

Is there a solution to it?

Many thanks (again)

 

Ed

 

 

How to learn Maple Programming effectively, whether Python will help?

My objective is to write a procedure that will read data from xml at different mentioned condition, read ICBO value at different condition of VGS i.e ICBO value at VGS=5V

BJT_ICBO := proc(parsedXML, VGS at condition )
 

 

end proc;

can some one help me to write procedure 

kindly send me OHAM source code in Maple for PDEs. I need it.

Hi, can someone explain me why CodeGeneration in C throws the error : Error, (in Print) improper op or subscript selector ? Interestingly, CodeGeneration in Python or Matlab works. Source code is attached. Thanks in advance!

membrane_energy.mw
 

 

Membrane Energy

 

restart; with(VectorCalculus); with(LinearAlgebra); with(CodeGeneration)

Define variables

 

Vectors for vertices of current position

v1 := Vector(3, symbol = v1_i) = Vector[column]([[v1_i[1]], [v1_i[2]], [v1_i[3]]], ["x", "y", "z"]) 

v2 := Vector(3, symbol = v2_i) = Vector[column]([[v2_i[1]], [v2_i[2]], [v2_i[3]]], ["x", "y", "z"])NULL

v3 := Vector(3, symbol = v3_i) = Vector[column]([[v3_i[1]], [v3_i[2]], [v3_i[3]]], ["x", "y", "z"])NULL

n := `&x`(v2-v1, v3-v1)

v4 := v1+n/norm(n, 2)^.5

Vector for vertices of next position

v1n := Vector(3, symbol = v1n_i) = Vector[column]([[v1n_i[1]], [v1n_i[2]], [v1n_i[3]]], ["x", "y", "z"])NULL

v2n := Vector(3, symbol = v2n_i) = Vector[column]([[v2n_i[1]], [v2n_i[2]], [v2n_i[3]]], ["x", "y", "z"])NULL

v3n := Vector(3, symbol = v3n_i) = Vector[column]([[v3n_i[1]], [v3n_i[2]], [v3n_i[3]]], ["x", "y", "z"])NULL

nn := `&x`(v2n-v1n, v3n-v1n)

v4n := v1n+nn/norm(nn, 2)^.5``

``

 

Define Transformation

 

V := LinearAlgebra:-Transpose(Matrix([v2-v1, v3-v1, v4-v1]))

Dimension(V) = 3, 3 

Vn := LinearAlgebra:-Transpose(Matrix([v2n-v1n, v3n-v1n, v4n-v1n]))

Dimension(Vn) = 3, 3NULL

Note we have Vn = T*V and if the current triangle is not degenerate, then T = Vn/V. As we can pre-compute 1/V we define a new matrix for it:

Vinv := Matrix(3, 3, symbol = Vinv_ij) =

Matrix(%id = 18446746713267339006)

(1.2.1)

T := MatrixMatrixMultiply(Vn, Vinv)

Dimension(T) = 3, 3``

``

``

Define Energy

 

E := Trace(MatrixMatrixMultiply(T, LinearAlgebra:-Transpose(T)))``

``

``

Gradient and Hessian

 

gradE := Gradient(E, [v1n[1], v1n[2], v1n[3], v2n[1], v2n[2], v2n[3], v3n[1], v3n[2], v3n[3]])

Dimension(gradE) = 9NULL

CodeGeneration[C](gradE, defaulttype = numeric, optimize = tryhard, functionprecision = double, precision = double, deducetypes = false, resultname = 'gradE')t1 = v2n_i[0] - v1n_i[0];
t2 = v2n_i[1] - v1n_i[1];
t3 = v2n_i[2] - v1n_i[2];
t4 = t1 * Vinv_ij[0][0] + t2 * Vinv_ij[1][0] + t3 * Vinv_ij[2][0];
t5 = t1 * Vinv_ij[0][1] + t2 * Vinv_ij[1][1] + t3 * Vinv_ij[2][1];
t6 = t1 * Vinv_ij[0][2] + t2 * Vinv_ij[1][2] + t3 * Vinv_ij[2][2];
t7 = v3n_i[0] - v1n_i[0];
t8 = v3n_i[1] - v1n_i[1];
t9 = v3n_i[2] - v1n_i[2];
t10 = t7 * Vinv_ij[0][0] + t8 * Vinv_ij[1][0] + t9 * Vinv_ij[2][0];
t11 = t7 * Vinv_ij[0][1] + t8 * Vinv_ij[1][1] + t9 * Vinv_ij[2][1];
t12 = t7 * Vinv_ij[0][2] + t8 * Vinv_ij[1][2] + t9 * Vinv_ij[2][2];
t13 = t2 * t9 - t3 * t8;
t14 = fabs(t13);
t15 = t1 * t9 - t3 * t7;
t16 = fabs(t15);
t17 = t1 * t8 - t2 * t7;
t18 = fabs(t17);
t19 = pow(t14, 0.2e1) + pow(t16, 0.2e1) + pow(t18, 0.2e1);
t20 = pow(t19, -0.5e1 / 0.4e1);
t19 = t19 * t20;
t21 = Vinv_ij[0][0] * t13;
t22 = Vinv_ij[1][0] * t15;
t23 = Vinv_ij[2][0] * t17;
t24 = (t23 + t21 - t22) * t19;
t25 = -v2n_i[2] + v3n_i[2];
t26 = fabs(t15) / t15;
t27 = -v2n_i[1] + v3n_i[1];
t28 = fabs(t17) / t17;
t21 = t23 + t21 - t22;
t22 = (t16 * t25 * t26 + t18 * t27 * t28) * t20;
t23 = 0.1e1 / 0.2e1;
t29 = Vinv_ij[0][1] * t13;
t30 = Vinv_ij[1][1] * t15;
t31 = Vinv_ij[2][1] * t17;
t32 = (t31 + t29 - t30) * t19;
t29 = t31 + t29 - t30;
t30 = Vinv_ij[0][2] * t13;
t15 = Vinv_ij[1][2] * t15;
t17 = Vinv_ij[2][2] * t17;
t31 = (t17 + t30 - t15) * t19;
t15 = t17 + t30 - t15;
t17 = t6 + t12;
t30 = t5 + t11;
t33 = t4 + t10;
t13 = fabs(t13) / t13;
t34 = -v2n_i[0] + v3n_i[0];
t35 = (t14 * t25 * t13 - t18 * t34 * t28) * t20;
t35 = t17 * Vinv_ij[1][2] - t24 * (t23 * t35 * t21 - t19 * (t25 * Vinv_ij[0][0] - t34 * Vinv_ij[2][0])) + t30 * Vinv_ij[1][1] - t31 * (t23 * t35 * t15 - t19 * (t25 * Vinv_ij[0][2] - t34 * Vinv_ij[2][2])) - t32 * (t23 * t35 * t29 - t19 * (t25 * Vinv_ij[0][1] - t34 * Vinv_ij[2][1])) + t33 * Vinv_ij[1][0];
t36 = (t14 * t27 * t13 + t16 * t34 * t26) * t20;
t34 = Vinv_ij[2][2] * t17 - t24 * (-t23 * t36 * t21 + t19 * (t27 * Vinv_ij[0][0] - t34 * Vinv_ij[1][0])) + t30 * Vinv_ij[2][1] - t31 * (-t23 * t36 * t15 + t19 * (t27 * Vinv_ij[0][2] - t34 * Vinv_ij[1][2])) - t32 * (-t23 * t36 * t29 + t19 * (t27 * Vinv_ij[0][1] - t34 * Vinv_ij[1][1])) + t33 * Vinv_ij[2][0];
t36 = (t16 * t9 * t26 + t18 * t8 * t28) * t20;
t36 = t24 * (-t23 * t36 * t21 - t19 * (-t8 * Vinv_ij[2][0] + t9 * Vinv_ij[1][0])) + t31 * (-t23 * t36 * t15 - t19 * (-t8 * Vinv_ij[2][2] + t9 * Vinv_ij[1][2])) + t32 * (-t23 * t36 * t29 - t19 * (-t8 * Vinv_ij[2][1] + t9 * Vinv_ij[1][1])) + t4 * Vinv_ij[0][0] + t5 * Vinv_ij[0][1] + t6 * Vinv_ij[0][2];
t37 = (t14 * t9 * t13 - t18 * t7 * t28) * t20;
t9 = t24 * (-t23 * t37 * t21 + t19 * (-t7 * Vinv_ij[2][0] + t9 * Vinv_ij[0][0])) + t31 * (-t15 * t23 * t37 + t19 * (-t7 * Vinv_ij[2][2] + t9 * Vinv_ij[0][2])) + t32 * (-t23 * t29 * t37 + t19 * (-t7 * Vinv_ij[2][1] + t9 * Vinv_ij[0][1])) + t4 * Vinv_ij[1][0] + t5 * Vinv_ij[1][1] + t6 * Vinv_ij[1][2];
t37 = (t14 * t8 * t13 + t16 * t7 * t26) * t20;
t4 = t24 * (t23 * t37 * t21 - t19 * (-t7 * Vinv_ij[1][0] + t8 * Vinv_ij[0][0])) + t31 * (t15 * t23 * t37 - t19 * (-t7 * Vinv_ij[1][2] + t8 * Vinv_ij[0][2])) + t32 * (t23 * t29 * t37 - t19 * (-t7 * Vinv_ij[1][1] + t8 * Vinv_ij[0][1])) + t4 * Vinv_ij[2][0] + t5 * Vinv_ij[2][1] + t6 * Vinv_ij[2][2];
t5 = (t16 * t3 * t26 + t18 * t2 * t28) * t20;
t5 = t10 * Vinv_ij[0][0] + t11 * Vinv_ij[0][1] + t12 * Vinv_ij[0][2] + t24 * (t21 * t23 * t5 + t19 * (-t2 * Vinv_ij[2][0] + t3 * Vinv_ij[1][0])) + t31 * (t15 * t23 * t5 + t19 * (-t2 * Vinv_ij[2][2] + t3 * Vinv_ij[1][2])) + t32 * (t23 * t29 * t5 + t19 * (-t2 * Vinv_ij[2][1] + t3 * Vinv_ij[1][1]));
t6 = (-t18 * t1 * t28 + t14 * t3 * t13) * t20;
t3 = t10 * Vinv_ij[1][0] + t11 * Vinv_ij[1][1] + t12 * Vinv_ij[1][2] + t24 * (t21 * t23 * t6 - t19 * (-t1 * Vinv_ij[2][0] + t3 * Vinv_ij[0][0])) + t31 * (t15 * t23 * t6 - t19 * (-t1 * Vinv_ij[2][2] + t3 * Vinv_ij[0][2])) + t32 * (t23 * t29 * t6 - t19 * (-t1 * Vinv_ij[2][1] + t3 * Vinv_ij[0][1]));
t6 = (t16 * t1 * t26 + t14 * t2 * t13) * t20;
t1 = t10 * Vinv_ij[2][0] + t11 * Vinv_ij[2][1] + t12 * Vinv_ij[2][2] + t24 * (-t21 * t23 * t6 + t19 * (-t1 * Vinv_ij[1][0] + t2 * Vinv_ij[0][0])) + t31 * (-t15 * t23 * t6 + t19 * (-t1 * Vinv_ij[1][2] + t2 * Vinv_ij[0][2])) + t32 * (-t23 * t29 * t6 + t19 * (-t1 * Vinv_ij[1][1] + t2 * Vinv_ij[0][1]));
t2 = 0.2e1;
gradE[0] = -t2 * (-t24 * (t23 * t22 * t21 + t19 * (t25 * Vinv_ij[1][0] - t27 * Vinv_ij[2][0])) + t33 * Vinv_ij[0][0] + t30 * Vinv_ij[0][1] + t17 * Vinv_ij[0][2] - t32 * (t23 * t22 * t29 + t19 * (t25 * Vinv_ij[1][1] - t27 * Vinv_ij[2][1])) - t31 * (t23 * t22 * t15 + t19 * (t25 * Vinv_ij[1][2] - t27 * Vinv_ij[2][2])));
gradE[1] = -t2 * t35;
gradE[2] = -t2 * t34;
gradE[3] = t2 * t36;
gradE[4] = t2 * t9;
gradE[5] = t2 * t4;
gradE[6] = t2 * t5;
gradE[7] = t2 * t3;
gradE[8] = t2 * t1;

``

``

``

``

``

Hessian

 

``

hessE := Hessian(E, [v1n[1], v1n[2], v1n[3], v2n[1], v2n[2], v2n[3], v3n[1], v3n[2], v3n[3]])

Dimension(hessE)

9, 9

(1.5.1)

 

CodeGeneration[C](hessE, optimize = tryhard, deducetypes = false, resultname = 'hessE')

Error, (in Print) improper op or subscript selector

 

``

````

``

``

``

``


 

Download membrane_energy.mw

 

 

 

Cannot find integration proplem_in_maple.mw

restart

with(LinearAlgebra)

with(orthopoly)

``

with(student)

Digits := 32

32

(1)

interface(rtablesize = 100)

10

(2)

a := 0; b := 1; N := 5; h := (b-a)/N; B[0] := 1; B[1] := x; n := 2; B[2] := x^2+2; alpha := 1/2

0

 

1

 

5

 

1/5

 

1

 

x

 

2

 

x^2+2

 

1/2

(3)

NULL

for j from 3 to N do B[j] := expand(x*B[j-1]-B[j-2]) end do

x^3+x

 

x^4-2

 

x^5-3*x-x^3

(4)

for i from 0 to N do x[i] := h*i+a end do

0

 

1/5

 

2/5

 

3/5

 

4/5

 

1

(5)

y := sum(c[s]*B[s], s = 0 .. N)

c[0]+c[1]*x+c[2]*(x^2+2)+c[3]*(x^3+x)+c[4]*(x^4-2)+c[5]*(x^5-3*x-x^3)

(6)

yt := subs(x = t, y)

c[0]+c[1]*t+c[2]*(t^2+2)+c[3]*(t^3+t)+c[4]*(t^4-2)+c[5]*(t^5-3*t-t^3)

(7)

k := expand(int(yt*sin(t)*x, t = 0 .. x))

x*c[0]+22*x*c[4]-c[1]*cos(x)*x^2-c[2]*cos(x)*x^3+2*c[2]*sin(x)*x^2-c[3]*cos(x)*x^4+3*c[3]*sin(x)*x^3+5*c[3]*cos(x)*x^2-c[4]*cos(x)*x^5+4*c[4]*sin(x)*x^4+12*c[4]*cos(x)*x^3-24*c[4]*sin(x)*x^2-c[5]*cos(x)*x^6+5*c[5]*sin(x)*x^5+21*c[5]*cos(x)*x^4-63*c[5]*sin(x)*x^3-123*c[5]*cos(x)*x^2-x*cos(x)*c[0]-22*x*cos(x)*c[4]+x*c[1]*sin(x)-5*x*c[3]*sin(x)+123*x*c[5]*sin(x)

(8)

k4 := k*y

(x*c[0]+22*x*c[4]-c[1]*cos(x)*x^2-c[2]*cos(x)*x^3+2*c[2]*sin(x)*x^2-c[3]*cos(x)*x^4+3*c[3]*sin(x)*x^3+5*c[3]*cos(x)*x^2-c[4]*cos(x)*x^5+4*c[4]*sin(x)*x^4+12*c[4]*cos(x)*x^3-24*c[4]*sin(x)*x^2-c[5]*cos(x)*x^6+5*c[5]*sin(x)*x^5+21*c[5]*cos(x)*x^4-63*c[5]*sin(x)*x^3-123*c[5]*cos(x)*x^2-x*cos(x)*c[0]-22*x*cos(x)*c[4]+x*c[1]*sin(x)-5*x*c[3]*sin(x)+123*x*c[5]*sin(x))*(c[0]+c[1]*x+c[2]*(x^2+2)+c[3]*(x^3+x)+c[4]*(x^4-2)+c[5]*(x^5-3*x-x^3))

(9)

f := (8*x^3*(1/3)-2*x^(1/2))*y/GAMMA(1/2)+(1/1260)*x+k4

((8/3)*x^3-2*x^(1/2))*(c[0]+c[1]*x+c[2]*(x^2+2)+c[3]*(x^3+x)+c[4]*(x^4-2)+c[5]*(x^5-3*x-x^3))/Pi^(1/2)+(1/1260)*x+(x*c[0]+22*x*c[4]-c[1]*cos(x)*x^2-c[2]*cos(x)*x^3+2*c[2]*sin(x)*x^2-c[3]*cos(x)*x^4+3*c[3]*sin(x)*x^3+5*c[3]*cos(x)*x^2-c[4]*cos(x)*x^5+4*c[4]*sin(x)*x^4+12*c[4]*cos(x)*x^3-24*c[4]*sin(x)*x^2-c[5]*cos(x)*x^6+5*c[5]*sin(x)*x^5+21*c[5]*cos(x)*x^4-63*c[5]*sin(x)*x^3-123*c[5]*cos(x)*x^2-x*cos(x)*c[0]-22*x*cos(x)*c[4]+x*c[1]*sin(x)-5*x*c[3]*sin(x)+123*x*c[5]*sin(x))*(c[0]+c[1]*x+c[2]*(x^2+2)+c[3]*(x^3+x)+c[4]*(x^4-2)+c[5]*(x^5-3*x-x^3))

(10)

"f(x):=((8/3 x^3-2 sqrt(x)) (c[0]+c[1] x+c[2] (x^2+2)+c[3] (x^3+x)+c[4] (x^4-2)+c[5] (x^5-3 x-x^3)))/(sqrt(Pi))+1/1260 x+(x c[0]+22 x c[4]+x c[1] sin(x)-5 x c[3] sin(x)+123 x c[5] sin(x)-x cos(x) c[0]-22 x cos(x) c[4]-c[1] cos(x) x^2-c[2] cos(x) x^3+2 c[2] sin(x) x^2-c[3] cos(x) x^4+3 c[3] sin(x) x^3+5 c[3] cos(x) x^2-c[4] cos(x) x^5+4 c[4] sin(x) x^4+12 c[4] cos(x) x^3-24 c[4] sin(x) x^2-c[5] cos(x) x^6+5 c[5] sin(x) x^5+21 c[5] cos(x) x^4-63 c[5] sin(x) x^3-123 c[5] cos(x) x^2) (c[0]+c[1] x+c[2] (x^2+2)+c[3] (x^3+x)+c[4] (x^4-2)+c[5] (x^5-3 x-x^3))"

proc (x) options operator, arrow; ((8/3)*x^3-2*sqrt(x))*(c[0]+Typesetting:-delayDotProduct(c[1], x, true)+c[2]*(x^2+2)+c[3]*(x^3+x)+c[4]*(x^4-2)+c[5]*(x^5-3*x-x^3))/sqrt(Pi)+Typesetting:-delayDotProduct(1/1260, x, true)+(Typesetting:-delayDotProduct(x, c[0], true)+22*x*c[4]+Typesetting:-delayDotProduct(x, c[1], true)*sin(x)-5*x*c[3]*sin(x)+123*x*c[5]*sin(x)-Typesetting:-delayDotProduct(x, cos(x), true)*c[0]-22*x*cos(x)*c[4]-c[1]*cos(x)*x^2-c[2]*cos(x)*x^3+2*c[2]*sin(x)*x^2-c[3]*cos(x)*x^4+3*c[3]*sin(x)*x^3+5*c[3]*cos(x)*x^2-c[4]*cos(x)*x^5+4*c[4]*sin(x)*x^4+12*c[4]*cos(x)*x^3-24*c[4]*sin(x)*x^2-c[5]*cos(x)*x^6+5*c[5]*sin(x)*x^5+21*c[5]*cos(x)*x^4-63*c[5]*sin(x)*x^3-123*c[5]*cos(x)*x^2)*(c[0]+Typesetting:-delayDotProduct(c[1], x, true)+c[2]*(x^2+2)+c[3]*(x^3+x)+c[4]*(x^4-2)+c[5]*(x^5-3*x-x^3)) end proc

(11)

NULL

"H(f,alpha,x):=Int((x-s)^(alpha-1)*f(s)/GAMMA(alpha), s = 0 .. x)"

proc (f, alpha, x) options operator, arrow; Int((x-s)^(alpha-1)*f(s)/GAMMA(alpha), s = 0 .. x) end proc

(12)

`assuming`([value(%)], [x > 0])

proc (f, alpha, x) options operator, arrow; Int((x-s)^(alpha-1)*f(s)/GAMMA(alpha), s = 0 .. x) end proc

(13)

H(f, alpha, x)

Int((((8/3)*s^3-2*s^(1/2))*(c[0]+c[1]*s+c[2]*(s^2+2)+c[3]*(s^3+s)+c[4]*(s^4-2)+c[5]*(s^5-3*s-s^3))/Pi^(1/2)+(1/1260)*s+(s*c[0]+22*s*c[4]+c[1]*s*sin(s)-5*s*c[3]*sin(s)+123*s*c[5]*sin(s)-s*cos(s)*c[0]-22*s*cos(s)*c[4]-c[1]*cos(s)*s^2-c[2]*cos(s)*s^3+2*c[2]*sin(s)*s^2-c[3]*cos(s)*s^4+3*c[3]*sin(s)*s^3+5*c[3]*cos(s)*s^2-c[4]*cos(s)*s^5+4*c[4]*sin(s)*s^4+12*c[4]*cos(s)*s^3-24*c[4]*sin(s)*s^2-c[5]*cos(s)*s^6+5*c[5]*sin(s)*s^5+21*c[5]*cos(s)*s^4-63*c[5]*sin(s)*s^3-123*c[5]*cos(s)*s^2)*(c[0]+c[1]*s+c[2]*(s^2+2)+c[3]*(s^3+s)+c[4]*(s^4-2)+c[5]*(s^5-3*s-s^3)))/((x-s)^(1/2)*Pi^(1/2)), s = 0 .. x)

(14)

z := value(%)

int((((8/3)*s^3-2*s^(1/2))*(c[0]+c[1]*s+c[2]*(s^2+2)+c[3]*(s^3+s)+c[4]*(s^4-2)+c[5]*(s^5-3*s-s^3))/Pi^(1/2)+(1/1260)*s+(s*c[0]+22*s*c[4]+c[1]*s*sin(s)-5*s*c[3]*sin(s)+123*s*c[5]*sin(s)-s*cos(s)*c[0]-22*s*cos(s)*c[4]-c[1]*cos(s)*s^2-c[2]*cos(s)*s^3+2*c[2]*sin(s)*s^2-c[3]*cos(s)*s^4+3*c[3]*sin(s)*s^3+5*c[3]*cos(s)*s^2-c[4]*cos(s)*s^5+4*c[4]*sin(s)*s^4+12*c[4]*cos(s)*s^3-24*c[4]*sin(s)*s^2-c[5]*cos(s)*s^6+5*c[5]*sin(s)*s^5+21*c[5]*cos(s)*s^4-63*c[5]*sin(s)*s^3-123*c[5]*cos(s)*s^2)*(c[0]+c[1]*s+c[2]*(s^2+2)+c[3]*(s^3+s)+c[4]*(s^4-2)+c[5]*(s^5-3*s-s^3)))/((x-s)^(1/2)*Pi^(1/2)), s = 0 .. x)

(15)

`assuming`([value(%)], [x > 0])

int((((8/3)*s^3-2*s^(1/2))*(c[0]+c[1]*s+c[2]*(s^2+2)+c[3]*(s^3+s)+c[4]*(s^4-2)+c[5]*(s^5-3*s-s^3))/Pi^(1/2)+(1/1260)*s+(s*c[0]+22*s*c[4]+c[1]*s*sin(s)-5*s*c[3]*sin(s)+123*s*c[5]*sin(s)-s*cos(s)*c[0]-22*s*cos(s)*c[4]-c[1]*cos(s)*s^2-c[2]*cos(s)*s^3+2*c[2]*sin(s)*s^2-c[3]*cos(s)*s^4+3*c[3]*sin(s)*s^3+5*c[3]*cos(s)*s^2-c[4]*cos(s)*s^5+4*c[4]*sin(s)*s^4+12*c[4]*cos(s)*s^3-24*c[4]*sin(s)*s^2-c[5]*cos(s)*s^6+5*c[5]*sin(s)*s^5+21*c[5]*cos(s)*s^4-63*c[5]*sin(s)*s^3-123*c[5]*cos(s)*s^2)*(c[0]+c[1]*s+c[2]*(s^2+2)+c[3]*(s^3+s)+c[4]*(s^4-2)+c[5]*(s^5-3*s-s^3)))/((x-s)^(1/2)*Pi^(1/2)), s = 0 .. x)

(16)

``


Download proplem_in_maple.mw
 

Could anyone give an example how to use the hint option in polynomial solutions in PDEtools in maple?

The dsolve numeric events syntax requires the use of If(a,b,c) rather than the usual if then else syntax. Also, the possible action parts of an event are truly mysterious as are discrete variables. Has anyone plaed around with this much? For example, can the If's be nested? I know I can test that in a toy situation but there are many such questions that arise and I don't want to reinvent the wheel.

Can Maple auto switch input language according to mode of editing?

I would like to:
In 2D-math mode- auto set (after pressing F5 or clicking "math" button) english language
In Text-mode- auto set (after pressing F5 or clicking "text" button) my native language

How Can I set up this option?

Hello,

I obtained a mode shape from a vibration problem.

I want to normalized mode shape for the comparison of responses corresponding to different modes.

How I can normalize the mode shape that provided in the maple file?

The figure corresponds to this mode shape is plotted that is attached.

Thanks

mode_shapes.mw


 

a := Vector(325, {(1) = 0, (2) = 0., (3) = 0., (4) = 0.1e-3, (5) = 0.1e-3, (6) = 0.2e-3, (7) = 0.4e-3, (8) = 0.7e-3, (9) = 0.10e-2, (10) = 0.16e-2, (11) = 0.23e-2, (12) = 0.33e-2, (13) = 0.44e-2, (14) = 0.65e-2, (15) = 0.89e-2, (16) = 0.114e-1, (17) = 0.139e-1, (18) = 0.162e-1, (19) = 0.178e-1, (20) = 0.186e-1, (21) = 0.183e-1, (22) = 0.171e-1, (23) = 0.150e-1, (24) = 0.120e-1, (25) = 0.85e-2, (26) = 0.51e-2, (27) = 0.16e-2, (28) = -0.19e-2, (29) = -0.51e-2, (30) = -0.79e-2, (31) = -0.103e-1, (32) = -0.120e-1, (33) = -0.132e-1, (34) = -0.138e-1, (35) = -0.136e-1, (36) = -0.129e-1, (37) = -0.118e-1, (38) = -0.106e-1, (39) = -0.94e-2, (40) = -0.83e-2, (41) = -0.75e-2, (42) = -0.71e-2, (43) = -0.69e-2, (44) = -0.71e-2, (45) = -0.75e-2, (46) = -0.79e-2, (47) = -0.83e-2, (48) = -0.84e-2, (49) = -0.81e-2, (50) = -0.73e-2, (51) = -0.60e-2, (52) = -0.43e-2, (53) = -0.20e-2, (54) = 0.11e-2, (55) = 0.46e-2, (56) = 0.82e-2, (57) = 0.117e-1, (58) = 0.149e-1, (59) = 0.174e-1, (60) = 0.191e-1, (61) = 0.200e-1, (62) = 0.198e-1, (63) = 0.187e-1, (64) = 0.167e-1, (65) = 0.139e-1, (66) = 0.103e-1, (67) = 0.65e-2, (68) = 0.28e-2, (69) = -0.5e-3, (70) = -0.27e-2, (71) = -0.45e-2, (72) = -0.56e-2, (73) = -0.62e-2, (74) = -0.64e-2, (75) = -0.64e-2, (76) = -0.62e-2, (77) = -0.60e-2, (78) = -0.58e-2, (79) = -0.57e-2, (80) = -0.59e-2, (81) = -0.62e-2, (82) = -0.69e-2, (83) = -0.78e-2, (84) = -0.90e-2, (85) = -0.103e-1, (86) = -0.122e-1, (87) = -0.138e-1, (88) = -0.150e-1, (89) = -0.153e-1, (90) = -0.147e-1, (91) = -0.133e-1, (92) = -0.111e-1, (93) = -0.82e-2, (94) = -0.49e-2, (95) = -0.13e-2, (96) = 0.25e-2, (97) = 0.62e-2, (98) = 0.96e-2, (99) = 0.126e-1, (100) = 0.150e-1, (101) = 0.167e-1, (102) = 0.176e-1, (103) = 0.176e-1, (104) = 0.169e-1, (105) = 0.155e-1, (106) = 0.135e-1, (107) = 0.112e-1, (108) = 0.89e-2, (109) = 0.68e-2, (110) = 0.50e-2, (111) = 0.37e-2, (112) = 0.28e-2, (113) = 0.23e-2, (114) = 0.22e-2, (115) = 0.21e-2, (116) = 0.22e-2, (117) = 0.22e-2, (118) = 0.21e-2, (119) = 0.19e-2, (120) = 0.15e-2, (121) = 0.8e-3, (122) = -0., (123) = -0.11e-2, (124) = -0.25e-2, (125) = -0.40e-2, (126) = -0.68e-2, (127) = -0.97e-2, (128) = -0.127e-1, (129) = -0.154e-1, (130) = -0.175e-1, (131) = -0.189e-1, (132) = -0.193e-1, (133) = -0.187e-1, (134) = -0.171e-1, (135) = -0.146e-1, (136) = -0.113e-1, (137) = -0.76e-2, (138) = -0.42e-2, (139) = -0.9e-3, (140) = 0.23e-2, (141) = 0.52e-2, (142) = 0.76e-2, (143) = 0.96e-2, (144) = 0.110e-1, (145) = 0.118e-1, (146) = 0.121e-1, (147) = 0.118e-1, (148) = 0.110e-1, (149) = 0.100e-1, (150) = 0.91e-2, (151) = 0.84e-2, (152) = 0.78e-2, (153) = 0.75e-2, (154) = 0.76e-2, (155) = 0.79e-2, (156) = 0.85e-2, (157) = 0.92e-2, (158) = 0.98e-2, (159) = 0.103e-1, (160) = 0.103e-1, (161) = 0.98e-2, (162) = 0.88e-2, (163) = 0.72e-2, (164) = 0.51e-2, (165) = 0.24e-2, (166) = -0.15e-2, (167) = -0.57e-2, (168) = -0.99e-2, (169) = -0.137e-1, (170) = -0.164e-1, (171) = -0.184e-1, (172) = -0.196e-1, (173) = -0.197e-1, (174) = -0.189e-1, (175) = -0.171e-1, (176) = -0.146e-1, (177) = -0.115e-1, (178) = -0.81e-2, (179) = -0.47e-2, (180) = -0.16e-2, (181) = 0.8e-3, (182) = 0.24e-2, (183) = 0.34e-2, (184) = 0.40e-2, (185) = 0.43e-2, (186) = 0.43e-2, (187) = 0.42e-2, (188) = 0.41e-2, (189) = 0.41e-2, (190) = 0.43e-2, (191) = 0.47e-2, (192) = 0.53e-2, (193) = 0.62e-2, (194) = 0.76e-2, (195) = 0.92e-2, (196) = 0.109e-1, (197) = 0.127e-1, (198) = 0.146e-1, (199) = 0.160e-1, (200) = 0.166e-1, (201) = 0.162e-1, (202) = 0.149e-1, (203) = 0.128e-1, (204) = 0.99e-2, (205) = 0.65e-2, (206) = 0.28e-2, (207) = -0.10e-2, (208) = -0.47e-2, (209) = -0.82e-2, (210) = -0.112e-1, (211) = -0.137e-1, (212) = -0.154e-1, (213) = -0.164e-1, (214) = -0.166e-1, (215) = -0.159e-1, (216) = -0.147e-1, (217) = -0.129e-1, (218) = -0.110e-1, (219) = -0.90e-2, (220) = -0.73e-2, (221) = -0.59e-2, (222) = -0.49e-2, (223) = -0.44e-2, (224) = -0.41e-2, (225) = -0.41e-2, (226) = -0.42e-2, (227) = -0.43e-2, (228) = -0.43e-2, (229) = -0.41e-2, (230) = -0.36e-2, (231) = -0.29e-2, (232) = -0.18e-2, (233) = -0.3e-3, (234) = 0.16e-2, (235) = 0.38e-2, (236) = 0.62e-2, (237) = 0.88e-2, (238) = 0.121e-1, (239) = 0.151e-1, (240) = 0.175e-1, (241) = 0.192e-1, (242) = 0.198e-1, (243) = 0.194e-1, (244) = 0.181e-1, (245) = 0.159e-1, (246) = 0.122e-1, (247) = 0.80e-2, (248) = 0.34e-2, (249) = -0.9e-3, (250) = -0.41e-2, (251) = -0.68e-2, (252) = -0.87e-2, (253) = -0.98e-2, (254) = -0.103e-1, (255) = -0.103e-1, (256) = -0.98e-2, (257) = -0.92e-2, (258) = -0.86e-2, (259) = -0.80e-2, (260) = -0.76e-2, (261) = -0.75e-2, (262) = -0.77e-2, (263) = -0.82e-2, (264) = -0.89e-2, (265) = -0.98e-2, (266) = -0.109e-1, (267) = -0.117e-1, (268) = -0.121e-1, (269) = -0.119e-1, (270) = -0.111e-1, (271) = -0.96e-2, (272) = -0.74e-2, (273) = -0.46e-2, (274) = -0.7e-3, (275) = 0.36e-2, (276) = 0.80e-2, (277) = 0.121e-1, (278) = 0.150e-1, (279) = 0.173e-1, (280) = 0.188e-1, (281) = 0.193e-1, (282) = 0.189e-1, (283) = 0.176e-1, (284) = 0.155e-1, (285) = 0.128e-1, (286) = 0.98e-2, (287) = 0.67e-2, (288) = 0.38e-2, (289) = 0.15e-2, (290) = -0.1e-3, (291) = -0.12e-2, (292) = -0.18e-2, (293) = -0.21e-2, (294) = -0.22e-2, (295) = -0.22e-2, (296) = -0.21e-2, (297) = -0.22e-2, (298) = -0.24e-2, (299) = -0.27e-2, (300) = -0.33e-2, (301) = -0.42e-2, (302) = -0.54e-2, (303) = -0.68e-2, (304) = -0.85e-2, (305) = -0.103e-1, (306) = -0.130e-1, (307) = -0.154e-1, (308) = -0.170e-1, (309) = -0.177e-1, (310) = -0.173e-1, (311) = -0.160e-1, (312) = -0.138e-1, (313) = -0.108e-1, (314) = -0.75e-2, (315) = -0.38e-2, (316) = -0., (317) = 0.37e-2, (318) = 0.71e-2, (319) = 0.101e-1, (320) = 0.124e-1, (321) = 0.141e-1, (322) = 0.149e-1, (323) = 0.152e-1, (324) = 0.152e-1, (325) = 0.149e-1})

_rtable[18446746442173411926]

(1)

``

t := Vector(325, {(1) = 0, (2) = 0.67e-2, (3) = 0.134e-1, (4) = 0.202e-1, (5) = 0.269e-1, (6) = 0.336e-1, (7) = 0.403e-1, (8) = 0.471e-1, (9) = 0.538e-1, (10) = 0.637e-1, (11) = 0.736e-1, (12) = 0.836e-1, (13) = 0.935e-1, (14) = .1098, (15) = .1261, (16) = .1424, (17) = .1586, (18) = .1764, (19) = .1943, (20) = .2121, (21) = .2299, (22) = .2465, (23) = .2632, (24) = .2798, (25) = .2965, (26) = .3109, (27) = .3253, (28) = .3397, (29) = .3542, (30) = .3686, (31) = .3830, (32) = .3974, (33) = .4118, (34) = .4284, (35) = .4450, (36) = .4615, (37) = .4781, (38) = .4938, (39) = .5095, (40) = .5253, (41) = .5410, (42) = .5567, (43) = .5724, (44) = .5882, (45) = .6039, (46) = .6204, (47) = .6368, (48) = .6533, (49) = .6697, (50) = .6843, (51) = .6989, (52) = .7135, (53) = .7281, (54) = .7448, (55) = .7615, (56) = .7781, (57) = .7948, (58) = .8113, (59) = .8278, (60) = .8442, (61) = .8607, (62) = .8775, (63) = .8943, (64) = .9112, (65) = .9280, (66) = .9468, (67) = .9655, (68) = .9843, (69) = 1.0031, (70) = 1.0190, (71) = 1.0348, (72) = 1.0507, (73) = 1.0665, (74) = 1.0794, (75) = 1.0924, (76) = 1.1053, (77) = 1.1183, (78) = 1.1312, (79) = 1.1442, (80) = 1.1571, (81) = 1.1700, (82) = 1.1842, (83) = 1.1984, (84) = 1.2126, (85) = 1.2268, (86) = 1.2459, (87) = 1.2651, (88) = 1.2842, (89) = 1.3034, (90) = 1.3198, (91) = 1.3362, (92) = 1.3527, (93) = 1.3691, (94) = 1.3844, (95) = 1.3996, (96) = 1.4149, (97) = 1.4302, (98) = 1.4454, (99) = 1.4607, (100) = 1.4760, (101) = 1.4913, (102) = 1.5075, (103) = 1.5238, (104) = 1.5400, (105) = 1.5563, (106) = 1.5733, (107) = 1.5904, (108) = 1.6075, (109) = 1.6246, (110) = 1.6410, (111) = 1.6574, (112) = 1.6739, (113) = 1.6903, (114) = 1.7021, (115) = 1.7140, (116) = 1.7258, (117) = 1.7377, (118) = 1.7495, (119) = 1.7614, (120) = 1.7732, (121) = 1.7851, (122) = 1.7964, (123) = 1.8076, (124) = 1.8189, (125) = 1.8302, (126) = 1.8475, (127) = 1.8649, (128) = 1.8822, (129) = 1.8995, (130) = 1.9168, (131) = 1.9341, (132) = 1.9514, (133) = 1.9687, (134) = 1.9856, (135) = 2.0026, (136) = 2.0195, (137) = 2.0365, (138) = 2.0507, (139) = 2.0649, (140) = 2.0791, (141) = 2.0933, (142) = 2.1075, (143) = 2.1217, (144) = 2.1359, (145) = 2.1501, (146) = 2.1674, (147) = 2.1846, (148) = 2.2018, (149) = 2.2191, (150) = 2.2341, (151) = 2.2492, (152) = 2.2643, (153) = 2.2793, (154) = 2.2949, (155) = 2.3105, (156) = 2.3261, (157) = 2.3417, (158) = 2.3576, (159) = 2.3735, (160) = 2.3895, (161) = 2.4054, (162) = 2.4203, (163) = 2.4353, (164) = 2.4503, (165) = 2.4653, (166) = 2.4839, (167) = 2.5025, (168) = 2.5211, (169) = 2.5397, (170) = 2.5561, (171) = 2.5725, (172) = 2.5888, (173) = 2.6052, (174) = 2.6226, (175) = 2.6399, (176) = 2.6572, (177) = 2.6746, (178) = 2.6930, (179) = 2.7114, (180) = 2.7297, (181) = 2.7481, (182) = 2.7634, (183) = 2.7787, (184) = 2.7940, (185) = 2.8094, (186) = 2.8226, (187) = 2.8358, (188) = 2.8490, (189) = 2.8622, (190) = 2.8755, (191) = 2.8887, (192) = 2.9019, (193) = 2.9151, (194) = 2.9302, (195) = 2.9453, (196) = 2.9604, (197) = 2.9755, (198) = 2.9940, (199) = 3.0126, (200) = 3.0311, (201) = 3.0496, (202) = 3.0659, (203) = 3.0822, (204) = 3.0985, (205) = 3.1149, (206) = 3.1302, (207) = 3.1455, (208) = 3.1609, (209) = 3.1762, (210) = 3.1915, (211) = 3.2069, (212) = 3.2222, (213) = 3.2375, (214) = 3.2545, (215) = 3.2715, (216) = 3.2885, (217) = 3.3055, (218) = 3.3223, (219) = 3.3391, (220) = 3.3560, (221) = 3.3728, (222) = 3.3888, (223) = 3.4047, (224) = 3.4206, (225) = 3.4365, (226) = 3.4494, (227) = 3.4622, (228) = 3.4750, (229) = 3.4879, (230) = 3.5007, (231) = 3.5136, (232) = 3.5264, (233) = 3.5392, (234) = 3.5529, (235) = 3.5667, (236) = 3.5804, (237) = 3.5941, (238) = 3.6116, (239) = 3.6292, (240) = 3.6468, (241) = 3.6644, (242) = 3.6810, (243) = 3.6976, (244) = 3.7143, (245) = 3.7309, (246) = 3.7508, (247) = 3.7707, (248) = 3.7905, (249) = 3.8104, (250) = 3.8273, (251) = 3.8442, (252) = 3.8610, (253) = 3.8779, (254) = 3.8938, (255) = 3.9096, (256) = 3.9255, (257) = 3.9414, (258) = 3.9559, (259) = 3.9705, (260) = 3.9851, (261) = 3.9997, (262) = 4.0149, (263) = 4.0301, (264) = 4.0452, (265) = 4.0604, (266) = 4.0779, (267) = 4.0953, (268) = 4.1128, (269) = 4.1302, (270) = 4.1459, (271) = 4.1615, (272) = 4.1771, (273) = 4.1927, (274) = 4.2114, (275) = 4.2300, (276) = 4.2486, (277) = 4.2673, (278) = 4.2833, (279) = 4.2993, (280) = 4.3153, (281) = 4.3313, (282) = 4.3485, (283) = 4.3657, (284) = 4.3829, (285) = 4.4001, (286) = 4.4182, (287) = 4.4362, (288) = 4.4543, (289) = 4.4724, (290) = 4.4881, (291) = 4.5037, (292) = 4.5194, (293) = 4.5351, (294) = 4.5472, (295) = 4.5593, (296) = 4.5715, (297) = 4.5836, (298) = 4.5957, (299) = 4.6079, (300) = 4.6200, (301) = 4.6321, (302) = 4.6456, (303) = 4.6591, (304) = 4.6726, (305) = 4.6861, (306) = 4.7059, (307) = 4.7256, (308) = 4.7454, (309) = 4.7652, (310) = 4.7819, (311) = 4.7986, (312) = 4.8153, (313) = 4.8320, (314) = 4.8474, (315) = 4.8627, (316) = 4.8781, (317) = 4.8935, (318) = 4.9088, (319) = 4.9242, (320) = 4.9396, (321) = 4.9550, (322) = 4.9662, (323) = 4.9775, (324) = 4.9887, (325) = 5.0000})

_rtable[18446746442112534638]

(2)

``


 

Download mode_shapes.mw


 

a := Vector(325, {(1) = 0, (2) = 0., (3) = 0., (4) = 0.1e-3, (5) = 0.1e-3, (6) = 0.2e-3, (7) = 0.4e-3, (8) = 0.7e-3, (9) = 0.10e-2, (10) = 0.16e-2, (11) = 0.23e-2, (12) = 0.33e-2, (13) = 0.44e-2, (14) = 0.65e-2, (15) = 0.89e-2, (16) = 0.114e-1, (17) = 0.139e-1, (18) = 0.162e-1, (19) = 0.178e-1, (20) = 0.186e-1, (21) = 0.183e-1, (22) = 0.171e-1, (23) = 0.150e-1, (24) = 0.120e-1, (25) = 0.85e-2, (26) = 0.51e-2, (27) = 0.16e-2, (28) = -0.19e-2, (29) = -0.51e-2, (30) = -0.79e-2, (31) = -0.103e-1, (32) = -0.120e-1, (33) = -0.132e-1, (34) = -0.138e-1, (35) = -0.136e-1, (36) = -0.129e-1, (37) = -0.118e-1, (38) = -0.106e-1, (39) = -0.94e-2, (40) = -0.83e-2, (41) = -0.75e-2, (42) = -0.71e-2, (43) = -0.69e-2, (44) = -0.71e-2, (45) = -0.75e-2, (46) = -0.79e-2, (47) = -0.83e-2, (48) = -0.84e-2, (49) = -0.81e-2, (50) = -0.73e-2, (51) = -0.60e-2, (52) = -0.43e-2, (53) = -0.20e-2, (54) = 0.11e-2, (55) = 0.46e-2, (56) = 0.82e-2, (57) = 0.117e-1, (58) = 0.149e-1, (59) = 0.174e-1, (60) = 0.191e-1, (61) = 0.200e-1, (62) = 0.198e-1, (63) = 0.187e-1, (64) = 0.167e-1, (65) = 0.139e-1, (66) = 0.103e-1, (67) = 0.65e-2, (68) = 0.28e-2, (69) = -0.5e-3, (70) = -0.27e-2, (71) = -0.45e-2, (72) = -0.56e-2, (73) = -0.62e-2, (74) = -0.64e-2, (75) = -0.64e-2, (76) = -0.62e-2, (77) = -0.60e-2, (78) = -0.58e-2, (79) = -0.57e-2, (80) = -0.59e-2, (81) = -0.62e-2, (82) = -0.69e-2, (83) = -0.78e-2, (84) = -0.90e-2, (85) = -0.103e-1, (86) = -0.122e-1, (87) = -0.138e-1, (88) = -0.150e-1, (89) = -0.153e-1, (90) = -0.147e-1, (91) = -0.133e-1, (92) = -0.111e-1, (93) = -0.82e-2, (94) = -0.49e-2, (95) = -0.13e-2, (96) = 0.25e-2, (97) = 0.62e-2, (98) = 0.96e-2, (99) = 0.126e-1, (100) = 0.150e-1, (101) = 0.167e-1, (102) = 0.176e-1, (103) = 0.176e-1, (104) = 0.169e-1, (105) = 0.155e-1, (106) = 0.135e-1, (107) = 0.112e-1, (108) = 0.89e-2, (109) = 0.68e-2, (110) = 0.50e-2, (111) = 0.37e-2, (112) = 0.28e-2, (113) = 0.23e-2, (114) = 0.22e-2, (115) = 0.21e-2, (116) = 0.22e-2, (117) = 0.22e-2, (118) = 0.21e-2, (119) = 0.19e-2, (120) = 0.15e-2, (121) = 0.8e-3, (122) = -0., (123) = -0.11e-2, (124) = -0.25e-2, (125) = -0.40e-2, (126) = -0.68e-2, (127) = -0.97e-2, (128) = -0.127e-1, (129) = -0.154e-1, (130) = -0.175e-1, (131) = -0.189e-1, (132) = -0.193e-1, (133) = -0.187e-1, (134) = -0.171e-1, (135) = -0.146e-1, (136) = -0.113e-1, (137) = -0.76e-2, (138) = -0.42e-2, (139) = -0.9e-3, (140) = 0.23e-2, (141) = 0.52e-2, (142) = 0.76e-2, (143) = 0.96e-2, (144) = 0.110e-1, (145) = 0.118e-1, (146) = 0.121e-1, (147) = 0.118e-1, (148) = 0.110e-1, (149) = 0.100e-1, (150) = 0.91e-2, (151) = 0.84e-2, (152) = 0.78e-2, (153) = 0.75e-2, (154) = 0.76e-2, (155) = 0.79e-2, (156) = 0.85e-2, (157) = 0.92e-2, (158) = 0.98e-2, (159) = 0.103e-1, (160) = 0.103e-1, (161) = 0.98e-2, (162) = 0.88e-2, (163) = 0.72e-2, (164) = 0.51e-2, (165) = 0.24e-2, (166) = -0.15e-2, (167) = -0.57e-2, (168) = -0.99e-2, (169) = -0.137e-1, (170) = -0.164e-1, (171) = -0.184e-1, (172) = -0.196e-1, (173) = -0.197e-1, (174) = -0.189e-1, (175) = -0.171e-1, (176) = -0.146e-1, (177) = -0.115e-1, (178) = -0.81e-2, (179) = -0.47e-2, (180) = -0.16e-2, (181) = 0.8e-3, (182) = 0.24e-2, (183) = 0.34e-2, (184) = 0.40e-2, (185) = 0.43e-2, (186) = 0.43e-2, (187) = 0.42e-2, (188) = 0.41e-2, (189) = 0.41e-2, (190) = 0.43e-2, (191) = 0.47e-2, (192) = 0.53e-2, (193) = 0.62e-2, (194) = 0.76e-2, (195) = 0.92e-2, (196) = 0.109e-1, (197) = 0.127e-1, (198) = 0.146e-1, (199) = 0.160e-1, (200) = 0.166e-1, (201) = 0.162e-1, (202) = 0.149e-1, (203) = 0.128e-1, (204) = 0.99e-2, (205) = 0.65e-2, (206) = 0.28e-2, (207) = -0.10e-2, (208) = -0.47e-2, (209) = -0.82e-2, (210) = -0.112e-1, (211) = -0.137e-1, (212) = -0.154e-1, (213) = -0.164e-1, (214) = -0.166e-1, (215) = -0.159e-1, (216) = -0.147e-1, (217) = -0.129e-1, (218) = -0.110e-1, (219) = -0.90e-2, (220) = -0.73e-2, (221) = -0.59e-2, (222) = -0.49e-2, (223) = -0.44e-2, (224) = -0.41e-2, (225) = -0.41e-2, (226) = -0.42e-2, (227) = -0.43e-2, (228) = -0.43e-2, (229) = -0.41e-2, (230) = -0.36e-2, (231) = -0.29e-2, (232) = -0.18e-2, (233) = -0.3e-3, (234) = 0.16e-2, (235) = 0.38e-2, (236) = 0.62e-2, (237) = 0.88e-2, (238) = 0.121e-1, (239) = 0.151e-1, (240) = 0.175e-1, (241) = 0.192e-1, (242) = 0.198e-1, (243) = 0.194e-1, (244) = 0.181e-1, (245) = 0.159e-1, (246) = 0.122e-1, (247) = 0.80e-2, (248) = 0.34e-2, (249) = -0.9e-3, (250) = -0.41e-2, (251) = -0.68e-2, (252) = -0.87e-2, (253) = -0.98e-2, (254) = -0.103e-1, (255) = -0.103e-1, (256) = -0.98e-2, (257) = -0.92e-2, (258) = -0.86e-2, (259) = -0.80e-2, (260) = -0.76e-2, (261) = -0.75e-2, (262) = -0.77e-2, (263) = -0.82e-2, (264) = -0.89e-2, (265) = -0.98e-2, (266) = -0.109e-1, (267) = -0.117e-1, (268) = -0.121e-1, (269) = -0.119e-1, (270) = -0.111e-1, (271) = -0.96e-2, (272) = -0.74e-2, (273) = -0.46e-2, (274) = -0.7e-3, (275) = 0.36e-2, (276) = 0.80e-2, (277) = 0.121e-1, (278) = 0.150e-1, (279) = 0.173e-1, (280) = 0.188e-1, (281) = 0.193e-1, (282) = 0.189e-1, (283) = 0.176e-1, (284) = 0.155e-1, (285) = 0.128e-1, (286) = 0.98e-2, (287) = 0.67e-2, (288) = 0.38e-2, (289) = 0.15e-2, (290) = -0.1e-3, (291) = -0.12e-2, (292) = -0.18e-2, (293) = -0.21e-2, (294) = -0.22e-2, (295) = -0.22e-2, (296) = -0.21e-2, (297) = -0.22e-2, (298) = -0.24e-2, (299) = -0.27e-2, (300) = -0.33e-2, (301) = -0.42e-2, (302) = -0.54e-2, (303) = -0.68e-2, (304) = -0.85e-2, (305) = -0.103e-1, (306) = -0.130e-1, (307) = -0.154e-1, (308) = -0.170e-1, (309) = -0.177e-1, (310) = -0.173e-1, (311) = -0.160e-1, (312) = -0.138e-1, (313) = -0.108e-1, (314) = -0.75e-2, (315) = -0.38e-2, (316) = -0., (317) = 0.37e-2, (318) = 0.71e-2, (319) = 0.101e-1, (320) = 0.124e-1, (321) = 0.141e-1, (322) = 0.149e-1, (323) = 0.152e-1, (324) = 0.152e-1, (325) = 0.149e-1})

_rtable[18446746442173411926]

(1)

``

t := Vector(325, {(1) = 0, (2) = 0.67e-2, (3) = 0.134e-1, (4) = 0.202e-1, (5) = 0.269e-1, (6) = 0.336e-1, (7) = 0.403e-1, (8) = 0.471e-1, (9) = 0.538e-1, (10) = 0.637e-1, (11) = 0.736e-1, (12) = 0.836e-1, (13) = 0.935e-1, (14) = .1098, (15) = .1261, (16) = .1424, (17) = .1586, (18) = .1764, (19) = .1943, (20) = .2121, (21) = .2299, (22) = .2465, (23) = .2632, (24) = .2798, (25) = .2965, (26) = .3109, (27) = .3253, (28) = .3397, (29) = .3542, (30) = .3686, (31) = .3830, (32) = .3974, (33) = .4118, (34) = .4284, (35) = .4450, (36) = .4615, (37) = .4781, (38) = .4938, (39) = .5095, (40) = .5253, (41) = .5410, (42) = .5567, (43) = .5724, (44) = .5882, (45) = .6039, (46) = .6204, (47) = .6368, (48) = .6533, (49) = .6697, (50) = .6843, (51) = .6989, (52) = .7135, (53) = .7281, (54) = .7448, (55) = .7615, (56) = .7781, (57) = .7948, (58) = .8113, (59) = .8278, (60) = .8442, (61) = .8607, (62) = .8775, (63) = .8943, (64) = .9112, (65) = .9280, (66) = .9468, (67) = .9655, (68) = .9843, (69) = 1.0031, (70) = 1.0190, (71) = 1.0348, (72) = 1.0507, (73) = 1.0665, (74) = 1.0794, (75) = 1.0924, (76) = 1.1053, (77) = 1.1183, (78) = 1.1312, (79) = 1.1442, (80) = 1.1571, (81) = 1.1700, (82) = 1.1842, (83) = 1.1984, (84) = 1.2126, (85) = 1.2268, (86) = 1.2459, (87) = 1.2651, (88) = 1.2842, (89) = 1.3034, (90) = 1.3198, (91) = 1.3362, (92) = 1.3527, (93) = 1.3691, (94) = 1.3844, (95) = 1.3996, (96) = 1.4149, (97) = 1.4302, (98) = 1.4454, (99) = 1.4607, (100) = 1.4760, (101) = 1.4913, (102) = 1.5075, (103) = 1.5238, (104) = 1.5400, (105) = 1.5563, (106) = 1.5733, (107) = 1.5904, (108) = 1.6075, (109) = 1.6246, (110) = 1.6410, (111) = 1.6574, (112) = 1.6739, (113) = 1.6903, (114) = 1.7021, (115) = 1.7140, (116) = 1.7258, (117) = 1.7377, (118) = 1.7495, (119) = 1.7614, (120) = 1.7732, (121) = 1.7851, (122) = 1.7964, (123) = 1.8076, (124) = 1.8189, (125) = 1.8302, (126) = 1.8475, (127) = 1.8649, (128) = 1.8822, (129) = 1.8995, (130) = 1.9168, (131) = 1.9341, (132) = 1.9514, (133) = 1.9687, (134) = 1.9856, (135) = 2.0026, (136) = 2.0195, (137) = 2.0365, (138) = 2.0507, (139) = 2.0649, (140) = 2.0791, (141) = 2.0933, (142) = 2.1075, (143) = 2.1217, (144) = 2.1359, (145) = 2.1501, (146) = 2.1674, (147) = 2.1846, (148) = 2.2018, (149) = 2.2191, (150) = 2.2341, (151) = 2.2492, (152) = 2.2643, (153) = 2.2793, (154) = 2.2949, (155) = 2.3105, (156) = 2.3261, (157) = 2.3417, (158) = 2.3576, (159) = 2.3735, (160) = 2.3895, (161) = 2.4054, (162) = 2.4203, (163) = 2.4353, (164) = 2.4503, (165) = 2.4653, (166) = 2.4839, (167) = 2.5025, (168) = 2.5211, (169) = 2.5397, (170) = 2.5561, (171) = 2.5725, (172) = 2.5888, (173) = 2.6052, (174) = 2.6226, (175) = 2.6399, (176) = 2.6572, (177) = 2.6746, (178) = 2.6930, (179) = 2.7114, (180) = 2.7297, (181) = 2.7481, (182) = 2.7634, (183) = 2.7787, (184) = 2.7940, (185) = 2.8094, (186) = 2.8226, (187) = 2.8358, (188) = 2.8490, (189) = 2.8622, (190) = 2.8755, (191) = 2.8887, (192) = 2.9019, (193) = 2.9151, (194) = 2.9302, (195) = 2.9453, (196) = 2.9604, (197) = 2.9755, (198) = 2.9940, (199) = 3.0126, (200) = 3.0311, (201) = 3.0496, (202) = 3.0659, (203) = 3.0822, (204) = 3.0985, (205) = 3.1149, (206) = 3.1302, (207) = 3.1455, (208) = 3.1609, (209) = 3.1762, (210) = 3.1915, (211) = 3.2069, (212) = 3.2222, (213) = 3.2375, (214) = 3.2545, (215) = 3.2715, (216) = 3.2885, (217) = 3.3055, (218) = 3.3223, (219) = 3.3391, (220) = 3.3560, (221) = 3.3728, (222) = 3.3888, (223) = 3.4047, (224) = 3.4206, (225) = 3.4365, (226) = 3.4494, (227) = 3.4622, (228) = 3.4750, (229) = 3.4879, (230) = 3.5007, (231) = 3.5136, (232) = 3.5264, (233) = 3.5392, (234) = 3.5529, (235) = 3.5667, (236) = 3.5804, (237) = 3.5941, (238) = 3.6116, (239) = 3.6292, (240) = 3.6468, (241) = 3.6644, (242) = 3.6810, (243) = 3.6976, (244) = 3.7143, (245) = 3.7309, (246) = 3.7508, (247) = 3.7707, (248) = 3.7905, (249) = 3.8104, (250) = 3.8273, (251) = 3.8442, (252) = 3.8610, (253) = 3.8779, (254) = 3.8938, (255) = 3.9096, (256) = 3.9255, (257) = 3.9414, (258) = 3.9559, (259) = 3.9705, (260) = 3.9851, (261) = 3.9997, (262) = 4.0149, (263) = 4.0301, (264) = 4.0452, (265) = 4.0604, (266) = 4.0779, (267) = 4.0953, (268) = 4.1128, (269) = 4.1302, (270) = 4.1459, (271) = 4.1615, (272) = 4.1771, (273) = 4.1927, (274) = 4.2114, (275) = 4.2300, (276) = 4.2486, (277) = 4.2673, (278) = 4.2833, (279) = 4.2993, (280) = 4.3153, (281) = 4.3313, (282) = 4.3485, (283) = 4.3657, (284) = 4.3829, (285) = 4.4001, (286) = 4.4182, (287) = 4.4362, (288) = 4.4543, (289) = 4.4724, (290) = 4.4881, (291) = 4.5037, (292) = 4.5194, (293) = 4.5351, (294) = 4.5472, (295) = 4.5593, (296) = 4.5715, (297) = 4.5836, (298) = 4.5957, (299) = 4.6079, (300) = 4.6200, (301) = 4.6321, (302) = 4.6456, (303) = 4.6591, (304) = 4.6726, (305) = 4.6861, (306) = 4.7059, (307) = 4.7256, (308) = 4.7454, (309) = 4.7652, (310) = 4.7819, (311) = 4.7986, (312) = 4.8153, (313) = 4.8320, (314) = 4.8474, (315) = 4.8627, (316) = 4.8781, (317) = 4.8935, (318) = 4.9088, (319) = 4.9242, (320) = 4.9396, (321) = 4.9550, (322) = 4.9662, (323) = 4.9775, (324) = 4.9887, (325) = 5.0000})

_rtable[18446746442112534638]

(2)

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Determine the polynomials P∈R₃ [X] such that P (-1) = - 18 and whose remainders in the Euclidean division by X-1, X-2 and X-3 are equal to 6.

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