Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hello everybody,

While i was trying to work on a physical math problem, a system of 4 integral equations is obtained. The right hand sides of these equations are known functions of r. The left hand sides contain double integrals with respect to lambda and t. i believe that an analytical determination of the 4 unknown functions f_1(t), f_2(t), f_3(t), and f_4(t) is far from being trivial, thus recourse to a numerical technique is necessary and indispensable.

 

i tried to express the unknown functions as series expansions in t and solve the resulting linear system of equations for the expansion coefficients, but unfortunately the coefficients are very large and the solution is strongly dependent on the number of coefficients. i was wondering whether someone here has some experience with such integral problems and is willing to assist and help. Any hint is highly appreciated.

 

i attach a Maple script including the equations.

Thank you,

 

>>>>>> Question.mw

I am trying to use Maple to solve a set of 5 equations, but cannot get a solution. Or there is no solution??

Any help? (Yes, the L function is a likelihood function and I am doing MLE for 5 variables..)


 

``

h := 4

4

(1)

k := Matrix(3, 4, {(1, 1) = 11.0, (1, 2) = 7.0, (1, 3) = 7.0, (1, 4) = 11.0, (2, 1) = 5.0, (2, 2) = 7.0, (2, 3) = 12.0, (2, 4) = 12.0, (3, 1) = 1., (3, 2) = 9.0, (3, 3) = 7.0, (3, 4) = 19.0})

Matrix(%id = 18446746279852723246)

(2)

A := Vector[row](3, {(1) = 6.0, (2) = 13.0, (3) = 18.0})

Vector[row](%id = 18446746279852713854)

(3)

B := Vector[row](3, {(1) = 3.0, (2) = 4.0, (3) = 4.0})

Vector[row](%id = 18446746279852763126)

(4)

"l(N1,M1,lambda,phi,r):=product((phi*(N1-'B[i]'+r*'A[i]'))^('k[i][1]')*(1/(2)*lambda*(M1-'A[i]'))^('k[i][2]'+'k[i][3]')*(1-phi*(N1-'B[i]'+r*'A[i]')-lambda*(M1-'A[i]'))^('k[i][4]')   ,i=1..(h-1))"

proc (N1, M1, lambda, phi, r) options operator, arrow, function_assign; product((phi*(N1-'B[i]'+r*'A[i]'))^'k[i][1]'*((1/2)*lambda*(M1-'A[i]'))^('k[i][2]'+'k[i][3]')*(1-phi*(N1-'B[i]'+r*'A[i]')-lambda*(M1-'A[i]'))^'k[i][4]', i = 1 .. h-1) end proc

(5)

``

``

NULL

fsolve({diff(ln(l(N1, M1, lambda, phi, r)), M1) = 0, diff(ln(l(N1, M1, lambda, phi, r)), N1) = 0, diff(ln(l(N1, M1, lambda, phi, r)), lambda) = 0, diff(ln(l(N1, M1, lambda, phi, r)), phi) = 0, diff(ln(l(N1, M1, lambda, phi, r)), r) = 0}, {M1, N1, lambda, phi, r}, N1 = 0 .. infinity, M1 = 0 .. infinity, lambda = 0 .. 1, phi = 0 .. 1, r = 0 .. 1)

``


 

Download PlayGround.mw

I would like to find a fixed point of f^4 in tems of a and b. I define function as

 

I calculate f(f(f(f(x,y))))  and Iet f(f(f(f(x,y)))) = (x,y), then use the solve command as:

solve({b^4*(a*(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)^2-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)*b^2*(a*x-x^2-x*y)*x*y)*(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)*(a*x-x^2-x*y)*x*y = y, a*(a*(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)^2-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)*b^2*(a*x-x^2-x*y)*x*y)-(a*(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)^2-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)*b^2*(a*x-x^2-x*y)*x*y)^2-(a*(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)^2-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)*b^2*(a*x-x^2-x*y)*x*y)*b^3*(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)*(a*x-x^2-x*y)*x*y = x}, {x, y})

My computer was freezing. How can I get my result. Thank you

 

 

I try to write a Maple Code. But I can' t finish it. 

This is very important for me. Could you help me? download_Maple Code.mw

Hi guys, 

I have tried to create a loop to solve a set of two equations, but can't seem to get it working. My initial equations are given by;

 

nstar := (F, L, sigma) -> ceil((ln(k*F) - ln(c(L, sigma)*B))/ln(Phi(L, sigma)))

 

and 

 

i := (F, L, sigma) -> r*(1 - (G(L, sigma)*Phi(L, sigma))^nstar(F, L, sigma)*B/F)/(1 - G(L, sigma)^nstar(F, L, sigma))

 

in which both are based on further rather simple equations. To these I am trying to apply the proc function where I am trying to find which i makes borth the equations above work :

 

i := proc(F,L,sigma)  

local k :=0.01 ;  

local eps := 0.01 ;  

do while(eps>0.001)  

nstar:= (6)

i := (7)

eps:= i -k:

k=i:

end do;

k;

end proc;


Error, Got internal error in Typesetting:-Parse : "'_Inert_DELAYLESSTHAN' is not a valid inert form"
 

But as you see I am here getting a error which I have not managed to fix. Can anyone see where I might have gone wrong? Could this be done by solve or fsolve? If yes, then how (have tried it as well without succeding)?

help me! 

 

I have a problem with the system, looking forward to everyone's help!

Greetings, 

Any maple user have any idea how to solve coupled difference scheme system of equations using crank nicolson scheme 

Hello!

How can I make MAPLE to create the solution of the following system?

https://math.stackexchange.com/questions/301068/how-do-you-find-a-corresponding-recurrence-relation-for-some-random-algorithm/301709

according to this link, how to parse or walk through the algorithm in maple to generate recurrence relation formula?

I have a differential equation involving several functions of the following form:

diff(h,z) = iAf + iBg,

where h, f and g are functions of the Cartesian coordinates x, y and R and the third coordinate corresponds to z = R for some fixed constant value R.  The derivative is then with respect to the coordinate z and A and B are constants, with i the usual imaginary unit.  Is there some way this equation could be solved explicitly with Maple?

Basically it spits out the subset of values for which a division by zero error will occur for the function you specify on  range you specify for each of it's arguments, but I get an ambigous error when ever exponentiation features in the function I specify, which of course dramatically reduces the application of the calculator. Division,addition,substraction and multiplication are currently the only available arithmetic operators availble for the function window that I know the error will not occur.

If some one can help it is much appriciated

 

DIVISION_BY_ZERO_CALCULATOR.mw

hello everyone,
   INGT.mw
 

L__d := 100:

L__b := 200:

L__c := L__d+(1/2)*L__b;

200

(1)

X := .3;

.3

(2)

Error, (in plot) procedure expected, as range contains no plotting variable

 

`ΔE__g` := 1.155*X+.37*X^2;

.3798

(3)

V__0 := .6*`ΔE__g`;

.22788

(4)

m__D := 0.67e-1*m[e];

0.67e-1*m[e]

(5)

m__B := (0.67e-1+0.83e-1*X)*m[e];

0.919e-1*m[e]

(6)

Sol := solve(2*cos(L__d*sqrt(E__x))+(m__D*sqrt((V__0-E__x)/E__x)/m__B-m__B*sqrt(E__x/(V__0-E__x))/m__D)*sin(L__d*sqrt(E__x))-(m__D*sqrt((V__0-E__x)/E__x)/m__B+m__B*sqrt(E__x/(V__0-E__x))/m__D)*sin(L__d*sqrt(E__x))*exp(-sqrt(V__0-E__x)*L__b) = 0, E__x);

0.1110897170e-2, 0.3531161505e-2, -.2585338615+0.9991335677e-27*I

(7)

 

0.1110897170e-2, 0.3531161505e-2, -.2585338615+0.9991335677e-27*I

(8)

E__1 := 0.1110897170e-2:

K__1 := sqrt(E__1);

0.3333012406e-1

(9)

K__2 := sqrt(V__0-E__1);

.4762027959

(10)

C := cosh((1/2)*K__2*L__b);

0.2399908351e21

(11)

beta := m__D*K__2/(m__B*K__1);

10.41631973

(12)

B := -beta*sinh((1/2)*K__2*L__b);

-0.2499821271e22

(13)

A := -B*sin(K__1*L__d)+C*cos(K__1*L__d);

-0.7112056933e21

(14)

h := proc (x) options operator, arrow; piecewise(x <= -L__c, A*exp(K__2*(x+L__c)), -L__c < x and x < -(1/2)*L__b, -B*sin(K__1*(x+(1/2)*L__b))+C*cos(K__1*(x+(1/2)*L__b)), abs(x) <= (1/2)*L__b, (1/2)*exp(K__2*x)+(1/2)*exp(-K__2*x), (1/2)*L__b < x and x < L__c, -B*sin(K__1*(x-(1/2)*L__b))+C*cos(K__1*(x-(1/2)*L__b)), L__c <= x, A*exp(K__2*(x-L__c))) end proc:

'h(x)' = h(x);

h(x) = piecewise(x <= -200, -7.112056933*10^20*exp(95.24055918+.4762027959*x), -200 < x and x < -100, 2.499821271*10^21*sin(3.333012406+0.3333012406e-1*x)+2.399908351*10^20*cos(3.333012406+0.3333012406e-1*x), abs(x) <= 100, (1/2)*exp(.4762027959*x)+(1/2)*exp(-.4762027959*x), 100 < x and x < 200, 2.499821271*10^21*sin(0.3333012406e-1*x-3.333012406)+2.399908351*10^20*cos(0.3333012406e-1*x-3.333012406), 200 <= x, -7.112056933*10^20*exp(-95.24055918+.4762027959*x))

(15)

L__y := 200:

L__z := 200:

P := proc (x, y, z) options operator, arrow; h(x)*cos(Pi*y/L__y)*cos(Pi*z/L__z) end proc:

'Psi(x, y, z)' = P(x, y, z);

Psi(x, y, z) = piecewise(x <= -200, -7.112056933*10^20*exp(95.24055918+.4762027959*x), -200 < x and x < -100, 2.499821271*10^21*sin(3.333012406+0.3333012406e-1*x)+2.399908351*10^20*cos(3.333012406+0.3333012406e-1*x), abs(x) <= 100, (1/2)*exp(.4762027959*x)+(1/2)*exp(-.4762027959*x), 100 < x and x < 200, 2.499821271*10^21*sin(0.3333012406e-1*x-3.333012406)+2.399908351*10^20*cos(0.3333012406e-1*x-3.333012406), 200 <= x, -7.112056933*10^20*exp(-95.24055918+.4762027959*x))*cos((1/200)*Pi*y)*cos((1/200)*Pi*z)

(16)

INGT := proc (x__i) `assuming`([evalf(int(int(int(P(x, y, z)^2*exp(-lambda*sqrt((x-x__i)^2+y^2+z^2)), x = -infinity .. infinity), y = -L__y .. L__y), z = -L__z .. L__z))], [0 < lambda]) end proc

evalf(INGT(2))

``

Warning,  computation interrupted

 

``


 

Download INGT.mw
 

L__d := 100:

L__b := 200:

L__c := L__d+(1/2)*L__b;

200

(1)

X := .3;

.3

(2)

Error, (in plot) procedure expected, as range contains no plotting variable

 

`&Delta;E__g` := 1.155*X+.37*X^2;

.3798

(3)

V__0 := .6*`&Delta;E__g`;

.22788

(4)

m__D := 0.67e-1*m[e];

0.67e-1*m[e]

(5)

m__B := (0.67e-1+0.83e-1*X)*m[e];

0.919e-1*m[e]

(6)

Sol := solve(2*cos(L__d*sqrt(E__x))+(m__D*sqrt((V__0-E__x)/E__x)/m__B-m__B*sqrt(E__x/(V__0-E__x))/m__D)*sin(L__d*sqrt(E__x))-(m__D*sqrt((V__0-E__x)/E__x)/m__B+m__B*sqrt(E__x/(V__0-E__x))/m__D)*sin(L__d*sqrt(E__x))*exp(-sqrt(V__0-E__x)*L__b) = 0, E__x);

0.1110897170e-2, 0.3531161505e-2, -.2585338615+0.9991335677e-27*I

(7)

 

0.1110897170e-2, 0.3531161505e-2, -.2585338615+0.9991335677e-27*I

(8)

E__1 := 0.1110897170e-2:

K__1 := sqrt(E__1);

0.3333012406e-1

(9)

K__2 := sqrt(V__0-E__1);

.4762027959

(10)

C := cosh((1/2)*K__2*L__b);

0.2399908351e21

(11)

beta := m__D*K__2/(m__B*K__1);

10.41631973

(12)

B := -beta*sinh((1/2)*K__2*L__b);

-0.2499821271e22

(13)

A := -B*sin(K__1*L__d)+C*cos(K__1*L__d);

-0.7112056933e21

(14)

h := proc (x) options operator, arrow; piecewise(x <= -L__c, A*exp(K__2*(x+L__c)), -L__c < x and x < -(1/2)*L__b, -B*sin(K__1*(x+(1/2)*L__b))+C*cos(K__1*(x+(1/2)*L__b)), abs(x) <= (1/2)*L__b, (1/2)*exp(K__2*x)+(1/2)*exp(-K__2*x), (1/2)*L__b < x and x < L__c, -B*sin(K__1*(x-(1/2)*L__b))+C*cos(K__1*(x-(1/2)*L__b)), L__c <= x, A*exp(K__2*(x-L__c))) end proc:

'h(x)' = h(x);

h(x) = piecewise(x <= -200, -7.112056933*10^20*exp(95.24055918+.4762027959*x), -200 < x and x < -100, 2.499821271*10^21*sin(3.333012406+0.3333012406e-1*x)+2.399908351*10^20*cos(3.333012406+0.3333012406e-1*x), abs(x) <= 100, (1/2)*exp(.4762027959*x)+(1/2)*exp(-.4762027959*x), 100 < x and x < 200, 2.499821271*10^21*sin(0.3333012406e-1*x-3.333012406)+2.399908351*10^20*cos(0.3333012406e-1*x-3.333012406), 200 <= x, -7.112056933*10^20*exp(-95.24055918+.4762027959*x))

(15)

L__y := 200:

L__z := 200:

P := proc (x, y, z) options operator, arrow; h(x)*cos(Pi*y/L__y)*cos(Pi*z/L__z) end proc:

'Psi(x, y, z)' = P(x, y, z);

Psi(x, y, z) = piecewise(x <= -200, -7.112056933*10^20*exp(95.24055918+.4762027959*x), -200 < x and x < -100, 2.499821271*10^21*sin(3.333012406+0.3333012406e-1*x)+2.399908351*10^20*cos(3.333012406+0.3333012406e-1*x), abs(x) <= 100, (1/2)*exp(.4762027959*x)+(1/2)*exp(-.4762027959*x), 100 < x and x < 200, 2.499821271*10^21*sin(0.3333012406e-1*x-3.333012406)+2.399908351*10^20*cos(0.3333012406e-1*x-3.333012406), 200 <= x, -7.112056933*10^20*exp(-95.24055918+.4762027959*x))*cos((1/200)*Pi*y)*cos((1/200)*Pi*z)

(16)

INGT := proc (x__i) `assuming`([evalf(int(int(int(P(x, y, z)^2*exp(-lambda*sqrt((x-x__i)^2+y^2+z^2)), x = -infinity .. infinity), y = -L__y .. L__y), z = -L__z .. L__z))], [0 < lambda]) end proc

evalf(INGT(2))

``

Warning,  computation interrupted

 

``


 

Download INGT.mw

 

I'm trying to calculate a triple integral complicated by a procedure that changes each time a variable xi, while the program takes a lot of time and it gives me the message "Warning, computation interrupted". If anyone can help me I will be very happy

Is there something I should be doing whenever I use simplify to avoid things like this, or should I stop using the "is" function all together?

 

interface(showassumed = 0):

 

sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1)

(n-k+1)*binomial(n+1, k)/(k+1) = binomial(n+1, k+1)

(1)

#And we have:
is(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1))

FAIL

(2)

#And since:
is(simplify(convert(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1), 'factorial')))

true

(3)

is(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1)) = is(simplify(convert(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1), 'factorial')))


 

Download main.mw

Hello people :) 

As the captian says, im trying to remove an old task i've made.
But i get this:

Error in Get, invalid object [_XML_reply_data_get("reference" =
"_Maplets_reference_12","parameter" =
"value",_XML_content("Task,UserTasks,Nyops",&Entity "#xc3",&Enity
"#xa6","tning"))]

And i have no idea what it is, but it won't erase my task :'D

Thanks a bunch in advance! 

Have a great weekend you all
Best regards Lucas :)

A few seconds after calling up Help starts zucking araound and the whole computer then freezes. Ctrl-Alt-Delete doesn't work, hard reset required. Very funny. Am I alone?

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