Hi, 

I have a list of integers (>1) and for all of them I define an alias (in the attached file I've tried two different names for them : a[n] or a||n) wich represents the nth roots of the unity.
When I apply the procedure allvalues to a specific alias it returns the algebraic values of the corresponding roots of the unity.
But when aplied to the list of aliases it gives me back only the name of the alias, not the algebraic values.

How can I fix this ?

TIA

Download allvalues.mw

Hello,

I have the general function F(x,g(y)), and I don't understand the following notation of the derivative of  F w.r.t  y in Maple ?  What is D₂(F) ?  Can we provide a concrete example ?

Thank you!

Dear Users!

Hope you would be fine with everything. I want to evaluate an expression (diff(u(y, t), y)+diff(diff(u(y, t), y), t)) for various values of b at y = 0, t=1. Please help me to evaluate it. Thanks in advance,

restart; with(plots); a := .7; L := 8; HAA := [0, 2, 5, 10];

for i to nops(HAA) do

b := op(i, HAA);

PDE1[i] := diff(u(y, t), t) = diff(u(y, t), y, y)+diff(diff(u(y, t), y, y), t)-b*u(y, t)+T(y, t);

PDE2[i] := diff(T(y, t), t) = (1+(1+(a-1)*T(y, t))^3)*(diff(T(y, t), y, y))+(a-1)*(1+(a-1)*T(y, t))^2*(diff(T(y, t), y))^2+T(y, t)*(diff(T(y, t), y, y))+(diff(T(y, t), y))^2;

ICandBC[i] := {T(L, t) = 0, T(y, 0) = 0, u(0, t) = t, u(L, t) = 0, u(y, 0) = 0, (D[1](T))(0, t) = -1};

PDE[i] := {PDE1[i], PDE2[i]}; pds[i] := pdsolve(PDE[i], ICandBC[i], numeric)

end do;
 

with(RegularChains):
with(ChainTools):
with(MatrixTools):
with(ConstructibleSetTools):
with(ParametricSystemTools):
with(SemiAlgebraicSetTools):
with(FastArithmeticTools):
R := PolynomialRing([x,y,z,a,b]):
sys := [x^2 + y^2 - x*y - 1 = 0, y^2 + z^2 - y*z - a^2 = 0, z^2 + x^2 - x*z - b^2 = 0,x > 0, y > 0, z > 0, a - 1 >= 0, b-a >= 0, a+1-b > 0]:

dec := RealTriangularize(sys,R): # very slow
Display(dec, R);

dec := LazyRealTriangularize(sys,R): # it is faster
dec2 := value(dec): # very slow
value(dec2); 

find a , b to satisfy sys have real solution

expect  one of solution is below, but above function are very slow, load a very time still no result, where is wrong?

R1 = a^2+a+1-b^2;
R1 = a^2-1+b-b^2;

[R1 > 0, R2 > 0]

Hi,

Is it possible to force Maple to simplify these Sum(s) ?
SimplifySum.mw
 

Thanks in advance

Hi, 

I can't find a unique way to define a mixture of two random variables that enables at the same time to compute its PDF and generate a sample.
In the attached file you will find two methods :

1. the first one is the most formal and only CAS are supposed to be able to allow its implementation:
    it enables computing the PDF and the CDF (trivial) but fails to generate a sample.
   (PS : in a first attempt I had defined only the PDF, which should have been enough for method=envelope does work... ... at my opinion)
    
2. the second method is the one one would use in non CAS languages (for instance Matlab, R, ...). It enables generating a sample (of course) but fails to compute the PDF (which is not very surprising).

So my question: does anyone here would have some suggestions to make one these two methods capable to compute both the PDF (eventually the CDF) and generate samples ?

PS: still have this kind of problems (tomleslie suggested months ago that using interface(rtablesize=10) could help but it's not the case here)
Maple Worksheet - Error
Failed to load the worksheet /maplenet/convert/Mixture_of_random_variables.mw .
 

Download Mixture_of_random_variables.mw

Hi 

I got, a bit by mistake, a weird result that seems to come from the way "Maple" manipulates infinity (please have a look at the results below)
I couldn't find a correct explanation to these results in the help pages dedicated to infinity or evaluation.

Could anyone explain me why, in some circumstances, 'infinity' seems to be a name (for instance infinity*Pi; does not return  infinity but infiniy/Pi).
Thanks in advance

 

Download Infinity.mw

Dear Users!

Hope you would be fine with everything. I have following code to generate marix A of order M by M

restart; with(LinearAlgebra); with(linalg); Digits := 30; M := 10; nu := 1;

for k1 while k1 <= M do

C[k1] := simplify(sum((-1)^(k1-1-i1)*GAMMA(k1-1+i1+2*nu)*GAMMA(nu+1/2)*x^i1/(GAMMA(i1+nu+1/2)*factorial(k1-1-i1)*factorial(i1)*GAMMA(2*nu)), i1 = 0 .. k1-1))

end do;

A := evalm(Matrix(M, M, proc (i, j) options operator, arrow; eval(C[j], x = (i-1)/(M-1)) end proc))

I want to split (or decompose) A into two parts Ad and Ab 

A = Ab + Ad

where Ad is M by M matrix of all entries of A but first and last rows of Ad shoud be zero

and Ab is M by M matrix with zero entries expect first and last rows.

For exmaple for M = 5, A, Ab and Ad are given as,

Ab := Matrix(5, 5, {(1, 1) = 1, (1, 2) = -2, (1, 3) = 3, (1, 4) = -4, (1, 5) = 5, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (5, 1) = 1, (5, 2) = 2, (5, 3) = 3, (5, 4) = 4, (5, 5) = 5});

Ad := Matrix(5, 5, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (2, 1) = 1, (2, 2) = -1, (2, 3) = 0, (2, 4) = 1, (2, 5) = -1, (3, 1) = 1, (3, 2) = 0, (3, 3) = -1, (3, 4) = 0, (3, 5) = 1, (4, 1) = 1, (4, 2) = 1, (4, 3) = 0, (4, 4) = -1, (4, 5) = -1, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 0});

Please help me to fix this problem.
Special request @acer @Carl Love @Kitonum @Preben Alsholm

Hi,

How can I force the command InsertContent(Worksheet(Group(Input( T )))) to display the variable eq as it appears in label (2) ?

(a screen capture of the output of InsertContent(Worksheet(Group(Input( T )))) is given after the Maple code)

Download Layout.mw

Hi!

There is a (relatively) known software code (written in C), called ." GKLS-generator" or "GKLS" to generate, according to certain user paramenters, optimization test functions. The code is available for free at the web

http://wwwinfo.deis.unical.it/%7Eyaro/GKLS.html

The download with the files of the GKLS is the following:  download

I would like to write this code in Maple. In the attached zip there is a PDF explaining how to build these functions. For now, I tried the follwoing Maple code GKLS_v4.mw

I think I'm doing something wrong, since the drawing generated by the attached Maple does not look much like the PDF in the attached zip (Fig. 1 of page 8).

Please, Can you help me with this?

Many thanks in advance for your comments.

Hi User!

Hope you would be fine with everything. I have a vector "POL" of M dimension obatined for the following expression

restart; with(LinearAlgebra); nu := 1; M := 3;
for k while k <= M do
Poly[k] := simplify(sum(x^i*GAMMA(nu+1)/(factorial(i)*GAMMA(2*nu)), i = 0 .. k-1))
end do;
POL := `<,>`(seq(Poly[k], k = 1 .. M))

and I want to construct a matrix of M by M by collocating it on the points x=i/(M-1) for i=0,1,2,...,M-1 like the following way,

For M=3 I need

Matrix(3, 3, {(1, 1) = Poly[1](0), (1, 2) = Poly[1](1/2), (1, 3) = Poly[1](1), (2, 1) = Poly[2](0), (2, 2) = Poly[2](1/2), (2, 3) = Poly[2](1), (3, 1) = Poly[3](0), (3, 2) = Poly[3](1/2), (3, 3) = Poly[3](1)});

For M=4 I need

Matrix(4, 4, {(1, 1) = Poly[1](0), (1, 2) = Poly[1](1/3), (1, 3) = Poly[1](2/3), (1, 4) = Poly[1](1), (2, 1) = Poly[2](0), (2, 2) = Poly[2](1/3), (2, 3) = Poly[2](2/3), (2, 4) = Poly[2](1), (3, 1) = Poly[3](0), (3, 2) = Poly[3](1/3), (3, 3) = Poly[3](2/3), (3, 4) = Poly[3](1), (4, 1) = Poly[4](0), (4, 2) = Poly[4](1/3), (4, 3) = Poly[4](2/3), (4, 4) = Poly[4](1)})

and general form is like this

[[[Poly[1](0/(M-1)),Poly[1](1/(M-1)),Poly[1]((2)/(M-2)),...,Poly[1]((M-1)/(M-1))],[Poly[2](0/(M-1)),Poly[2]((1)/(M-1)),Poly[2]((2)/(M-1)),...,Poly[2]((M-1)/(M-1))],[Poly[3]((0)/(M-1)),Poly[3]((1)/(M-1)),Poly[3]((2)/(M-1)),...,Poly[3]((M-1)/(M-1))],[...,...,...,...,...],[Poly[M]((0)/(M-1)),Poly[M]((1)/(M-1)),Poly[M]((2)/(M-1)),...,Poly[M]((M-1)/(M-1))]]];

Another problem is I want to define a vector of M dimension using a function f(x)=sin(x) and two points a=1, b=2 like the following way,

Vec:=[[[a],[f((1)/(M-1))],[f((2)/(M-1))],[f((3)/(M-1))],[...],[f((M-1)/(M-1))],[b]]]
Please fix my problem. I'm waiting for your kind response.
Special request @acer @acer @Carl Love @Kitonum @Preben Alsholm

Dear Users!

Hope you would be fine with everything. I want the simpliest for of the following expression in two step:

diff(U(X, Y, Z, tau), tau)+U(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), X))+V(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Y))+W(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Z))+u[delta]*lambda[1]*(diff(U(X, Y, Z, tau), tau, tau))/L[delta]+u[delta]*lambda[1]*(diff(U(X, Y, Z, tau), tau))*(diff(U(X, Y, Z, tau), X))/L[delta]+u[delta]*lambda[1]*U(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), tau, X))/L[delta]+u[delta]*lambda[1]*(diff(V(X, Y, Z, tau), tau))*(diff(U(X, Y, Z, tau), Y))/L[delta]+u[delta]*lambda[1]*V(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), tau, Y))/L[delta]+u[delta]*lambda[1]*(diff(W(X, Y, Z, tau), tau))*(diff(U(X, Y, Z, tau), Z))/L[delta]+u[delta]*lambda[1]*W(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), tau, Z))/L[delta];
Step 1:
diff(U(X, Y, Z, tau), tau)+U(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), X))+V(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Y))+W(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Z))+u[delta]*lambda[1]*(diff(diff(U(X, Y, Z, tau), tau)+U(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), X))+V(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Y))+W(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Z)), tau))/L[delta];
Step 2: (final form I need)
(1+(u[delta] lambda[1])/(L[delta]) (&PartialD;)/(&PartialD;tau)) ((&PartialD;)/(&PartialD;tau) U(X,Y,Z,tau)+U(X,Y,Z,tau) ((&PartialD;)/(&PartialD;X) U(X,Y,Z,tau))+V(X,Y,Z,tau) ((&PartialD;)/(&PartialD;Y) U(X,Y,Z,tau))+W(X,Y,Z,tau) ((&PartialD;)/(&PartialD;Z) U(X,Y,Z,tau)));
I'm waiting for your response.
Special request:
@acer @Carl Love @Kitonum @Preben Alsholm

Hi

I would like to use  the Liebniz notation that someone from the technical support posted here
Writing Derivatives at a Point Using Leibniz Notation
to display a formula that is not just a partial derivative but a more complex expression invoking partial derivatives. 
Typically an expression like this one:

2*(Diff(f(mu__1, mu__2), mu__1))^2*lambda__1^2-(Diff(f(mu__1, mu__2), mu__1))^2*mu__1^2+2*(Diff(f(mu__1, mu__2), mu__2))^2*lambda__2^2-(Diff(f(mu__1, mu__2), mu__2))^2*mu__2^2+2*(Diff(f(mu__1, mu__2), mu__1))*(Diff(f(mu__1, mu__2), mu__2))*lambda__1*lambda__2-2*(Diff(f(mu__1, mu__2), mu__1))*mu__1*(Diff(f(mu__1, mu__2), mu__2))*mu__2

Could anyone help me to do this?
Thanks in advance

(PS: I'm still using Maple 2015.2)

Dear Users!

Hoped everything going fine with you. I want to make animation of ten solutions as given bellow but fail to do that. Please see it fix the problem. I shall be very thankful to u.
SOLNSuy[1, 1] := 2.5872902469406659197*10^(-20)-.65694549571241255901*y+1.9708364871372376767*y^2-1.3138909914248251176*y^3-1.6010739356637904911*10^(-19)*y^4;
SOLNSuy[2, 1] := -4.002204462000*10^(-20)-1.7879176897079605225*y+5.3637530691192141414*y^2-3.5758353794044226250*y^3-6.8309939211286845440*10^(-12)*y^4;
SOLNSuy[3, 1] := -1.1953264450000*10^(-19)-3.2481690589079594122*y+9.7445071767154794599*y^2-6.4963381177952273213*y^3-1.2292726248071398400*10^(-11)*y^4;
SOLNSuy[4, 1] := -2.6720465500000*10^(-19)-4.9239979672954025921*y+14.771993901873204315*y^2-9.8479959345587718955*y^3-1.9029826928878336000*10^(-11)*y^4;
SOLNSuy[5, 1] := 3.416928541000*10^(-20)-6.7268498492441931137*y+20.180549547714413714*y^2-13.453699698443639810*y^3-2.6580790570532587008*10^(-11)*y^4;
SOLNSuy[6, 1] := -2.554122292000*10^(-20)-8.5884528335125514887*y+25.765358500514014457*y^2-17.176905666966875698*y^3-3.4587270427710613504*10^(-11)*y^4;
SOLNSuy[7, 1] := -9.206107680000*10^(-20)-10.456823708331499352*y+31.370471124965259849*y^2-20.913647416590986491*y^3-4.2774005353527132160*10^(-11)*y^4;
SOLNSuy[8, 1] := 1.9644186790000*10^(-19)-12.293003938471349390*y+36.879011815379230436*y^2-24.586007876856948223*y^3-5.0932823222176363520*10^(-11)*y^4;
SOLNSuy[9, 1] := -3.775112769000*10^(-19)-14.068404975282556550*y+42.205214925807397100*y^2-28.136809950465931724*y^3-5.8908824448577377280*10^(-11)*y^4;
SOLNSuy[10, 1] := 1.146281780000*10^(-19)-15.762658869974768890*y+47.287976609878780960*y^2-31.525317739837422477*y^3-6.6589592851037286400*10^(-11)*y^4;
plots[animate](plot, [SOLNSuy[A, 1], y = 0 .. 1], A = 1 .. 10);

Special request:
@acer @Carl Love @Kitonum @Preben Alsholm

Here is a little animation to wish all of you a Merry Christmas

FireWorks.mw