MaplePrimes Questions

How do I get Maple to factorize this simple expression without too much effort?

f:=3/2 + sqrt(8*k + 2) + 2*k

I want to create a distribution table and then find expected value,variance and standard deviation.

For example : X=-1,P(X)=0.2


E(X) would then equal -1*0.2+0*0.25+1*0.35+2*0.2.

How can I do all of this with Maple ? 

How should linearization a nonlinear equation with maple?

I'm trying to use the ExpectedValue function to get the next close value of a stock.

restart; with(Finance)

W := WienerProcess()

T := 1.0

S := SamplePath(W(t), t = 0 .. T, timesteps = 100, replications = 10^4)

A := S[1 .. 10^4, 50]

TI := 1

AN := 100 (Start Value)

sigma := 3.5 (volatility)

r := 0.5e-1    (interest)

ANF := AN*exp((r-(1/2)*sigma^2)*TI+sigma*W(TI))       (ANF: is the forecasting Value)

ExpectedValue(ANF, timesteps = 100, replications = 10^3)

Is this approach right?

Why it be like that and how to solve it ?

> ODEtools[declare]((S, L, B)(t), prime = t);
         ODEtools[declare](S(t), L(t), B(t), prime = t)
> DE1 := diff(S(t), t) = -L*S*beta-`μS`+mu;
            DE1 := --- S(t) = -L S beta - μS + mu
> DE2 := diff(L(t), t) = L*S*beta-(gamma+mu)*S;
          DE2 := --- L(t) = beta S L - (gamma + mu) S
> DE3 := diff(B(t), t) = L*gamma-gamma*mu;
              DE3 := --- B(t) = L gamma - gamma mu
> init_conds := S(0) >= 0, L(0) >= 0, B(0) >= 0;
         init_conds := 0 <= S(0), 0 <= L(0), 0 <= B(0)
> sys := {init_conds, diff(B(t), t) = L*gamma-gamma*mu, diff(L(t), t) = L*S*beta-(gamma+mu)*S, diff(S(t), t) = -L*S*beta-`&mu;S`+mu};

> sol := dsolve(sys, numeric, parameters = [mu, beta, gamma, S(t), L(t), B(t)], method = rkf45);

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

> sol(parameters = [mu = .234, beta = 2.345, gamma = 5.678, S(t) = 6.678, L(t) = 6.789, B(t) = 7.123]);
           sol(parameters = [mu = 0.234, beta = 2.345, gamma = 5.678, S(t) = 6.678, L(t) = 6.789, B(t) = 7.123])

Is the following a bug? I am using Maple 2019  64 bit with latest Physics package 357 on windows 10.



pde :=  diff(w(x,y,z),x)+(y^2- a*exp(alpha*x)*(x*y-1))*diff(w(x,y,z),y)+(c*exp(beta*x)*z^2+b*exp(-beta*x))*diff(w(x,y,z),z)= 0;

diff(w(x, y, z), x)+(y^2-a*exp(alpha*x)*(x*y-1))*(diff(w(x, y, z), y))+(c*exp(beta*x)*z^2+b*exp(-beta*x))*(diff(w(x, y, z), z)) = 0

Error, (in depends) too many levels of recursion


pde :=  diff(w(x,y,z),x)+ (b*exp(alpha*x)*y^2 + a*exp(beta*x)*(beta- a*b*exp((alpha+beta)*x)))*diff(w(x,y,z),y)+(c*z^2*exp(gamma*x)+ d*z + k*exp(-gamma*x))*diff(w(x,y,z),z)= 0;

diff(w(x, y, z), x)+(b*exp(alpha*x)*y^2+a*exp(beta*x)*(beta-a*b*exp((alpha+beta)*x)))*(diff(w(x, y, z), y))+(c*z^2*exp(gamma*x)+d*z+k*exp(-gamma*x))*(diff(w(x, y, z), z)) = 0

Error, (in depends) too many levels of recursion


pde :=  x*diff(w(x,y,z),x)+ ( a1*exp(alpha*x)*y^2 + beta*y+ a1*b2^2*x^(2*beta)*exp(alpha*x))*diff(w(x,y,z),y)+(a2*x^(2*n)*z^2*exp(lamba*x)+(b2*x^n*exp(lambda*x) - n)*z + c*exp(lambda*x))*diff(w(x,y,z),z)= 0;

x*(diff(w(x, y, z), x))+(a1*exp(alpha*x)*y^2+beta*y+a1*b2^2*x^(2*beta)*exp(alpha*x))*(diff(w(x, y, z), y))+(a2*x^(2*n)*z^2*exp(lamba*x)+(b2*x^n*exp(lambda*x)-n)*z+c*exp(lambda*x))*(diff(w(x, y, z), z)) = 0

Error, (in depends) too many levels of recursion




I want to find following NxN matrix P                                           (N=2^k.M where k and M are a positive integers)  

My Code Try:

for i from 1 to M do
S:= (sqrt(2)/2^k)*Matrix(M,M, (i,j)-> `if`(`and`(i::odd,j=1) ,-1/(i*(i-2)),0)):   
end do:
C:= (1/2^k)*BandMatrix( [ [ seq(-1/(2*sqrt(2)*(i-1)*(i-3)), i=4..M)], [ 1, seq(0*i,i=1..M-1) ],[ seq(4/2*(i-3),i=2..M)]
              ); #I think the matrix C is not same in the question
end proc: 


Is there any way to make this kind of problem in Maple?

I have to find the intersection of subsets, and if there is no intersection then to multiply elements of the subsets. For example,

A={x6,x4,x2,x7,x8,x9,x10},  B={x2,x3,x5,x8} and C={x4,x9,x11,x12,x13}.

Now, the intersection of A and B is {x2}, after that, I don't have the intersection with C, so the solution is x2x4, x2x9, x2x11, x2x11 and x2x13.

Another solution is to make the intersection of A and C and it will be {x4,x9} and after that, I don't have the intersection with B so I have to multiply x4 and x9 with elements in B (obviously, the first solution is better because it has fewer terms)

Is something like this is possible to do in Maple and how?

Thanks in advance! 


I am using Maple to solve a couple of differential equations.  Here is what I did so far

k := 141/10000;
yB0 := 296/1000;
e := -148/1000;
Ff0 := 67844/1000;
Far0 := 323066/1000;
FB0 := 135688/1000;
P0 := 10;
x0 := 0;
a := 38/1000;
dsys:={diff(x(w),w)=(k*((yB0*p(w)*(1 - x(w)))/(1 + e*x(w)))^(1/3)*(Ff0/(Far0 + FB0)*p(w)*((Ff0/FB0 - 1/2*x(w))/(1 + e*x(w))))^(2/3))/FB0,
diff(p(w),w)=P0*(-a)/(2*p(w)/P0)*(1 + e*x(w)),x(0)=x0,p(0)=P0}:

Maple returns neither an error message or a solution.   I am sure I have mistyped something or did not understand how dsolve works at all.  

Can you help me out?

Many thanks


PS. How to plot the solution?  



On CBS tv show Survivor S38E4, an interesting scenario arose. There was initially 2 teams comprising 6 persons (blue team) and 9 persons (yellow team). Then they decided to mix it up, and split it into 3 teams. Each player was randomly assigned a buff, (red, green or orange =3 colored buffs *5).= 3 teams of 5.

What was interesting was 5 out of the original 6 blue team are now in the new red team. 5 of the original yellow team are in the new green team and 4 of the original yellow team are in the new orange team. 

What is the chances of that happening?
A couple of attempts:

How i can generate Pr matrix when P= -x and x0=-1 , x1=-2/3 , x2=-1/3 , and x3=0 with the help loop?

Hi everybody:

I have one equation:

EQ := V^3-R*T*V^2/P-(B^2+P*B*R*T*sqrt(T)/(P-A))*V-A*B/(P*sqrt(T)) = 0;
how can I obtain these derivatives:


I just noticed with chagrin that one of my favorite menu commands, Edit -> Remove output -> From worksheet, is missing from Maple 2019's Standard GUI. Is there a keyboard command or toolbar item to replace it?

How can I plot Y in terms of X (Y is the vertical axis and X is the horizontal axis) in below equation with Maple?

X^3-24.478115*X^2/Y-(0.2038793409e-2+19.08455282*Y/(Y-97.539))*X-.2550630228/Y = 0



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