#Most  dediction of  depth of field of optical lens  involves various simplification,  hence cannot be used  for  close up photography.  With Maple, it is easy to obtain  precise   Depth of field  formuar for optical lens  without  any simplification

> restart; h := H = F^2/(N*coc)+F; E0 := 1/d+1/D0 = 1/F; E1 := 1/(d+e)+1/D2 = 1/F; E2 := a/(d+e) = coc/delta; E3 := a = F/N; eq := {E0, E1, E2, E3, h}; var := {D2, N, coc, d, delta}; e := -delta; sol1 := solve(eq, var); t1 := op(sol1)[1]; Dfar := op(t1)[2]; e := delta; sol2 := solve(eq, var); t2 := op(sol2)[1]; Dnear := op(t2)[2];

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I have use a ''for cycle'' in order to get a series of points. I would like to save those points in a vector in order to use it for the ''PolynomialFit'' comand. The problem is that the points that I save are sort randomly. How can I take the value of the vector A in the right sequence? in the underline string you can plot the walue of A over t (which is not sorted). I can not use the sort command as I used for t even for A because the points are not increasing.

This is my code:

restart;

Atot := 0:

for ii from 0 by 0.01 to 2 do

PtotFkt := ii->  ii^2 :

Ptot := PtotFkt(ii):

Atot := Atot+0.01*Ptot:

A[ii] := Atot: #Save points in a Table

t[ii] := ii: #Save point in a table

end do;

AV := convert(A, list): #conversion from table to list
nops(AV);  #number of points

timme := convert(t, list): #conversion from table to list
nops(timme); #number of points

with(Statistics); #PolynomialFit

X := Vector(AV, datatype = float);

Y := Vector(sort(timme), datatype = float);

plot(Y, X, style = point, symbol = asterisk, color = blue);

regress := PolynomialFit(10, X, Y, time);

curve1 := plot(regress, time = 0 .. 2);

In Mathematica I've a function which allows me to send a mail. I use it when I run some long time computations and I want to get an information that they are finished, etc. Is there any way to do the same thing in maple?

Hi!I am running some grid computations and I found that I could speed up my computations if my nodes could share some partial results. It seems that Grid:-Send and Grid:-Receive is almost perfect. The problem is that Grid:-Receive blocks the computations where I cannot ensure that a message will ever be send. I've tried to run Grid:-Receive on a thread in an possible infinite loop but it still blocks.

Some pieces of code below:

SignatureReciever:=proc(SigContainer::uneval,stopValue::uneval)
  while eval(stopValue) do
    SigContainer := eval(SigContainer) union {convert(Grid:-Receive(),string)};
  end do;
end proc:

SendMessage:=proc(message::string, id::integer)
  Threads[Seq](proc(i) if i <> id then Grid:-Send(i,message) end if end proc,i=0..Grid:-NumNodes()-1);
end proc:

In the main procedure run on a node I have

Threads:-Create(SignatureReciever('Signatures','stopValue'));

....

....

SendMessage(signature,id);

....

....

stopValue := false;

Do you have any suggestions how to solve my problem?

in this code count.mw the error is about the dsolve between do and end do  but the dsolve actually works and can give me the value I want if there is no cycle outside like this count......mw , there is no big difference between two code about the dsolve funtion except the one in cycle is writen together not in several lines, why it happens and how to fix it?

Hello dears! Hope everything going fine with you. I have faced problem while solving the system of equations using fsolve command please find the attacment and fixed my problem.

I am very thankful to you for this favour. 

VPM_Help.mw

Mob #: 0086-13001903838

can we solve analytically a system of non-linear algebraic equation? my system is like:

b1 = a x + b y + c z

b2 = d x² + e y² + f z²

b3 = g x³ + h y³ + k z³

thanks

I am trying to use Compiler:-Compile with a generated function having a Vector as an argument. My function is (in a simplified form)

Mapt:=proc (pv) options operator, arrow; rtable(1 .. 6, {1 = .998026692438229*pv[1]-.605526643146912*pv[2]+0.154549004943741e-1*pv[6]+0.140818440886566e-5*pv[5], 2 = 0.651134546344795e-2*pv[1]+.998026692438228*pv[2]-0.510903331894809e-1*pv[6]+0.229399145141077e-8*pv[5], 3 = -.500000000000002*pv[3]-5.95856898901206*pv[4], 4 = .125869147673385*pv[3]-.499999999999996*pv[4], 5 = 0.510903331894806e-1*pv[1]-0.154549004943901e-1*pv[2]-40.6778361021594*pv[6]+.999998210424947*pv[5], 6 = .999998210424947*pv[6]-0.229399145141220e-8*pv[1]-0.140818440886565e-5*pv[2]+0.897571581395136e-7*pv[5]}, datatype = anything, subtype = Vector[column], storage = rectangular, order = Fortran_order) end proc;

Since this returns a Vector it cannot be compiled as is. So I split off the first output element (with the idea to later on do this with the others as well):

xpr:=eval(Mapt(<pv[1],pv[2],pv[3],pv[4],pv[5],pv[6]>))[1];
f1:=unapply(xpr,pv);
f1(<0.001,0.001,0,0,0,0>); # test f1: works
          0.000392500049291317

sf1:=Compiler:-Compile(f1); # this works, too

sf1(<0.001,0.001,0,0,0,0>); # but this fails
Error, (in sf1) invalid input: expecting a hardware float[8] rtable, but received 1


The examples in the Helpfile run so I think my installation is ok (my old Maple 15 won't even run the examples, but that is a different story). I have been banging my head against the wall here, trying many different ways, but none of them successfull. Worse, I do not understand the error message at all. Test program attached.

Mac OS X 10.10.5

Thanks for any hint,

M.D.

Compiler.mw

I tried to make a procedure that would find the determinant of any 3x3 matrix but I keep getting unterminated procedure what should I change??

Code:
DeterminantMat:=proc(matA::Array)
    local  i::integer,  j::integer,  x::integer,  y::integer,  A::integer,  B::integer,  indice::integer,  S::integer:
      A:=0:  B:=0:  S:=0: i:= 1:  j:=1:  x:=1:  y := 1:  indice:=1:

for x from 1 to 3 do
   indice := 1:  
   for i  from 1 to  3 do  
       if x = i then
           end do:
        else if x <>i then
           for j from 1 to 3 do
                  if y = j then  end do:  
                  else if indice = 1 then  A := matA(i,j):  indice := 2:  
                     else if indice = 2 then  B:=matA(i,j):  indice :=3:    
                       else if indice = 3 then  B :=B * matA(i,j):  indice :=4:    
                         else if indice = 4 then  A := A * matA(i,j):      
                             if x = 2 then  S := S + (-1 * matA(x,y)) * (A-B):
                               else  S := S + matA(x,y) * (A-B):   end if:   end if:
 end do:
 end if:
 end do:
 end do:
 end proc:

hi.i encounter with another error for solving couple equations.

bcs := {f1(0) = 0, f1(L) = 0, f2(0) = 0, f2(L) = 0, f3(0) = 0, f3(L) = 0, ((D@@1)(f2))(0) = 0, ((D@@1)(f2))(L) = 0, ((D@@1)(f3))(0) = 0, ((D@@1)(f3))(L) = 0}; sys := subs(omega^2 = omega2, {PDE[111], PDE[222], PDE[333]}); sys2 := PDEtools:-dchange({x = L*y, f1(x) = g1(y), f2(x) = g2(y), f3(x) = g3(y)}, sys, [g1, g2, g3, y]); indets(sys2, specfunc(diff)); solve(sys2, {diff(g3(y), `$`(y, 4)), diff(g1(y), y, y, y), diff(g2(y), y, y, y, y)}); sys3 := subs(omega2 = 10^19*omega3, sys2); bcs3 := {g1(0) = 0, g1(1) = 0, g2(0) = 0, g2(1) = 0, g3(0) = 0, g3(1) = 0, ((D@@1)(g2))(0) = 0, ((D@@1)(g2))(1) = 0, ((D@@1)(g3))(0) = 0, ((D@@1)(g3))(1) = 0}; extra_bcs := `minus`({seq(seq(((D@@i)(g1))(a), i = 0 .. 1), a = 0 .. 1), seq(seq(((D@@i)(g2))(a), i = 0 .. 1), a = 0 .. 1), seq(seq(((D@@i)(g3))(a), i = 0 .. 3), a = 0 .. 1)}, `~`[lhs](bcs3)); dsys4 := {bcs3, sys3}; ds := dsys4[1]; indets(dsys4[1], specfunc(diff)); solve(dsys4[1], {diff(g3(y), `$`(y, 4)), diff(g1(y), y, y, y), diff(g2(y), y, y, y, y)}); newsys := {ds[2], ds[3], diff(ds[1], y)}; indets(newsys, specfunc(diff)); S := solve(newsys, {diff(g1(y), `$`(y, 3)), diff(g2(y), `$`(y, 4)), diff(g3(y), `$`(y, 4))}); nops(%); bcs2 := eval[recurse](convert(ds[1], D), `union`({y = 0}, bcs3)); nops(`union`(bcs3, {bcs2}));

Error, (in simpl/eval) numeric exception: division by zero

division_by_zero.mw

please help.thanks..

hi.how i can allocate infinite value for a parameter such as N ,which is attached below ( N := infinite) .i encounter with error.please see it and help

thanks..

infinite.mw

Hi!

For some reason my three equation with three unknowns won't be solved. Anyone who can help? I tried the following:

Really appreciate anyone who can help me out!

I an experimenting with Groebner basis. Have a set 17 equations. There are 12 unknowns. Using 14 of the equations and tdeg, the system produced 65 equations. How do I get a list of the monomials in this new list?

how to do optimization for two equations in terms of two variables

LPSolve({eq1}, {eq2}, assume = {nonnegative});

eq1 is a rational function and eq2 is a very large rational function

after run , it return error, objective function must be specified as a linear polynomial or vector

da := [LengthSplit(Flatten([[1,m],[2,m2],[seq([i+1,close3[i][1]], i=2..4)]]),2)];
f := PolynomialInterpolation(da, z):
solution := solve(f=-z, z, explicit);
zz := [x1,x2,x3,x4];
sigma := symMonomial(zz); #sigma := [x1+x2+x3+x4, x1*x2+x1*x3+x1*x4+x2*x3+x2*x4+x3*x4, x1*x2*x3+x1*x2*x4+x1*x3*x4+x2*x3*x4, x1*x2*x3*x4]
sys1 := subs([x1=solution[1],x2=solution[2],x3=solution[3],x4=solution[4]], sigma[1]):
sys2 := subs([x1=solution[1],x2=solution[2],x3=solution[3],x4=solution[4]], sigma[2]):
sys3 := subs([x1=solution[1],x2=solution[2],x3=solution[3],x4=solution[4]], sigma[3]):
sys4 := subs([x1=solution[1],x2=solution[2],x3=solution[3],x4=solution[4]], sigma[4]):
da := [seq([i,close3[i][1]], i=1..5)];

with(Optimization):
LPSolve(sys1, {sys2}, assume = {nonnegative});

Hi all,

I would like to plot a function U(x,t) in an interval [-2,0] such that

U(x,t)=u0(z)+t*u1(z) where  z=x/t,

u0(z)=z^2/3+sqrt(-z) and

diff(u1(z), z)=9/4*(84*(-z)^(11/2)-8*z^7+540*(-z)^(5/2)+324*z^4-324*z)*u1(z)/((z^2+3*sqrt(-z))*(2*(-z)^(3/2)+3)*(8*z^6+66*(-z)^(9/2)-189*z^3+216*(-z)^(3/2)+81))

I used numeric method rkf45 to solve and plot u1(z) with initial condition u1(-2)=1.

I can also use dchange to change variable z to x as variable and t as parameter.

But, I have difficullty to go back to U(x,t).

If someone have any idea.

Thanks in advance.