## fsolve give me no awenser ( a blank )...

i have 4 equation and 4 variables with DirectSearch package it will give me a solution but not in a good time
when i try fsolve it just give me a blank
these are my equations :
POL[0] := .42810/(.65429+c[-2])

POL[1] := -8.4078*c[-1]-162.64*c[0]+84.228*c[1]-6/(.80888+c[-2])^2+9.7066/(.80888+c[-2])^3-3.9257/(.80888+c[-2])^4+(1/2*(.42786*c[-1]+.42786*c[0]+.42786*c[1]+.65429/(.80888+c[-2])))*(-49.180*c[-1]+31.921*c[0]-8.6921*c[1]+2/(.80888+c[-2])-3.2355/(.80888+c[-2])^2+1.3086/(.80888+c[-2])^3)

POL[2] := 53.965*c[-1]+43.012*c[0]-103.98*c[1]-6/(1.+c[-2])^2+12./(1.+c[-2])^3-6./(1.+c[-2])^4+(1/2*(.50000*c[-1]+.50000*c[0]+.50000*c[1]+1./(1.+c[-2])))*(22.229*c[-1]-37.815*c[0]+22.229*c[1]+2/(1.+c[-2])-4./(1.+c[-2])^2+2./(1.+c[-2])^3)

POL[3] := -30.115*c[-1]+43.264*c[0]+52.171*c[1]-6/(1.2363+c[-2])^2+14.836/(1.2363+c[-2])^3-9.1704/(1.2363+c[-2])^4+(1/2*(.52893*c[-1]+.52893*c[0]+.52893*c[1]+1.5284/(1.2363+c[-2])))*(-4.5997*c[-1]+16.892*c[0]-26.026*c[1]+2/(1.2363+c[-2])-4.9452/(1.2363+c[-2])^2+3.0568/(1.2363+c[-2])^3)

i even change digits to 100 but still no awenser

my fsolve syntax

K := fsolve({seq(POL[v], v = 0 .. 2*N+2)})

the awenser fsolve gave me

K:=

thats all it gave me

## issue with fsolve and Directsearch command in mapl...

Hi,

I have three simultaneous equations  with three unknown variables (E, W, T). When I solve these  simultaneous equations with fsolve command without specifying any range for variables, I don't get desirable root ( equation sol4 in maple worksheet- {E = 0.1007672475e-2, T = .7969434549, W = 0.1937272759e-2}). For this problem, I know the correct root {E = 2843.916504, T = .2782913990, W = 5344.844134} beforehand which maximize the objective function TP (equation sol8 in maple worksheet) and when I specify the narrow range of variables around the already known correct root in the fsolve command, then I get correct root ( equation sol5 in maple worksheet). If I don't know the actual answer (correct roots of the simultaneous equation) beforehand, How  could I get the correct root with fsolve command because it is very tedious work to specify different range in fsolve command repetitively to solve it by trial and error.

I also tried Direct Search method as suggested in this forum  but DirectSearch is also not able to provide the correct root (equation sol6 in maple worksheet). If I specify the narrow range around known root in direct search method ( equation sol6a in maple worksheet), then it would provide close to optimal root but if I don't know the correct root beforehand, then I couldn't specify the narrow range of variables, then how can I get correct root through direct search command.

Equation sol10 in maple worksheet  (objective function value at correct root) confirms that {E = 2843.916504, T = .2782913990, W = 5344.844134} is the correct root because it provide the value of objective function (TP) equal to 78285.85621 as opposed to negative value (TP value -12.53348074 in equation sol9)  produced by incorrect root  {E = 0.1007672475e-2, T = .7969434549, W = 0.1937272759e-2}).

Is there any method which would provide all the roots of these simultaneous equations which also include correct root. Maple worksheet is attached.

I am trying fsolve and direct search method with known root so that I could get the proper procedure to get the correct root which I can apply to another problem (set of similar simultaneous equations) for which I don't know correct root beforehand.

## Nonlinear fit of difficult function...

I have a data point set:

```x_val:=<250,300,350,397,451,497,547,593,647,691,745,788,840,897>:
y_val:=<0,0.5,2,6.3,23.2,48.7,71.2,83.4,90.1,92.8,94.7,95.7,96.9,97.8>:```

I want to make a least square fit using this difficult function:

`function:=x->1-exp(-(k*exp(-(E/(8.314*873.15))*((873.15/x)-1)))*(0.026/350))`

but both Statistics[Fit]:

```with(Statistics):fit_nelog:=Fit(1-exp(-(k*exp(-(E/(8.314*873.15))*((873.15/x)-1)))*(0.026/350)),<x_val|y_val>,x,parameternames=[k,E],output=[parametervector,residualsumofsquares]);
```

and DirectSearch[DataFit]:

`with(DirectSearch):fit_nelog2:=DataFit(1-exp(-(k*exp(-(E/(8.314*873.15))*((873.15/x)-1)))*(0.026/350)),x_val,y_val,x,method=cdos);`

give wrong k,E parameters. The correct parameter values were obtained with Excel Solver:

```k=27843.3551042397

E=68.4```

The approximately correct parameters were fitted when using logarithm form of the function.
How can I obtain correct parameter values in Maple using given form of the function?

## Where is "lib" folder in Maple on OS X?...

Maple tech support sent me a third party application for my Maple 2016 to solve a problem that I'm working on. I was instructed to copy and paste a few items from the download: "to your "<maple>/lib" folder" Unfortunately I cannot access "lib" in my Maple "Applications" folder on my OS X MacBook Pro.

This is what Maple Tech Support sent me:

"Another option you may want to look into is the "DirectSearch" package (which is third-party, and not supported by us), which would need to be downloaded from the Maplesoft Application Centre:

There is a function "GlobalOptima()", which allows one to search for a global minimum to the objective function, as opposed to a local minimum like commands such as "LSSolve()". To install, you can extract the files "DirectSearch.mla", "DirectSearch.help", and "DirectSearch.hdb" to your "<maple>/lib" folder."

Any suggestions?

## Inequality proved with Maple

Maple

How to prove the inequality  provided , ? That problem was posed  by Israeli mathematician nicked by himself as arqady in Russian math forum and was not answered there.I know how to prove that with Maple and don't know how to prove that without Maple. Neither  nor  work here. The difficulty consists in the nonlinearity both the target function and the main constraint. The first step is to linearize the main constraint and the second step is to reduce the number of variables to one.

restart; A := eval(x^(4*y)+y^(4*x), [x = sqrt(u), y = sqrt(v)]);

 (1)

B := expand(A);

 (2)

C := eval(B, u = 2-v);

 (3)

It is more or less clear that the plot of F is symmetric wrt  the straight line v=1. This motivates the following change of variable  to obtain an even function.

F := simplify(expand(eval(C, v = z+1)), symbolic, power);

 (4)

The plots suggest the only maximim of F at z=0 and its concavity.

Student[Calculus1]:-FunctionPlot(F, z = -1 .. 1);

Student[Calculus1]:-FunctionPlot(diff(F, z, z), z = -1 .. 1);

As usually, numeric global solvers cannot prove certain inequalities. However, the GlobalSearch command of the DirectSearch package indicates the only local maximum of  F and F''.

Digits := 25; DirectSearch:-GlobalSearch(F, {z = -1 .. 1}, maximize, solutions = 3, tolerances = 10^(-15)); DirectSearch:-GlobalSearch(diff(F, z, z), {z = -1 .. 1}, maximize, solutions = 3, tolerances = 10^(-15));

 (5)

The series command confirms a local maximum of F at z=0.

series(F, z, 6);

 (6)

The extrema command indicates only the value of F at a critical point, not outputting its position.

extrema(F, z); extrema(F, z, 's');

 (7)

solve(F = 2);

 (8)

DirectSearch:-SolveEquations(F = 2, {z = -1 .. 1}, AllSolutions, solutions = 3);

 (9)

DirectSearch:-SolveEquations(F = 2, {z = -1 .. 1}, AllSolutions, solutions = 3, assume = integer);

 (10)

PS. I see my proof needs an additional explanation. The DirectSearch command establishes the only both local and global  maximum of F is located at z= -1.98*10^(-13) up to default error 10^(-9). After that  the series command confirms a local maximum at z=0. Combining these, one draws the conclusion that the global maximum is placed exactly at z=0 and equals 2. In order to confirm that the only real root of F=2 at z=0  is found approximately and exactly by the DirectSearch.

## Minimum of maximum of parametric polynomial...

Let us consider the maximum value of the polynomial

x^4+c*x^2+x^3+d*x-c-1

on the interval x=-1..1 as a function g of the parameters c and d. General considerations suggest its continuity. However, a plot3d of g does not  confirm it.  Also the question arises "Is the function g(c,d) bounded from below?". Here is my try with the DirectSearch and NLPSolve:

 (1)

 (2)

DirectSearch:-GlobalOptima( (a, b) -> g(a, b), variables = [a, b])

## Problem with help to DirectSearch...

Executing HelpTools:-Database:-ConvertAll(): produced file DirectSearch.help apparently without content. How can all content within DirectSearch.hdb be converted to a .help file accessible through help in Maple 2016?

## DirectSearch Help migration into M2015...

So I installed copied DirectSearch.hdp and DirectSearch.mla into my Maple2015\lib directory and the program works (all the functions are there) but I cant get help menu by querying ?DirectSearch.

I'm running win7 64bit btw

so under

?hdb

i put this into maple:

HelpTools:-Database:-ConvertAll();

but i get error....

"Converting C:\\Program Files\\Maple 2015\\lib\\DirectSearch.hdb to C:\\Program Files\\Maple 2015\\lib\\DirectSearch.help"
Warning, .hdb help databases are deprecated, 'C:\Program Files\Maple 2015\lib\DirectSearch.hdb' will not be used, see ?HelpTools,Migrate help page for more information
Error, (in HelpTools:-HelpCallUI) cannot create help database: 'unable to open database file'

any clue?

ps I asked the same question for M18 but I managed to get the help to work in that instance.

http://www.mapleprimes.com/questions/204423-Help-Build-For-GlobalSearch-Package

(i also copied DirectSearch.hdp and DirectSearch.mla to Maple2015\bin.X86_64_WINDOWS directory but no joy, there is no .help file created in either bin or lib directories)

by: Maple

@Markiyan Hirnyk   I try not to use this package, as I think the results are not reliable enough. Here is the example, where instead of the three real roots it finds only one, despite the hint to look for the three roots:

restart;

DirectSearch:-SolveEquations(100^x=x^100, AllSolutions, solutions=3);

There are many other examples, particularly in discrete optimization in which it returns false results. Here is one example (well-known to you).

## why SolveEquations show diffrent solutions...

eq:=[2*x-0.2e-1*y-2.04*sqrt(-v^2+1)*v, 2*y-0.2e-1*x-2.16*sqrt(-u^2+1)*u, 2*u+2.16*u^2*y/sqrt(-u^2+1)-2.16*sqrt(-u^2+1)*y, 2*v+2.04*v^2*x/sqrt(-v^2+1)-2.04*sqrt(-v^2+1)*x] ;

i do as follows using DirectSearch package v.2

i find the solutions not the same,some time the results not much difference,but another,sols1 have one solution,sols2 have three solutions.in some time,some solutions are lost，the result show  me  random.may i have run the command serveral times? regards.

## prevent rounding numbers in DirectSearch....

hello

I have a system of equation. to solve i using DirectSearch pakage. i think in answer DirectSearch use rounding number but in answer it's second and third digit after the decimal point is important. please help me. bbw.mw

if b and c increase 0.01 and -0.01 it's ok. another main question is why by increasing the intensity answer don't change.

## DirectSearch does not work....

hi

i want to use Direct Search Package for solve system of equation but i have an error:

Error, SolveEquations is not a command in the DirectSearch package.

## Why doesn't it output?...

I solve the problem on computational geometry: "A cube of side one contains two cubes of sides a and b having non-overlapping interiors. How to prove the inequality a+b≤1?" To this end I use the DirectSearch package , namely,

Here are some comments to it. The cube of side a is centered at (x_1,y_1,z_1) and rotated by the angles phi_1, psi_1, theta_1 (see http://uk.wikipedia.org/wiki/%D0%95%D0%B9%D0%BB%D0%B5%D1%80%D0%BE%D0%B2%D1%96_%D0%BA%D1%83%D1%82%D0%B8 ) and the cube of side b is centered at (x_2,y_2,z_2) and rotated by the angles phi_2, psi_2, theta_2. The procedure

calculates the distance between these cubes, for example,

st := time(); dist(.2, .9, .2, .2, .2, .7, .7, .7, 0, 0, 0, 0, 0, 0); time()-st;

[HFloat(5.453016092898238e-11), [s1 = HFloat(0.2646161775314957),

s2 = HFloat(0.2828503247068887),

s3 = HFloat(0.29444713116943216),

t1 = HFloat(0.2646161774916062),

t2 = HFloat(0.28285032471998384),

t3 = HFloat(0.2944471311346344)], 2527]
191.133
Unfortunately, my code (which is syntactically correct) is spinning on my wondercomp during 10 hours without any output. I don't understand it at all. Your advices are welcome.

twocubes.mw

## How can I find the greatest value of this expressi...

I want to find the greatest value of this expression

f:=(x,y,z)->sqrt((x+1)*(y^2+2)*(z^3+3))+sqrt((y+1)*(z^2+2)*(x^3+3))+sqrt((z+1)*(x^2+2)*(y^3+3));

with x>0, y>0 , z>0,x+y+z=3.

I tried

restart:

f:=(x,y,z)->sqrt((x+1)*(y^2+2)*(z^3+3))+sqrt((y+1)*(z^2+2)*(x^3+3))+sqrt((z+1)*(x^2+2)*(y^3+3));

DirectSearch[GlobalOptima](f(x,y,z), {x>0, y>0 , z>0,x+y+z=3},maximize);

I got the output

[HFloat(infinity), [x = .591166078050740e52, y = .183647204560715e52, z = .786638021216969e52], 1249]