Hey guys,

I have to solve a bunch of systems of polynomial equations und dome restrictions given by inequalitites. I have 8 variables, 8 equations and and 13 inequalitites. Since the simple solve or SemiAlgebraic command are not able to solve every system I tryd some other ways. Right now I try to bring the set of equations and ineqaulities in a better from or structure using RealTriangulize from the RegularChains library. Later on I want to take those results and use solve or SemiAlgebraic again, hoping, that Maple than finds the solutions and is not calculating for houres without a result. I already know, that you can have diffrent outputs for RealTriangularize (I know list, record, piecewise and zerodimensional, althought the last one is not really helpful). Since I want to go on wirking with the results I need to have them in a form, that I can read of the new equations and inequalities to put them into solve. Often that works totaly fine, but sometimes I get an output I dont understand. I understand what It means but I dont understand why Maple uses that type of output. If you have a look in the attached file you can see what I mean:

I would like to get results like in dec_5334. I can easily go on working with this kind of form. In dec_5380 you can see a diffrent output. I dont see the point of giving me this output. the second line i basically epmty. and in the first line the solution is broken into peaces. when a certain solution just works under some inequalitites, why dont they put those four inequalities inside of the list in front of it? Is there a workaround for the "normal" output? Or is there a way to read off the lines from this kind of structure, with the open { in front ?

The same problem appears in dec_5382. WHy dont give me a list with to lists of equations and inequalities to show me both solutions?
In the last example dec_5382_record you can see the output when you change the corresponding option in RealTrinagularize. But here I again have the problem that I dont know how to read of the equations and inequalities from the open curly bracket.

If anyone could help me, I would be very glad. Thank yu in advance.

Regards

Felix

Download Output_of_RegularChains.mw

Does any one have any idea to demonstrate, using Maple, that for any couple (a, b) of strictly positive integers

(a*b)! / (a! * (b!)^a) 

is an integer?

Hi

Can someone improve my AI code so I get to the final team's config directly, rather than a series of set iterations? thanks 

teams.mw

set 1: Michael K, Andy C
set 2: Michael G, Mitch
set 3: Jez, Dean B
set 4: Anthony B, Rik B
set 5: Ilya, Fariborz
set 6: Eugene, Tania
set 7: Bill, Stevs
set 8: Victor, Jane
set 9: Nash, Ben
 

Why doesnt this example work in my Maple 2021.1 from the user manual?

restart;
L := [seq(i, i = 2 .. 1000)];
divisor := 2;
while (numelems(L) > 0)  do  divisable,  L:=selectremove(i->(i mod divisor=0), L):
Error, unterminated loop

n:=numelems(divisable);  

if (n>0) then  printf("%d integers%s whose smallest prime divisor is %d\\n",n,  'if'(n>1, "s", ""), divisor):  end if;  

divisor :=nextprime(divisor);  

end do:
Error, unable to parse
 

Is there a way to put in intervals and get the output as inequality Notation? Something like this ->

I have a system of 4 nonlinear equations in 4 lambda variables. I cannot obtain a solution using solve():

4_nonlinear_equations.mw

I can sometimes simplify similar systems by rescaling equations to reduce parameters. With only 3 parameters (sigma_v, sigma_d, sigma_d3) in this case, complexity arises from the interactions of the 4 lambdas in the 4 equations. Upon examining the equations (highlighted in yellow), I suspect hidden symmetries. Is it possible to solve the system by rewriting the equations in terms of each other to find an equivalent system? I am exploring if a smarter and simpler reformulation could lead to a solution. Thank you.

I am very frustrated with the geometry package.
I wanted to draw a circle thru 3 points and so I opened the geometry package help pages.
> restart;
> with(geometry);
> with(plots);

Here is the example given there
> circle(c1, [point(A, 0, 0), point(B, 2, 0), point(C, 1, 2)], 'centername' = O1)

As you can see the command uses the point command from the geometry package which is

> point(C, 1, 2)

Maple consistently uses := as the assignment operator. Not with this command. One would expect the syntax to be

>C:=point([-1. 2]);

or some such but no, that is not how it works.Notice that I am not alone in my opinion about this being a violation of standard Maple syntax; the Maple parser AGREES with me

> type(point(C,1,-3),point);
                             false

Perhaps I am just being grouchy but pointplot works fine with
> pointplot([[1, 3],[1.7, 2],[-1, 7]])

But
> pointplot([P1,P2,P3]);
Error, (in plots:-pointplot) number of elements in list must be a multiple of 2

Oh well, let’s see what we get with our circle construction
>display(c1);

Error, (in plots:-display) expecting plot structure but received: c1

Bad guess on my part.

> radius (c1)
yields the correct number and
> center(c1)
yields the name of the circle but
>coordinates(center_c1);
yields what I want. Peculiar but OK , let's go on.
I can write the equation of the circle now that I have the center and radius but hopefully I try

>  equation(c1); and get an error message!!!

The commands center, radius work but equation does not! Here is what works
> Equation(c1)

If one really wants to CONFUSE the user why not eQuaTiOn? Who would guess that? (Sorry to be sarcastic but …) At least with the equation and implicit plot one can finally get a plot of the circle. Is that CLUMSY?

sometimes I need to check if an ode is missing y(x) or not. Since diff(y(x),x) has y(x) in it, then can not just check if the ode has y(x) or not as is, as this will always gives true if diffy(y(x),x) is there of any order.

Currently what I do, is change all y',y'',y''', etc... to Z,Z^2,Z^3,etc... and then after that it is safe to check if y(x) exist or not.

Is there a better way to do this? Below is what I currently do and it works. Just wondering if there could a more elgent way to do this.

Download find_if_any_ode_has_yx_jan_6_2025.mw

I can do that for a cylinder (in green below) but not for a box geometry.

Box_geometry_and_pendulum.msim

intersections := proc(P, Q, T)
local R, W, w, t, a, b, sol, buff, v;
sol := []; if T = Y then W := X; else W := Y; end if;
R := resultant(P, Q, T);
print(`Résultant :`);
print(R);
w := fsolve(R, W); t := [];
for v in [w] do t := [op(t), fsolve(subs(W = v, P), T)]; end do;
for a in [w] do for b in [t] do if T = Y then buff := abs(subs(X = a, Y = b, P)) + abs(subs(X = a, Y = b, Q));
printf(`X=%a,   Y=%a   --->  %a\\n`, a, b, buff); if buff < 1/100000000 then sol := [op(sol), [a, b]]; end if;
else buff := abs(subs(X = b, Y = a, P)) + abs(subs(X = b, Y = a, Q));
printf(`X=%a,   Y=%a   --->  %a\\n`, b, a, buff); if buff < 1/100000000 then sol := [op(sol), [b, a]];
end if; end if; end do; end do;
printf(`Nombre de solutions :  %a\\n`, nops(sol)); print(sol); end proc;
Try with :
intersections(X^2 + Y^2 - 1, X - Y, X); Would you like to develop this procedure which does not give the number of solutions ?Thank you.

i want to factoring the (m+G'/G) in my long equation but i use some trick but still i can't get the exactly system and still G will remain in my system what should i factoring for remove this G(xi) from my system is all about factoring , my system of equation are wrong contain G(xi) How i can remove it by taking a factoring or any other technique,

not parameter is arbitrary except V and sigma''

Download G-factoring.mw

I see this question
https://mathematica.stackexchange.com/questions/309952/how-to-choose-6-numbers-from-the-following-set-so-that-they-represent-the-length
and tried

primes := [seq(ithprime(i), i = 1 .. 20)];
with(combinat);
all_combinations := choose(primes, 6);

I can not make next part.

I’m trying to solve a stiff system 1-D PDEs numerically in Maple but I’m getting the following error:

“Error, (in pdsolve/numeric/match_PDEs_BCs) cannot handle systems with multiple PDE describing the time dependence of the same dependent variable, or having no time dependence”

I included a picture of the PDEs and their BCs in the attached maple file. For easy reading, the attached file includes highlighted sections for parameters and variables. You can skip those to PDEs, BCs and ICs sections at the end of the document to reach the error I’m facing.

For reference, I used another software to solve the system and I was able to get the results in few seconds, so I think it is solvable. However, personally I prefer to use Maple so any inputs, insights, workarounds that I could use to handle the system in Maple would be of great help to me. Thank you.

question.mw