Good day! 

I have been wrestling with what appears to be a simple problem, but with no success and so, I thought I would reach out for support. 

Consider a two-dimensional strip of any given width, x, and depth, y.

I wish to maximize the quantity of strips that can fit inside a larger two-dimensional surface of any given width, X, and depth, Y. Overhanging is not permitted and all smaller strips must lie within the interior of the larger surface. 

I'm looking for a solution method that can calculate the best configuration necessary to fit the maximum number of smaller strips in the interior of the larger rectangle. Can someone suggest a way (if possible) to solve for this?

Thanks for reading.

diff(f(x), x) = a-a/((1+a*x)*(1/(1+a*x))^a)-a*f(x) where a is a constant and an initial condition f(0)= b is known Thank you.

Hello,

How do I isolate the variable ng in the following expression:

rho := `ρg`*ng + `ρp`*np + `ρw`*nw;
B := np/Kp + nw/Kw + ng/Kg;

C := (B/rho)^(1/2);

As you can see, I am running the isolate command, but it is not including the variable C, or it returns the wrong result.

isolate(((np/Kp + nw/Kw + ng/Kg)/(`ρg`*ng + `ρp`*np + `ρw`*nw))^(1/2), ng);
                               ( Kp nw + Kw np) Kg
                   ng = -     -----------------

                                          Kw Kp       

isolate(C=((np/Kp + nw/Kw + ng/Kg)/(`ρg`*ng + `ρp`*np + `ρw`*nw))^(1/2), ng);
                             0 = 0

Thanks.                

I think some form of simplify() would do but I am not sure how.

See the following script for more details:

Download rearrangingterms.mw

It must be something similar to this https://www.mapleprimes.com/maplesoftblog/201455-Rearranging-The-expression-Of-Equations, but my case is slighty different.

In certain tasks, I need to find all accurate positive (not just nonnegative) roots that exist of some multivariate polynomials like: 

nsd := 16*a*b*c*(9 + a^2 + b^2 + c^2)*(b*c + a*(b + c) + 3*(a + b + c)) - (3 + a + b + c)^2*(a*b + 3*c)*(3*b + a*c)*(3*a + b*c): # assume((a, b, c) >~ 0);

According to fsolve/details, for one general equation, the fsolve command only computes "a single real root", so it is inadequate to tackle this question. But if I use the solve command with floating-point values, the computation cannot finish in ten minutes instead! (Maybe a longer time will suffice, yet this is rather unacceptable.) 

Download solve_numerically.mws

Is there any workaround to obtain those (finitely many) positive solutions completely?

Dear all:

    I am using maple2022 to learn Fourier Series package - Maple Application Center (maplesoft.com) . the author provide the package here:

cgi.math.muni.cz/kriz/xsrot/fourierseries/  I use the lastest version: Package FourierTrigSeries version 0.41 

there is no .mla so I do not know how to use this package.(the package is a little old). 

please enlight me if you know how to install this old package.

but the author provide the code inside fourierseries-structs.mws 

here is what I do:

1. first delete some lines which is not useful(which I shared in the attachment as FourierTrigSeries.mw)

and remain everything inside module and save as .mw (maybe the orginal .mws is a old version of maple files)

2. export as .FourierTrigSeries.mpl (also attached)

3. use the examples.mws (the code also from author)

I got error as:

the package can be recognized, but the first line wil give some error which is out of my knowledge field.

everything mentioned above is here, including the original author's files.

fouriertrigseries_0_41en_mapleprime.zip

Could you please have a look. your idea is valuable to me.

PS: this package is not available The Fourier Series package for Maple - Maple Application Center (maplesoft.com) whenI try to learn  Teaching Fourier Series with Maple II 

if anyone keep it before, please share it.

thanks for your help.

rockyicer 

restart;  
with(geometry):  
with(plots):  
_EnvHorizontalName = 'x':  _EnvVerticalName = 'y':
point(A, -1, 9):                                                                                                       
point(B, -5, 0):
point(C, 6, 0):
triangle(ABC,[A,B,C]):
midpoint(M1,A,C): midpoint(M2,B,C):midpoint(M3,A,B):
rotation(J, C, Pi/2, 'counterclockwise', M1):triangle(AJC,[A,J,C]):
rotation(Ii, C, Pi/2, 'counterclockwise', M2):triangle(BIC,[B,Ii,C]):
rotation(K, A, Pi/2, 'counterclockwise', M3):triangle(AKB,[A,K,B]):
midpoint(O1,K,J): coordinates(O1):
midpoint(O2,A,Ii): coordinates(O2):  
poly:=[coordinates(A),coordinates(J),coordinates(Ii),coordinates(K)]:   

display(draw([A(color = black, symbol = solidcircle, symbolsize = 12), 
B(color = black, symbol = solidcircle, symbolsize = 12), 
C(color = black, symbol = solidcircle, symbolsize = 12), 
J(color = black, symbol = solidcircle, symbolsize = 12), 
polygonplot(poly,color = "DarkGreen", transparency = 0.5),
ABC(color = red ),
BIC(color = green),
AKB(color = grey),
AJC(color =blue)]),
textplot([[coordinates(A)[], "A"],[coordinates(J)[], "J"],[coordinates(Ii)[], "I"],   
[coordinates(B)[], "B"], [coordinates(K)[], "K"], 
[coordinates(C)[], "C"]], 
align = [above, right]),  axes = none);
Error, (in geometry:-draw) the option must be of type equation or name. I don't see how to correct this error/
 

Hi, I have the equation below and I'm trying to use "collect " to get the coefficient of dudy^2 and dvdx^2. I tried

aa1 := subs({gamma[1] = alpha[3]-alpha[2], gamma[2] = alpha[6]-alpha[5]}, collect(aa, {dudy^2, dvdx^2}))

But is not collecting the coefficient of dvdx^2. Please can someone help?

aa := alpha[1]*(cos(theta(x, y, t))^4*dudx^2+2*cos(theta(x, y, t))^3*dudx*sin(theta(x, y, t))*dvdx+2*cos(theta(x, y, t))^3*dudx*sin(theta(x, y, t))*dudy+2*cos(theta(x, y, t))^2*dudx*sin(theta(x, y, t))^2*dvdy+cos(theta(x, y, t))^2*sin(theta(x, y, t))^2*dvdx^2+2*cos(theta(x, y, t))^2*sin(theta(x, y, t))^2*dvdx*dudy+2*cos(theta(x, y, t))*sin(theta(x, y, t))^3*dvdx*dvdy+cos(theta(x, y, t))^2*sin(theta(x, y, t))^2*dudy^2+2*cos(theta(x, y, t))*sin(theta(x, y, t))^3*dudy*dvdy+sin(theta(x, y, t))^4*dvdy^2)+(alpha[2]+alpha[3]+gamma[2])*(-dudx*cos(theta(x, y, t))*sin(theta(x, y, t))*thetadot-(1/2)*dudx*cos(theta(x, y, t))*sin(theta(x, y, t))*dudy+(1/2)*dudx*cos(theta(x, y, t))*sin(theta(x, y, t))*dvdx+(1/2)*cos(theta(x, y, t))^2*dvdx*thetadot-(1/4)*cos(theta(x, y, t))^2*dvdx^2+(1/2)*cos(theta(x, y, t))^2*dudy*thetadot+(1/4)*cos(theta(x, y, t))^2*dudy^2-(1/2)*sin(theta(x, y, t))^2*dvdx*thetadot+(1/4)*sin(theta(x, y, t))^2*dvdx^2-(1/2)*sin(theta(x, y, t))^2*dudy*thetadot-(1/4)*sin(theta(x, y, t))^2*dudy^2+dvdy*sin(theta(x, y, t))*cos(theta(x, y, t))*thetadot-(1/2)*dvdy*sin(theta(x, y, t))*cos(theta(x, y, t))*dvdx+(1/2)*dvdy*sin(theta(x, y, t))*cos(theta(x, y, t))*dudy)+alpha[4]*(dudx^2+(1/2)*dvdx^2+dvdx*dudy+(1/2)*dudy^2+dvdy^2)+(alpha[5]+alpha[6])*(cos(theta(x, y, t))^2*dudx^2+2*cos(theta(x, y, t))*dudx*((1/2)*dvdx+(1/2)*dudy)*sin(theta(x, y, t))+cos(theta(x, y, t))^2*((1/2)*dvdx+(1/2)*dudy)^2+2*cos(theta(x, y, t))*((1/2)*dvdx+(1/2)*dudy)*dvdy*sin(theta(x, y, t))+sin(theta(x, y, t))^2*((1/2)*dvdx+(1/2)*dudy)^2+sin(theta(x, y, t))^2*dvdy^2)+gamma[1]*(sin(theta(x, y, t))^2*thetadot^2+sin(theta(x, y, t))^2*dudy*thetadot-sin(theta(x, y, t))^2*dvdx*thetadot+(1/4)*sin(theta(x, y, t))^2*dudy^2-(1/2)*sin(theta(x, y, t))^2*dudy*dvdx+(1/4)*sin(theta(x, y, t))^2*dvdx^2+cos(theta(x, y, t))^2*thetadot^2-cos(theta(x, y, t))^2*dvdx*thetadot+cos(theta(x, y, t))^2*dudy*thetadot+(1/4)*cos(theta(x, y, t))^2*dvdx^2-(1/2)*cos(theta(x, y, t))^2*dudy*dvdx+(1/4)*cos(theta(x, y, t))^2*dudy^2)+xi*(cos(theta(x, y, t))^2*dudx+2*cos(theta(x, y, t))*sin(theta(x, y, t))*((1/2)*dvdx+(1/2)*dudy)+sin(theta(x, y, t))^2*dvdy);

hi every body 

please How to write these solutions in fraction form

Download problem1.mw

How to get the series and plot.I got this error.

TL.mw

At the end of 2021, Mathematica added capability for integration:

https://blog.wolfram.com/2021/12/13/new-in-13-symbolic-numeric-computation/

Trying this in Maple, it does not look like it can solve it:

My questions are then, is there a way to get Maple to solve this? Does Maplesoft actively work on solving more integral types and is it likely support for this integral will be added at some point?

In Hansen's book "A table of Series and Products" there is an unsourced listed identity 43.6.1:

S1 := Sum(2^k*tanh(2^k*x), k = 0 .. n - 1) = 2^n*coth(2^n*x) -   coth(x)

It appears to be to be numerically correct, and can be obtained from a second identity

S6:=Sum(2^(-k)*tanh(2^(-k)*x), k = 1 .. n) =- 2^(-n)*coth(2^(-n)*x) + coth(x)

by "summing in reverse order". S6 is also numerically correct.

Starting from S1 and reversing the order, gives

S2 := Sum(2^(n - k - 1)*tanh(2^(n - k - 1)*x), k = 0 .. n - 1) = 2^n*coth(2^n*x) - coth(x)

Then shifting the index gives

 S3 := Sum(2^(-k)*tanh(2^(-k)*x), k = -n + 1 .. 0) =  2^n*coth(2^n*x) - coth(x)

both of which test OK numerically since n>0. Now it begins to get strange.

In S3, let n->-n (highly illegal) to obtain

S4 := Sum(2^(-k)*tanh(2^(-k)*x), k = n + 1 .. 0) = 2^(-n)*coth(2^(-n)*x) - coth(x)

and, surprisingly Maple tests S4 to be correct numerically.

Here's how that happened. The lower limit of the S4 sum exceeds the upper limit, so there are three possible ways to interpret this:

1. In standard mathematical usage, this is usually set to zero by caveat;

2. In a practical sense, one might expect the order of summation to be irrelevant so S4 is the same as

S5:= Sum(2^(-k)*tanh(2^(-k)*x), k = 0 .. n + 1) = 2^(-n)*coth(2^(-n)*x) - coth(x)

but that fails numerically.

3. Maple has a built-in algorithm (see the help page on "Sum") that interprets

Sum(f(k), k = m .. n) = -Sum(f(k), k = n + 1 .. m - 1)

when m exceeds n and that is why S4 works numerically and, when applied to S4 gives the result S6.

So where did Maple's prescription come from, and what is it's justification?

Thank you

This is from a graph G with vertex set {0,1,2,3,4,5,6,7,8,9} always labelled from {0,1,2,3,...,n-1}

Now to Split the List L to sublists like this

Now going through L list in details (All my lists will be like this only}

Sublist L1 will have all those from first in this firstly we see  edge {0,1} we take all those which take {0,1} in sequencial manner and put in sublist L1

Now as we proceed we see the next starting edge is {0,3} so their is none with {0,2} so we pick all those with {0,3} in the first sequencial manner and put in sublist L2

Similiar we pick all sublist from this with first element unique in the sequential manner and make a list of lists

Lk:=[L1,L2,L3,L4,....]

Code until L

which was done

Toy_code_(1).mw

Now again proceed we can observe we can see their none with {0,4} next is only with {0,5} 

Then i need write a function F which takes a List say L1 returns

all possible 2 element permutions from L1 list say [S1,S2] and [S2,S1] like that all possible as order also matter where that set is positioned

Given Graph G and Graph H how to store the list of all the various Subgraphs of Shape H in G with their vertex labels.

I have write a code but it may not be the optimal way to do it and it may be time consuming for even medium graphs too

Any way to optimize

Let From this list of subgraphs H of say [G0,G1,G2,.....] we pick NumberOfVertices(G) Graphs
say H= [H0,H1,H2,H3,....,Hn]

i) Now any two graph Hi,Hj have excatly one edge interection if (i,j) is an edge in G

 ii) An edge in  the list H will occur exactly twice only in the entire list of graphs

If these two conditions satifies all such H I need to save

Toycode until picking graphs

From that how to pick lists which satify conditions i) and ii) is another need help

Toy_code.mw

Please excuse my thickness if any.

In the following IF statement:

if 1 <> 2 then
    OuterThen;
    if 1 <> 2 then
        InnerThen;
    else
        InnerElse;
    end if;    
else
    OuterElse;
end if;

I expect the output:

OuterThen
InnerThen

but I only get:

OuterThen

Why?