How do I characterize this equation set? I think it has 6 solutions, equal in pairs, or 3 distinct solutions.

restart;

eq1 := x = (((72*5^(3/2)+270)*a^2-1344*5^(3/2)*a)*w+(9*5^(5/2)-1485)*a^2-2016*5^(3/2)*a-12544*5^(5/2))/(((288*sqrt(5)+216)*a^2-5376*sqrt(5)*a)*w+(36*5^(3/2)-1188)*a^2-8064*sqrt(5)*a+6272*5^(3/2)):

eq2:= a^3 = -(128*5^(5/2)*w)/9+(1600*w)/3+(544*5^(3/2))/9+15200/27:

eq3:=1+w+w*w = 0:##   or w = (sqrt(3)*%i)/2-1/2;

for s1 in [solve(eq2,a)] do
    for s2 in [solve(eq3,w)] do
        subs(a=s1, eq1):
        subs(w=s2,%):
        lprint("sol",simplify(%));
    end do;
end do;
 

Thermal_Stress_Distribution.mw

Download Thermal_Stress_Distribution.mw

The loop for HFS _data_2 and SFS_data_2 and the loop for HFS _data_3 and SFS_data_3 do not seem to be terminated. I do not know what it is the issue here. Anyone who can help this?

Negativity_(v12_beta_gamma_mu).mw

Thank you in advance,

simplify(sqrt((x^2 + y^2)/x)/sqrt(x^2 + y^2)) assuming x>0, y>0

is not sqrt(1/x), why?

Warning, data could not be converted to float Matrix

If we have two univariate polynomials $f(x)$ and $g(x)$ such that

$gcd(f(x),g(x))=1$

then we know there exist two other polynomials $a(x)$ and $b(x)$ such that $a(x)f(x)+b(x)g(x)=1$. For example, if $f(x)=x^3−1$ and $g(x)=x^2+2$, then we can set

$a(x)=\frac{2x−1}{9}$, $b(x)=\frac{−2x^2+x+4}{9}$

Here the polynomials $a(x)$ and $b(x)$ are known as Bezout polynomials and they can be found using the extended Euclidean algorithm, which I know how to do using pen and paper, but not in Maple.

So my question is: in Maple, is there a way, given $f(x)$ and $g(x)$, to solve for $a(x)$ and $b(x)$?

Another training example (number 2 and last) for finding all solutions to a system of equations:

f1 := x3^2-0.1*x1^4-0.05*x2^4+1;
f2 := x1^3+x2^3+0.05*x3^3-1; 
f3 := -2*cos(3*x1)+2*cos(3*x2)-2*cos(3*x3)+1;

In my version, there are 116 solutions.
Is it so?

What kind of solution is it (see (3))? Why is there no solution when I put the initial condition v(0)=C1? Secondly, eq. (2) can be reduced to a first-order differential equation?

Download CD_ode.mw

File:

PCA.mw

I am a student in the middle of a projekt, where math is an essential part of the task. I have done a lot of work in a maple document, but this document suddenly became corrupted. I've tried restarting and loading backups and f ollowed Can I repair a corrupted Maple document/worksheet file? (maplesoft.com) but the solutions didn't work on my document.

Also tried the DeleteBadCharacters() proccess, but i get the error "Error, (in XMLTools:-ParseString) Element type "Equation" must be followed by either attribute specifications, ">" or "/>"."

Is there a way to fix this issue, and prevent the same issue occuring in the future? 

Thanks in advance!

This is a training example for finding all solutions to a system of equations. If you look at the graph, you can count 36 solutions, but I managed to find 20 relatively good approximations. No attempts to get more solutions, which are also visible as intersections of graphs, did not lead to success. Therefore, there is a suspicion that there are only 20 solutions.
Is it so?

 restart: with(plots):
 a:=8.:
 f1 := x1^4-1.999*x1^2*x2^2+x2^4-1; 
 f2 := tan(x1+x2)-x2*sin(x1);
 implicitplot([f1, f2], x1 = -a .. a, x2 = -a .. a, numpoints = 25000, scaling = constrained,  color = [red, blue], thickness = 1);

   1, (3.192246883291975), (-3.0395187374365404)
   2, (3.0952031367176476), (-3.2447717313041897)
   3, (0.5881900748267959), (-1.160066226905079)
   4, (-0.936866718243322), (-1.3700058362814254)
   5, (-2.555853694651265), (-2.7399958564861953)
  6, (-3.2556241416421168), (-3.3964651254113774)
   7, (-3.583319843955091), (-3.7077839724189228)
   8, (-5.364827188794712), (-5.401998918608201)
   9, (-5.398295356665546), (-5.360818510223991)
  10, (-3.769206506106412), (-3.6477855329362683)
  11,(-1.3978806247566642), (-0.9772190664843745)
   12, (-1.192159295544978),(0.6492335177657542)
   13, (-3.0867255059416623),(2.927375855548188)
    14, (-3.18519036357835), (3.329801919022179)
   15, (2.0108268901120754), (2.243492422396739)
   16, (3.1133812329649766), (3.261937603184373)
   17, (4.0265558604742715), (4.130826167761226)
    18, (4.124539552922121), (4.019977762680433)
    19, (3.172338340844501), (3.018365965761908)
   20, (2.1945695320368097), (1.9558412553082192)

PROBLEM-IP.mw

Download PROBLEM-IP.mw

Hi !

I want to create a notation for a function, let's say :

f:=(x,y,z)->something

such that when I ask for

f(x,y,z) 

Maple returns

f^x,y(z) or anyother "nicer view" of that expression.

This is (I think) a similar action of replacing BesselJ(n,x) by J_n(x).

Many thanks for your answers !

Kevin

This is a follow-up to a previous question I asked that was answered with code that used "%.". From the documentation I can see that % is a nullary operator that gives us the value of "the last expression", which I think means the last result of an evaluated expression.

In my previous question, I wanted to be able to display for example, a constant times a matrix, without the product being evaluated.

For example, given A:=<1,2;3,4>:, we need to use Maple Input, and then we can write c__1.A and the output will be an expression that has c__1 then the dot product symbol and then the matrix A written out.

My question is simply: what exactly is "%."?

Hi all, 

I am working with the physics package and I want to know if there is a difference between Physics:-CompactDisplay and PDEtools:-declare ?

As well as the difference between Physics:-Simplify and simplify.

For both cases, can they be used as the same ? Are they incompatible in some case?

Thanks !

Kevin

I would like to display an expression that is a matrix, the dot operator, and another matrix. That is, I want to display a multiplication of matrices, without the multiplication being evaluated.

Something like

<1,2;3,4> '.' <6,7,8,9>

Is this possible?

Here is some context around why I want to do this. Perhaps the main reason I use Maple is for the symbolic math capabilities using 2d math input. I want to create worksheets that look like what I would write on paper. 

For example, let's say I have a matrix that is defined by <I, F;0,0>, where each of elements is actually another matrix. I want to multiply this matrix by its transpose, which would be something like <I, 0^T; F^T, 0^T>.

I would like to display <I, 0^T; F^T, 0^T> .  <I, F;0,0>.