Hi there,

So my problem is to find the solution(s) of a 3-D system. I can get Maple to spit out a solution (at times), but I am looking for reassurance that this is indeed the solution (if unique, and if not what the other solutions may be). Increasing Digits makes Maple "lose" the solution and return a blank-- normal behavior? Looking at the 3-D plot of the system offers something to puzzle over.

I set up the system in  (x,c,q):

xd := x^.5-.1*x-c;
cd := (.5/x^.5-.1-q)*c;
qd := -(q-.2e-1)*(q-.3e-1)+(q-.25e-1)*(.5/x^.5-.1-q)*c/(x^.5-.1*x-c);
 

I look for a solution with fsolve:

Digits:=10: interface(displayprecision=10):
ss:= fsolve({xd,cd/c,qd}, {x,c,q}, avoid={x=0, c=0, q=0});
xs:=subs(ss,x): cs:=subs(ss,c): qs:=subs(ss,q):

Maple gives:

ss := {c = 2.399289639, q = .2511089584e-1, x = 15.97164840}

If I raise digits to 15, Maple can't solve it anymore. Perhaps this is normal behavior.

I'd like some reassurance that this solution is indeed a solution. Simply feeding the fsolve output back into the system will not work because of a division by zero:

eval(xd,{x=xs,c=cs,q=qs}); eval(cd,{x=xs,c=cs,q=qs}); eval(qd,{x=xs,c=cs,q=qs});

yields:

0.
-.9597158556e-10
Float(-infinity)

I decided to look at the 3-D plot. The plot of the system suggests that there may be several solutions.

The plot:

plotopts:=style=patchcontour, shading=none,lightmodel=light3,axes=boxed:
px:=implicitplot3d({xd}, x=0..25,c=0..5,q=0.02..0.05, numpoints=10000, plotopts, colour=brown): pc:=implicitplot3d({cd/c}, x=0..25,c=0..5,q=0.02..0.05, numpoints=10000, plotopts, colour=green):
pq:=implicitplot3d({qd}, x=0..25,c=0..5,q=0.02..0.05, numpoints=10000, plotopts, colour=blue):
display3d({pq}, orientation=[-25,70]);
display3d({px,pc,pq}, orientation=[95,90], projection=1);

plot of third equation
plot of 3-D system

The plot is not very clean, and no matter how hard I've tried, by turning it around and zooming near the Maple solution, it is not clear that there are no other solutions. (well perhaps it is clear from the equations themselves, but I couldn't work it out and resorted to the numerical approach)

Does somebody have a sheet covering that algorithm for continous
anti-derivatives of rational functions (Bronstein's book §2.8
"Integration of transcendental functions")?

Or can show me, how to extract it from Maple's library in case
it is there (and I guess Maple covers that ...) for explicite
use?

Write a procedure

input:a polygon and a linear transformation

output :applying the transformation to the polygon
 

Find the coordinates of the linear transformation that would have  the a larger square to the pink (smaller) square.Apply the transformation to the blue square.
 

please help with this, thnaks

I have tried the Physics package. First of all, how can I define a non-ortogonal basis (using kets)? Suppose I have a basis formed by linearly independt vectors. How to set them non-ortogonal?

How does one do the indeterminate vector product with and Dyadic calculus operations with Maple 12?

I just upgraded to Maple 12 because of its ability to perform abstract index calculations. However, I'm having trouble getting started with it. My first problem is with the Simplify command: if I define a completely symmetric tensor using the command

Define(T,symmetric);

and an antisymmetric tensor using the command

Define(w,antisymmetric);

then

Simplify(T[mu,nu,rho]*w[mu,nu]);

correctly returns 0. However, if I define T to be symmetric in only its first two indices,

Define(T[mu,nu,rho],symmetric={mu,nu});

I have some tough maple questions if you guys think you can handle them, let me know, i could use the help but also if you like a challenge, i think you'll get a kick out of the questions.

write me a message and i will send you a link to the questions (i scanned and uploaded the image of the questions on the paper)  just a few questions but tough ones!!!

Any help would be appreciated!!

thanks guys.

 A RSA with the modulus n = 119 and the exponent e = 7, with the 95-character
alphabet consisting of the printable ASCII characters to encrypt the word “Yes”.
so that Y=58, e=70, s=84. Give your encryption as a list of three numbers.

Then use the same set (that is the modulus n = 119 and the exponent e = 7) to decrypy the list of number  [42,59,4,59,27,59]

Here is my code, what's wrong with it. Please help. Thanks

Can anyone help with a purely Maple solution to this problem? (i.e. not having to download anything extra.)

Just for reference I'm woking on problem number 26 in "Schaum's Outline Series " for tensor Calculus.

It gives you a Schwarzchild metric and asks you to calculate the Einstein Tensor.  I'm using the example of doing this that's given in the "tensor" package help pages.  However I'm not getting quite the right answer.