Hello, I have a somewhat math and Maple question I'm hoping some can help with.

I have this curve,

curve:=alpha^2*beta^10-alpha^2*beta^9+4*alpha*beta^7-2*alpha*beta^6-2*alpha*beta^5-alpha*beta^4+alpha*beta^3-2*beta+1;

and if I solve this system (numerically);

sol:= solve([curve=0,diff(curve,beta)=0],[alpha,beta]);

I get 6 special points (8 actually but two are critical). So I'll refer to them by subscript "i".

If I then do a coordinate transformation by;

alpha=exp(u)

beta=exp(v)

and convert the 6 coordinates and curve, I'll get everything in terms of (u,v) coordinates.

curve2:=subs([alpha=exp(u),beta=exp(v)],curve);

soluv:=map(ln,sol);  (this is just pseudo - I don't know how to do it this way)

So now the 6 points are referred to by (u_i,v_i).

Next, I want to expand this curve locally around these six points, using the following (where "z" is the local coordinate);

u -> u_i + z^2

v -> v_i + sum(a_j*z^j,j=1..n)

where n is reasonable, though around 15.

curve3(i):=subs(u=z^2 + cat(Ubp,i),curve2);

curve4(i,n):=subs(v=cat(Vbp,i)+sum(a[i,j]*z^j,j=1..n),curve3(i));

Here, I'm not sure of the pros/cons of cat() vs a[i,j]....

 

Anyway, I'll then have an equation in terms of only the local coordinate "z". If I then solve each coefficient of "z", at each order, I should then be able to determine the power series v(z). I reason that since the curve is initially equal to zero, that every non-zero power of z will have a coefficient/equation (in terms of unknowns a[i,j]) that should be equal to zero.

This is analagous to solving differential equations with power series...

 

However, I'm a little lost in implementing this,

I am currently trying, for instance,

l1:= series(curve4(1,10),z,0,9);

e1:= seq(coeff(l1,z,i),i=1..4):

s1:=seq(a[1,j],j=1..4):

sol:=solve(e1,s1);

I believe I am doing something wrong though bcause every odd power is zero.

 

Thank you a lot for any suggestions and/or help,

sbh

PS>

Ubp and Vbp are those 6 points - I just kept them as symbols initially because I was still getting odd-powered coefficients as zero, regardless of their actual values. Hence a little bit of the "math" side of the problem...

Hi, as the title says I am animating an implicitplot and want a different color for each curve left by the trace. I realize it may be easier to build plot structures using seq and display(..,insequence=false) but I thought I should learn more Maple ha ha. Plus  it seems easier to implement.

 Forgot to say I use Maple 15

For equation sol[2][1]=constant A,

 

 

> animate(implicitplot, [sol[2][1] = A, x = -6 .. 15, y = -15 .. 15, numpoints = 10^5], A = -10 .. 10, trace = 2, frames = 20);

 

 

I am trying to invert a function and, during the course, wind up with something like,

 

a_1*V^P*V + a_2*V^P*V^2 + a_3*V^P*V^3 + a_4*V^P*V^3 + a_5*V^P*V^3 + a_6*V^P*V^4 + \cdots

 

is there a way to get the poly into a form 

 

(a_1+a_2+...)*V^P + (b_1+b_2+...)*V^(P+1) + (c_1+c_2+...)*V^(P+2) + .....

 

?

Thanks. Attached is my Maple 16 sheet.

(1) (2) (3) Rearranging "main" leads to the following. (4) It can't take a series due to the series about zero, so I split it into (5) Then I'll get a polynomial expression, switch places of the two variables' leading terms, and substitute into the "original" polynomial (split).   (6) (7) (8) (9) (10) (11) Error, (in factor) 2nd argument, V, is not a valid algebraic extension

Download invert2.mw

Hello everyone,

Hello All, I read some other posts on "stack limits" and they were not too helpful. In a particular case there seemed to be a bug, as stated by a Maple kernel developer, but I can't imagine that being the problem here. I have a MacBook Pro (Intel) using Maple 11.02 with 2GB of RAM. The following code displays the stacklimit eror causing a failure with the kernel connection whenever I try to simplify the last line. Does anyone have any ideas? Thanks much, Steve. P.S. Here is the worksheet lines: restart one := 1/((x*Dd-x^2*Dcj)*sqrt(x^2-1))