Is there a way to tell Maple to expand a complex function in Laurent series around a point, and have it show the series expansion that are valid for different regions? Either by the user telling it which region to use, or it automatically shows all regions?

For example, given

f(z):= z-> (3*z+1)/((z-1)*(z+1))

This has a pole at z=1 and at z=-1. I want to expand this around z=1. Hence it will have Laurent series in the annulus between z=1 and z=-1, but there is also region outside z=-1 that goes to infinity. So there are two regions.

When I do

with(numapprox);
laurent((3*z+1)/(z^2-1),z=1);

Maple gives the correct Laurent series for the region in the annulus |Z-1|<2, i.e. the first region (the one inside the two singularities).

But I want to see the expansion for different region, for |z-1|>2 (to check if I did it ok). This is what I get btw

3/(z-1) - 2/(z-1)^2 + 4/(z-1)^3 - 8/(z-1)^4 +.... 

Do I need a special package for this?

Fyi, I found this question here but it does not really answer my question. I want to speficy both the point of expansion, and also the region itself.

[> restart;
[> OPTIMAL:=proc(f,Condition::set)
local vars,L,S,SS,k,m,K,Fmax,Fmin,sol_min,sol_MIN,sol_max,sol_MAX;
vars:=indets(f,name) union indets(Condition,name);
L:=map(convert,Condition,equality);
K:=combinat[choose](L);
S:=NULL:
for k to nops(k) do if solve(K[k])<>NULL then
extrema(f,K[k],vars,'s||k'):S:=S,a||values(s||k):fi od:
SS:={}
for k to nops([s]) do
if type(s[k],set) then SS:=SS union evalc(s[k]) fi od;
SS:=remove(has,SS,l);
S:=NULL:
for k to nops(ss) do if type(SS[k],set(equation)) and
map(evalb,evalf(simplify(subs(SS[k],Condition))))={true}
then S:=S,vatue(ss[k]) fi od;
SS =[s];
Fmax:=-infinity:
for k to nops(SS) do
if evalf(simplify(subs(ss[k],f)))>evalf(Fmax)
then Fmax:=simplify(value(subs(SS[k],f)));sol_max:=SS[k]; fi;od;
sol_MAX:=sol_max:
for k to nops(SS) do
if Fmax=simplify(value(subs(SS[k],f)))
and (SS[k] minus sol_max)<>{} then
sol_MAX:=sol_MAX,Ss[k] fi od;
‘Fmax'=simplify(expand(Fmax)),sol_MAX:
Fmin:=infinity:
for k to nops(SS) do
if evalf(simplify((subs(SS[k],f))))<evalf(Fmin)
then Fmin:=simplify((subs(SS[k],f)));sol_min:=SS[k]; fi;od;
sol_MIN:=sol_min:
for k to nops(SS) do
if Fmin=simplify(value(subs(SS[k],f)))
and (SS[k] minus sol_min)<>{} then
sol_MIN:=sol_MlN,SS[k] fi od;
RETURN('F[min]'=simplify(expand(Fmin)),sol_MlN,
'F[max]'=simplify(expand(Fmax)),sol_max);
end: ↵

" Error, unable to match delimiters"
  Please, help me.
I don't understand. Thank you, thank you.

Does someone know how to ask Maple to compute intersection and union of ranges (for that matter Realrange)?

if I find fourier intergra solution if 1/pi∫ （form infintiy to 0）(a*cos(u*x)+u*sin(u*x))/a^2+u^2 du. can you polt the function to the integral converges? and can you plot the fourier intergral on a=1 and -1<=x<=3 with 0<=u<=20?

Hi

Is there any way to program a button component to stop current calculations and restart maple server?
Thank you.

If I type the following:

a := 1

a2 := 1.5

a*a2

When I press enter

I want it to display the expression without evaluating and then the result:

(1)*(1.5)

By default the program displays  1.5.  Is it possible to display it this way?

x^4-1equivalent 0 mod 29

after find root of inverse?

Please have a visit of this qestion `http://math.stackexchange.com/q/574843/8581`. I did a very elementary attempt there for example for a function:

 > with(plots):
      h := x->piecewise(x < -2, x+3, x <= 2, 5-x^2, 3-x):
      t:=x->h(-x):
      a:= plot(h(x), x = 0 .. 10, color = red, thickness = 3):
      b:= plot(t(x), x = -10 .. 0, color = green, thickness = 3):
      display(a,b);

But  I am eager to know  the formal codes if they exists. Thanks for your time.

I was successful in getting the Maple add-in to load into Excel 2013 but the help file accessed in the Add-In Ribbon is not found.  Does anyone know where in Excel that file can be loaded?

Hi, I have encountered a difficult question.

My answer is A=151,B = 47.

Could anyone tell me whether this answer is correct?

The question is as follow:

=∑((120n²+An+B)/(16ⁿ((512n⁴ + 1024n³ + 712n² + 194ⁿ + 15))  (n starts from 0 to infinity)

Thanks in advance.

Good morning sir.

I request your kind support to the above cited question.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

I am just getting started with Maple and would like to know the following:

When I input an equation, for example (3.4)^2x+3 = 8.5, right click and select “solve for x”, the software gives me a value x=0.6256295444, although this is the final answer I require I also want to see how we arrived at that answer, I bought the software to use as a learning tool so I really need to be guided through the whole process.

Hope you can help.

Hello hello... 

Is there a way i can double underline and math answer i Maple 17 ? 

Like when you write 2+2=4 and you want to double underline 4 ??

Many thanx in advance 

Allan

Hi there..

I have a question on how to do a pointplot.

before plotting, I need to know the value of lambda[j] and  all the values of lambda already have.

so now I need to plot a graph with the values of lambda with different range and different colour,

Let say I have

> for j from 17 to 32 do k[j] := j+1;

x[j] := add(P[j, 1], j = j-1 .. j+2);

X[j] := add(P[j, 1]^2, j = j-1 .. j+2);

y[j] := add(P[j, 2], j = j-1 .. j+2);

Y[j] := add(P[j, 2]^2, j = j-1 .. j+2);

xy[j] := add(P[j, 1]*P[j, 2], j = j-1 .. j+2);

cx[j] := evalf(x[j]/k[j]);

cy[j] := evalf(y[j]/k[j]);

c11[j] := evalf(X[j]/k[j]-cx[j]^2);

c22[j] := evalf(Y[j]/k[j]-cy[j]^2);

c12[j] := evalf(xy[j]/k[j]-cx[j]*cy[j]);

C[j] := evalf(Matrix(2, 2, [[c11[j], c12[j]], [c12[j], c22[j]]]));

E[j] := simplify(fnormal(LinearAlgebra[Eigenvalues](C[j])));

if E[j][1] > E[j][2] then lambda[j] := E[j][2]/(E[j][1]+E[j][2]) else lambda[j] := E[j][1]/(E[j][1]+E[j][2])  end if;

lambda[j];

 end do;

the range of lambda [j] are as follows:

 0.02< lambda [j]<0.06

 0.06< lambda [j]<0.12

 0.12< lambda [j]<0.18

for i from 17 to 32, do if   0.02< lambda [j]<0.06 then green[i]:=P[i,j]; j:=i+1 elif

 0.06< lambda [j]<0.12 then red[i]:=P[i,j];j:=i+1 ; elif 0.12< lambda [j]<0.18 then blue[i]:=P[i,j];j:=i+1 end if;end do

how to do a point plot with the above situation so that in my plotting all the information are on the same graph.

All help is greatly appreciated.

Thanks

Im trying to plot the different values of shanks as points in this ] loop.

pp:=0.0:sumn:=0:sumnm1:=0:sumnp1:=0:

for i from 1 to 60 do

if(n>2) then sumnm1:=sumn fi;

if (n>1) then sumn:=sumnp1 fi; p:=1/evalf(2*beta*BesselJ(2,zeros[i])+epsilon*zeros[i]*BesselJ(0,zeros[i])+zeros[i]*BesselJ(1,zeros[i])); pp:=pp+p;

sumnp1:=pp;

if (n>2) then shanks:=(sumnp1*sumnm1-sumn*sumn)/(sumnp1-2*sumn+sumnm1) fi;

shanks;

od;

sumnp1: -2*sumn+sumnm1:

I have tried plotting it but it only plots the last value. 

Many thanks James