Hi all,

I have a bunch of polynomials in q that involve unknown roots of unity and I want to bound them above by another polynomial.

For example: f(q):=q³-a*q²+b*q²-5.

Here a and b are powers of some roots of unity. These roots/powers depend on some variables which are unimportant.

My incorrect method up until now was to let all root of unity equal 1 so they vanish, and then run a short script that finds all coefficients of the poly f and makes them positive. 

But in this case it returns an answer of q^3+5 as the quadratic terms vanish - I don;t want this to happen! I really want the bound q³+2*q²+5.

If I run the script that changes the coefficients first, then maple can't  recognise if -a is positive or negative and so this doesn't work. If it helps this is it:

f:=g[i,j]; 
coffs:=[];
for m from 0 to degree(f) do
   coffs:=[op(coffs), abs(coeff(f,q,m))] end do;
fabs:=0;
for m from 1 to degree(f,q)+1 do
   fabs:=fabs+coffs[m]*q^(m-1) end do;
      g[i,j]:=fabs end do;
                     end do;
Any ideas would be great. Thanks!

EDIT: to perhaps make it clearer. The kind of roots of unity i'm dealing with are things like z^{2*j*k+q*k+(1/2)*l} where z is a (q-1)th root of unity, and j,k,l are unknown integer variables. 

Hi everybody,

I use dsolve(..., numeric, events =[...], parameters = [...], range=0..TMAX) to solve a parameterized system of 2 ODEs (unknowns x(t) and v(t)).

The solution over the whole range [0, TMAX] is constructed by assembling partial solutions over adjacent subranges of [0, TMAX].

(please look the attached file and feel free to contact me if you need more details than those given below

There exist two types of solution :

• Type 1 : trivial solution : for all t in some range [a>=0, b<= TMAX], the solution is x(t)=0 and v(t)=0
• Type 2 : for all t in some range [b>=0, c<= TMAX] {x(t), v(t)} is the solution of the differential system

The end of the simulation corresponds :

• either to t=TMAX
• either to x(t) = CMAX where CMAX is some predefined value for x(t)
   

I use events to manage the two following situations 

• x(t) = CMAX
• x(t) = 0 and v(t) < 0 : this is the situation which describes the transition between Type 2 solutution and Type 1 solution

The global solution is constructed by assembling partial solutions over subranges [0, b[1]], [b[1], b[2]], [b[2], b[3]] ... where type 1 solutions "live" in [b[n], b[n+1]] if n is odd and type 2 solutions in  [b[n], b[n+1]] if  n is even.
 
The assembly of the partial solutions doesn't work correctly : I identified the reason but I'm not capable to fix it.
If you look to the red instructions on yellow background you will see they do not return the same answer than the pink instructions (look to the blue outputs over the plot) . 

This is probably due to a very big mistake on my part  but I can't fix it !

Once again, if my explanations are not sufficient or if I'm not enough clear, feel free to ask me any questions you need.

Thanks in advance

ParametricDsolve.mw

Why is maple showing 1D math when evaluating?

Dear sir,

I request to provide the procedure to evaluate the following double integral in steps. Please find the enclosed attachment

I wanted to calculate the bessel function's limit, but there is no results.

Download test.mw

Below is my attempt to distinguish between add vs sum commands.  In principle, the sum command is symbolic.  I attempt the comparison in general, but get an error for the add command.  This error appears to occur if I do not assign numeric values to the general variables in the function.  I would like to execute the comparison symbolically.  Can this be done or does add only execute numerical evaluations?

Download sum_vs_add.mw

sum_vs_add.mw

How can I find the next number in the following set of numbers?

3,10,2,7,7,?

Thank you for your help!

How do I extract harmonics and plot a spectrum from a piecewise function?
 

The function is "Ia" shown below near the bottom in the "Plot Line Current" section.

Download Graetz_Bridg7b.mw

Hello all, 

How to animate a set of vectors?

for example, 

q:=Matrix(3,10,(i,j)->i^2+j+2*i); # some matrix which holds the 3x1 vectors. 

with(plots):

animate(arrow,[q(..,i)],i = 1..10);

I get an error 

Error, unsupported type of index, i

In real use, the input to 'arrow' function will be a vector valued function so the 'animate' command will show the resulting vectors. 

thanks.

EngM.

Hello All, 

I am trying to solve a nonlinear equation as a part of inverse kinematic for a robot tip. 

The robot is mostly redundant, and thus, the optimization package is the best to use. 

I looked the NLPSolve function in matrix form. 

the equation(s) am trying to solve is of the following format

Tip - Desired = 0 

Tip is a 6x1 vector and is a function (or expression) of q1 ..., qn number of joints. 

Desired is 6x1 numerical values representing the desired Tip position and orientation. 

for example, for a planar robot with only x,y coordinates

<cos(q[1])*cos(q[3])-sin(q[1])*sin(q[3])+sin(q[1])*q[2]+cos(q[1]), sin(q[1])*cos(q[3])+cos(q[1])*sin(q[3])-cos(q[1])*q[2]+sin(q[1])> - <1,1> = 0

I am a bit confused on how to use the NPLSolve command in matrix form. 

I understand that I need to formulate a procedure p(v) where v is a vector (here it will be v := <q[1], .., q[n]> ) , however, I am not solving one objective function rather 6 of them for 6-degrees of freedom. 

I tried something like

p:=proc(q)
    <cos(q[1])*cos(q[3])-sin(q[1])*sin(q[3])+sin(q[1])*q[2]+cos(q[1]) - 1,sin(q[1])*cos(q[3])+cos(q[1])*sin(q[3])-cos(q[1])*q[2]+sin(q[1]) -1>;
    end proc;
    Optimization[NLPSolve](3,p,initialpoint = evalf(q_start),maximize = false)
where q_start is 3x1 vector giving the initial point. 

but I always get 

Error, (in Optimization:-NLPSolve) non-numeric result encountered

How can I solve for set of equations?

thanks.

EngM

Dear all, I've been given the following procedure:

> int_part:=proc(f,h,n::integer) local k,u,v,s;
     > u:=f;
     > v:=h;
     > s:=0;

     > for k from 1 to n do;
     > u:=int(u,t);
     > s:=s-(-1)^(k)*u*v;
     > v:=diff(v,t);

> od;
> s; end: 

To apply on the following function: f:=int((exp(-x*t))/sqrt(t(t+1)),t=1..infinity);

And f is a function of x. F(x).

It should give the asymptotic expansion up to O(x^-6). But probably I do something wrong. Can somebody help me please?

Best wishes, Math

I have a trigonometric equation that outputs with a solution in terms of _B1 which I want to remove.

restart: solve({7*cos(2*t)=7*cos(t)^2-5, t>=0, t<=2*Pi}, t, allsolutions, explicit);

output:

{t = arccos((1/7)*sqrt(14))},

{t = 2*Pi-arccos((1/7)*sqrt(14))},

{t = 2*arccos((1/7)*sqrt(14))*_B1-2*_B1*Pi+2*Pi*_Z1-arccos((1/7)*sqrt(14))+Pi}

Is there anyway to get rid of the _B1, or somehow evaluate it by a substitution?

Even numerically the answer still retains the _B1.

{t = 1.006853685}, {t = 5.276331623}, {t = -4.269477938*_B1+6.283185308*_Z1+2.134738969}

Also it would be nice to remove the _Z1 subscript too, as the domain of the equation is [0, 2pi].

I tried removing the 'AllSolutions' command , but then I am missing two solutions:

solve({7*cos(2*t)=7*cos(t)^2-5., t>=0 and t<=2*Pi}, t, Explicit);

 {t = 1.006853685}, {t = 2.134738969}

There should be 4 solutions in the domain [0, 2pi].

If the headline is not the appropriate means, then what is the command line based means of generating a new math container in a worksheet, suppose one has a button with the label "Create New Container inside Selected Section" if that makes my intent any more clear.

At first look the above movement seems to be impossible in real life.

The question is sort of convoluted, but I hope somebody can help.

I have a data set I pulled from an Excel Sheet of the temperature for every day for a year.

Currently, it's in an Array 365x2, where the first column is what day of the year it is and the second column is the temperature. I want to create a plot that on the x-axis shows the day, but on the y-axis shows the amount of a certain chemical in the trees. I have a function of temperature vs chemicals, but I want my graph to show the day of the year vs amount of chemical. How would I go about making such a plot? I don't know how to connect all three. 

Thanks!