## seq(i[1], i[1] = 1 .. 2) doesn't restore i...

```seq(i[1], i[1] = 1 .. 2);
i[1];
1, 2
2
```

I thought the note saying "The index variable i is NOT private to the seq invocation" referred only to parallel code.

## Precision and Plot Drivers...

Several years ago, acer posted a topic on how to overcome the limitation of hardware precision plotting drivers in Maple:

https://www.mapleprimes.com/posts/100884-Precision-And-Plot-Drivers

Currently, I want to plot (1-x)^(10^9) in the range of 0..10^(-15) smoothly.

plot((1-x)^(10^9), x=0..10^(-15)) does not work. Is there an updated option to this in Maple since 2011?

## Simplification of integral...

How do I simplify the integral,  where a(u) and b(u) are T-periodic and s,t belongs to the interval [0,T]

## Problems with getting consistent execution timings...

I have been using CodeTools::Usage with Maple 17 to compare timings of a couple of matrix inversion routines against each other and against the Maple library routines LinearAlgebra::MatrixInverse and LinearAlgebra::Determinant.

The small section of code that I use to collect the cpu times for each method is:

----------------------------------------

udata := Usage(invTest(x,y,z,delta,mu), output=['cputime', 'bytesused'],
iterations=nRepeats, quiet);
dat[1]:=udata[1]; dat[2]:=udata[2];

----------------------------------------
nRepeats has been set to 25.

In order to get the timings as accurate as possible, I only open a couple of terminal windows on my laptop so as to run the tests with as low a loaded machine as I can get. (I'm running Ubuntu 14.04 on an 8 core Intel (R) Core i7-3840QM, 2.8GHz CPU with 16Gb of memory.)

A test run consists of a sequence of test matrices each of which is run for an increasing sequence of matrix orders. I either time an implementation on its own or I time both an implementation and the Maple library routines. In the later case for each test matrix and order of matrix, I use Usage to first time the Maple routines and then the times for one of the implementations:

----------------------------------------

if compMaple then
udata := Usage(MatrixInverse(A), output=['cputime', 'bytesused'],
iterations=nRepeats, quiet);
mdat[1]:=udata[1]; mdat[2]:=udata[2];

udata := Usage(Determinant(A), output=[cputime, bytesused],
iterations=nRepeats, quiet);
mdat[1]:=mdat[1]+udata[1];
mdat[2]:=mdat[2]+udata[2];
else
mdat[1..2] := 0:
end if:

udata := Usage(invTest(x,y,z,delta,mu), output=['cputime', 'bytesused'],
iterations=nRepeats, quiet);
dat[1]:=udata[1]; dat[2]:=udata[2];

----------------------------------------

I have noticed the following:

a) If I time both Maple and an implementation, and the same implementation on its own I can get timings that vary up to a factor of 2 or more,

b) Changes in timings for the same test run and as close to the same environment as I can get (i.e., just the two user terminal windows open) can generate timing differences of up to 50%.

c) Sometimes `chaotic' timings are generated, for example,

n = 150, t = 3 (secs)
n = 200, t = 24 (secs)
n = 250, t = 18 (secs)

which cannot be reflecting the times required to perform the calculations. This type of behaviour always seems to occur when the reported memory bytecount is increasing from ~0.25* 10^9 to over 10^9.

Is there anything I can be doing here to get more consistent timings?

I want to use the timings from these tests in a journal article so it would be good to have the same test run under very similar conditions to return timings within a few percent difference of one another. I certainly get this sort of tolerances (<10%) if I use the Fortran cpu_time intrinsic to time Fortran code.

## Balancing Equations Function...

Hi,

As an example, I have these 3 equations below and I need to balance them similar to balancing a chemical equation.

Equation 1: E1=A+B+C+D
Equation 2: E2=A-B+C-D
Equation 3: E3=C

So, I am wondering if there are any functions or algorithms that allow me to input such that they will give me a result of

xE1 ± yE2 ± zE3 = wA

where w,x,y &z are integers and x,y & z can be zero.

Thanks.

## Print A - lambda I = some Matrix...

Ho do I print this?

A - lambdaI = some matrix

On the left of the equation I have the letter "A" a minus sign, the Greek letter "lambda" and the letter "I" right next to it.
The rest. from "=" on, is math.

Thank you!

mapleatha

## Creating monomials in n variables up to a given de...

I'm trying to create the set of monomials in n variables (given as a list var), up to a given degree d. Her eis my code. Any comments to make it better?

mondeg:=proc(var::list,d)
local n, mon, moni, i, j, m1, m;

n:=nops(var);
mon:={1};
moni:={1};
for i to d do
for m1 in moni do
#print(m1);
moni:=moni minus {m1};
#print(moni);
for j to n do
#print(var[j]);
m:=m1*var[j];
moni:=moni union {m};
#print("moni=",moni);
od;
od;
mon:=mon union moni;
#print(mon);
od;

mon;
end:

## Jacobian Matrix from the MapleSim Model...

Hello everyone,

I know that it is possible to obtain the DH parameters of a robot manipulator model in the MapleSim environment.

I was wondering if it is possible to obtain the Jacobian matrix of a robot manipulator from the MapleSim model?

Thank you,

## extract common factors from expression after colle...

Often after using collect(expression,x) the prefactors of x are within a bracket but typically contain factors in each term of the bracket that are equal and not pulled out of the bracket. Is there a way to ask maple to automatically factor out these after collecting?

I hope it is clear what I mean...

## dsolve/numeris vars option...

Hi,
Triing to solve some 2 differential equations system (plan mechanical movement), using "output=" as last option, I am interrested by the values of the second derivatives of the coordinates. The "output" runs fine to get t, x(t), y(t), dx/dt(t) and dy/dt(t). To get d^2x/dt^2 and d^2y/dt^2, I thought it would work to write something like (A is the times array) this :

dsol := dsolve(dsys, type = numeric,  {diff(x(t),t,t), diff(y(t),t,t},output = A),

But if I do this, I get next error message :

Error, (in dsolve/numeric/process_input) dependent variables must be functions of a single unknown, the independent variable. Got [diff(diff(x(t), t), t), diff(diff(y(t), t), t)]

Thanks

## Animating multiple plots using display command...

I generated a few plots using the plot command. When I try to animate them using the display command, only the first plot appears and not the rest. I can't figure out what the problem is. Any help is appreciated. I have attached below the commands I am using to generate the plots and animate them:

```restart; with(plots): with(OrthogonalExpansions): f := x -> x; L := 1: fexplt:=plot(f(x),x=-L..L): fs := n->FourierSeries(f(x),x=-L..L,n,'Coefficients'); fs(n);                   n                                             -----                                            \          (1 + i)                               )   2 (-1)        sin(Pi i x)                  /    -------------------------                 -----           Pi i                            i = 1                           nmax := 25:```

`display([seq(plot([f(x),fs(m)],x=-L..L),m=1..5)],insequence=true);`

If I just use

`seq(plot([f(x),fs(m)],x=-L..L),m=1..5);`

I get all the five plots output to the screen.  So, I know the plots are there. It's the animation part that doesn't seem to work. I am using Maple 2015 on a linux mint desktop.

Thanks.

## Matrix Maple Call...

Hello all,

I am looking for a maple command to do the following

#outline of idea, is a user would pre-define a number of rows and a single Matrix command would automatically generate a Matrix based on the data the user provides.

numRows:= ;#user would enter a number here

row1:=[1,2,3];  #user enters data for each row

row2:=[4,5,6,7];

row4:=['red','blue',7];

#user will enter a few more rows to match numRows, specified above

Matrix([[row1],[row2],[row3],....,[rown]]);#this matrix command would be generated based on the above entered data

I was thinking some form of counter could do this?  Any suggestions would be appreciated.

## How to properly determine roots when the solution ...

Hello everyone,

First I want to thank you for paying attention to my post.

I'm trying to determine the maximum of the following function:

Maple Code:

(1/4)*(-1/4+alpha*(-1+b)*e^2+((1-b)*alpha+(1/4)*b)*e)^2/((-1+e)^2*(b*e-1)*alpha*e*(-1+b))(1/4)*(-1/4+alpha*(-1+b)*e^2+((1-b)*alpha+(1/4)*b)*e)^2/((-1+e)^2*(b*e-1)*alpha*e*(-1+b))

e is my variable and I want to study it in [0,1[. I have a several parameters restriction like b in [0,1[ and alpha>1.

When I value this function for specific values (b=0.1, alpha=4 for instance) I get the equation and its associated graphic representation:

Maple Code:

-0.6944444445e-1*(-1/4-3.6*e^2+3.625000000*e)^2/((-1+e)^2*(.1*e-1)*e)

I'm only interested in the domain where e is betweeen 0 and 1. I clearly on the graph see that there is a maximum and when 1) I compute roots of the expression I get 2) following solutions:

1)

2)

0.9324708634, 0.07447358108, 0.6965691592, 1.345632810,

-0.07419084270.

Here: 0.6965691592 corresponds to the maximum I'm looking for.

So now when I try to get a generalization of this function according to my parameters and when I compute the first derivative with respect to e

1)

2)

3)...

the last is very big so I do not write it here.

To sum-up: I see that the solution I'm looking for exists but when it comes to use parameters I cannot define correct roots.

## RootOf, index=real...

RootOf has the option index=real[i]  for the i-th real root:

evalf([seq(RootOf(x*(x^2-1)*(x^2-4)+1/100, x, index=real[i]), i=1..5)]);
[-2.000416306, -0.9983310082, -0.002500019532, 1.001664362, 1.999582971]

This option does not seem to be documented. Why? Or, is it?

## importing very large matrix from textfile ...

Hi !

I am importing a matrix from a text file. I am using the command,

ImportMatrix("Filelocation/Filename.txt", 'source' = 'delimited', 'delimiter' = " ");

I see the following error:

Error, (in ImportMatrix) cannot interpret file

I think it is because of the huge size.(700 MB, and 28 GB respectively)

How to import such a matrix in maple?

thanks,

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