## Changing matrix...

I have a column matrix with all the elements 1.

A:=Matrix(100, 1, 1):

I want to generate another matrix B exactly same as A but with one element changed and keeping all other elements to be same. Manually, I could do by following way:

A[1,1]:=1.1;
A;
B:=A;

But I have to do this with each of 100 elements of A. For instance, in step 1 I want only the first element changed into 1.1. In step 2 I want only the second element changed keeping all others to be 1, and go upto 100.

Could anyone give me an easy way to do this? I would like to appreciate your help in advance.

## Numerical evaluation of integrals...

Hi all,

I'm trying to perform some calculations containing exponential integrals. Here is a snippet of my code:

restart;

H:=0.5:

q[0]:=10^5:
Es := 4*10^9:

p[0]:=10^6:
q[s]=10^10:

C := (q) -> q^(H+1.5):

G := (q) -> (int(q^3*C(q), q = q[0] .. q)):
P := (q) -> 1/sqrt(G(q)):

p := (xi) -> p[0]/P(xi*q[0]):
w:= (q,xi) -> 1/(Pi*(int(C(qs)*qs^3, qs = xi*q[0] .. q)))^(1/2):

U := (xi) -> (int(q*C(q)*w(q,xi)*(Int(exp(-(w(q, xi)*ps/Es)^2)/ps,ps=p(xi)..infinity)),q=xi*q[0]..q[s])):

My objective is to evaluate U for a set of discrete values of xi for further processing e.g. visualisation via plots. Neither value(U(xi)) nor evalf(U(xi)) produces a numerical result so I keep searching for solution. Does anybody have an advice how to solve U?

Regards, lassa

I have posted long time ago a patch for Shadebetween and you have transformed it into a hot fix:

In the last Maple 2015 update, the problem was not fixed.

Just curious: is it fixed in Maple 2016? Because I feel that the Maplesoft team is not "impressed" by such patches.

Edit. This was a comment related to acer's patch for NLPSolve, but it was transformed (I don't know why) into a separate question.

## Plotting and asymptotes...

Hi all.

1. When plotting the function y=(x-1)/(x-2) on Maple 2016, the asymptote along with the actual curve is drawn as "solid lines/curves".  The asymptote should have been drawn as a dotted line to indicate that x=2 is an asymptote so as to distinguish itself from the actual curve.   This confuses my students.

2. The other question is if I modify the equation to y=1+ (x-1)/(x-2), the plot only shows the asymptote at x=2 (again, a solid line).  There should be another asymptote at y=1, which is not shown.

Can someone please advise if Maple would fix this in the next update?    If not, how should one "fix" this when graphing such functions?

Many thanks.

## Plotting Heun functions...

One new feature of Maple 2016 is claimed to be

but when I try HeunD or HeunG there is no output -- no error message, nothing.  Is this behaviour what a user should expect of this command?

## Maple: Software Engineering Solutions

Maple 2016

Maple is a scientific software based on Computational Algebraic System (SAC) which has enabled this work entirely solve applied to Civil Engineering, Mechanical and Mecatrónica.The present problems in education, research and engineering are developed with static work sheets ie coding used innecesaria.Maple proposed models are shown below with an innovative structure; with the method of graphics algorithms and embedded components; putting aside the traditional and obsolete syntax; using dynamic worksheets as viable and optimal solutions to interpret and explain problems Ingineering.Design Advanced Analysis Tools (Applied Mathematics) Sophisticated Applications (efficient algorithms) and Multiple deployment options (different styles); this allowed generate math apps (applications engineering); can be interactive on the internet without the need to have the software installed on our computer; This way our projects can be used with a vision of sustainability around the world. Resulting in the generation of data and curves; which in turn will help you make better decisions analytical and predictive modeling in manufacturing and 3D objects; which would lead to new patterns of contrasting solutions.

ECI_2016.pdf

ECI_2016v_full.mw

Lenin Araujo Castillo

## Datatable understanding...

Hi,

I'm not sure that I mean datatable component corectly.

I also consider that I was done somthing wrong

Thank you for advanced for any help.

 >
 >

Oryginaly DataTable was inserted as a 3 x 3. I will traing to push maple to obtain 4 x 4 with specific row and column name.

 >
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 >
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 >
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wzel

## Help...for component embedeed...

The solution should show the procedure.
But without tutor.

Problem.mw

Atte.

Lenin Araujo Castillo

## New and improved integration results in Maple...

by: Maple 2016

The attached worksheet shows a small selection of new and improved results in integration for Maple 2016. Note that integration is a vast topic, so there will always be more improvements that can be made, but be sure that we are working on them.

A selection of new and improved integration results for Maple 2016

Indefinite integrals:

 > int(sqrt(1+sqrt(z-1)), z);
 (1.1)
 > int(arctan((-1+sec(x))^(1/2))*sin(x), x);
 (1.2)
 > int(((1+exp(I*x))^2+(1+exp(-I*x))^2)/(1-2*c*cos(x)+c^2), x);
 (1.3)
 > int(x^4/arccos(x)^(3/2),x);
 (1.4)

Definite integrals:

 > int(arcsin(sin(z)), z=0..1);
 (1.5)
 > int(sqrt(1 - sqrt(1+z)), z=0..1);
 (1.6)
 > int(z/(exp(2*z)+4*exp(z)+10),z = 0 .. infinity);
 (1.7)
 > simplify(int(sinh(a*abs(x-y)), y=0..c, 'method'='FTOC'));
 (1.8)
 > int(ln(x+y)/(x^2+y), [x=0..infinity, y=0..infinity]);
 (1.9)

Definite integrals with assumptions on the parameters:

 > int(x^(-ln(x)),x=0..b) assuming b > 0;
 (1.10)
 > int(exp(-z)*exp(-I*n*z)*cos(n*z),z = -infinity .. infinity) assuming n::integer;
 (1.11)

Integral of symbolic integer powers of sin(x) or cos(x):

 > int(sin(x)^n,x) assuming n::integer;
 (1.12)
 > int(cos(x)^n,x) assuming n::negint;
 (1.13)
 > int(cos(x)^n,x) assuming n::posint;
 (1.14)

 > int(sqrt(1+sqrt(x)), x);
 (2.1)
 > int(sqrt(1+sqrt(1+z)), z= 0..1);
 (2.2)
 > int(signum(z^k)*exp(-z^2), z=-infinity..infinity) assuming k::real;
 (2.3)
 > int(2*abs(sin(x*p)*sin(x)), x = 0 .. Pi) assuming p> 1;
 (2.4)
 > int(1/(x^4-x+1), x = 0 .. infinity);
 (2.5)

In Maple 2016, this multiple integral is computed over 3 times faster than it was in Maple 2015.

 > int(exp(abs(x1-x2))*exp(abs(x1-x3))*exp(abs(x3-x4))*exp(abs(x4-x2)), [x1=0..R, x2=0..R, x3=0..R, x4=0..R], AllSolutions) assuming R>0;
 (2.6)

Austin Roche
Mathematical Software, Maplesoft

## Float(undefined) as integral value...

hi.i am a problem with calculate numeric integral.

thanks

## Logarithmic equation...

Hej Mapleprimes,

I am making Maple sweat over a simple problem

11.00=11.244522435+log(x)

right click and solve for variable x.

So far Maple has been working for 10 minutes at allocatet 2 GB

Is there a short way to solve this faster?

Kind regards

Per Kirkegaard

## Problem with help to DirectSearch...

Executing HelpTools:-Database:-ConvertAll(): produced file DirectSearch.help apparently without content. How can all content within DirectSearch.hdb be converted to a .help file accessible through help in Maple 2016?

## New Thermal Engineering Applications on Application...

by: Maple 2016

Valery Ochkov and Volodymyr Voloshchuk have developed a series of thermal engineering applications in Maple 2016. The applications explore steam turbine power generation and refrigeration cycles, and use the ThermophysicalData package for fluid properties.

Their work can be found at the following locations on the Application Center.

I especially like

• this application, which optimizes the extraction pressures of a steam turbine to maximize its efficiency,
• and this application, which plots the state of a two-stage refrigeration cycle on a pressure-enthalpy chart.

using the code generator assistant I entered the following function

p := proc (z::(float[8]))

local a::integer, accm::(float[8]), k::integer, k1::(float[8]), c;
c := Array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], order = C_order, datatype = float[8]);
k1 := 1;
c[1] := evalf(sqrt(2*Pi));
a := 12;
for k to a-1 do c[k+1] := evalf(exp(a-k)*(a-k)^(k-1/2)/k1); k1 := -k1*k end do;
accm := c[1];
for k to a-1 do accm := accm+evalf(c[k+1]/(z+k)) end do;
accm := accm*evalf(exp(-z-a)*(z+a)^(z+1/2));
return accm/z
end proc

the code-generated julia code follows

function input(z)
c = [0,0,0,0,0,0,0,0,0,0,0,0]
k1 = 1
c[0] = (sqrt(2 * pi))
a = 12
for k = 1:a - 1
c[k] = (exp(a - k) * (a - k) ^ (k - 1//2) / k1)
k1 = -k1 * k
accm = c[0]
for k = 1:a - 1
accm = accm + (c[k] / (z + k))
accm = accm * (exp(-z - a) * (z + a) ^ (z + 1//2))
return(accm / z)
end

two things are wrong

1: no end after loop end

2: array index starts at 0, it should be 1 and of course the array references should reflect that

btw, it would be nice to be able to enter code tags like [code] code here [/code]