## Undesired expansion in solving...

In working on an answer to a recent question on MaplePrimes:
http://mapleprimes.com/questions/210948-Can-We-Trust-Maple

I noticed that in solving a "simple" system of two equations in two unknowns, potentially undesirable expansion occurs.
The two equations were only simple in the sense that the solving was very trivial, since the two unknowns occurred (almost) already isolated on the left:
eq1:=diff(x(t),t)=rhs1;
eq2:=1.2345*diff(v(t),t)=rhs2; #rhs2 is very complicated in the link given.
So in isolating I tried:
solve({eq1,eq2},{diff(x(t),t),diff(v(t),t)});
The resulting ode system took considerably longer to solve numerically than an unexpanded version.
It is trivial (of course) to do the solving without solve in this case.

Here is an extremely simple example, where the unknowns are already isolated, so that the equations themselves are actually the solution.

restart;
eq1:=a=b*(c+d);
solve(eq1,a); #No expansion
eq2:=e=b*(c+d)+f*(8+k);
solve({eq1,eq2},{a,e}); #Expanded:
{a = b*c+b*d, e = b*c+b*d+f*k+8*f}

Can expansion be avoided?

## Can this be simplified from a given rule...

Hello there,

I want to simplify this for a given rule in Maple

(-(1/2)*ib-(1/2)*ia+ic)*vc+(-(1/2)*ia-(1/2)*ic+ib)*vb+(-(1/2)*ic-(1/2)*ib+ia)*va

rule :  ia+ib+ic=0

A desired result should be

3/2*ic*vc+3/2*ib*vb+3/2*ia*va

but I can't apply this rule in Maple...  it seems like recursive and goes back again and again.

Can it break the recursive routine and make it as a desired result?

Thank you

## Fitting of surface from matrix data...

Hey guys,

I want to fit experimental data and I was wondering if there is a special PolynomialFit function for a surface.

My data consist of a X,Y, Matrix of densities and I want to have a function describing the surface of the values. On matlab the following code will do so:

[x, y, z] = prepareSurfaceData(temps, concs, densities);
ft = fittype('poly33');
fitresult = fit([x, y], z, ft);

Maybe that gives you a better view of what I want.

Best regards

Before version 2016 Maple was incredibly good at evaluating an infinite power series and returning a simple function, e.g. 1/(3x+2).  Now version 2016 just returns the input sum expression with no change.  Is there some new command to get the old results?

## 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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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