## Plot3d: How do I can draw a polynomial approximati...

Hi!

I want to plot the approximation of a surface by polynomials. The surface is given by (x,y,f(x,y)) where f(x,y) is given by the following expression

proc (x) options operator, arrow; (sum(i*cos((i+1)*(-2+4*x[1])+i), i = 1 .. 5))*(sum(i*cos((i+1)*(-2+4*x[2])+i), i = 1 .. 5)) end proc

with both variables varying in the interval [0,1]. Then, by using the Bernstein polynomials of two variables (see, for instance, this paper for details  https://www.sciencedirect.com/science/article/pii/0021904589900956), the graph of the resulting (plot3d) surface (x,y,p(x,y))  it is not even like to the original surfaces.

Please, see this PDF of what I have done:  plots.pdf

Some idea or suggestion?

Thanks!

## Error in creating array using loop...

I am trying to create an array whose elements are from another matrix. Suppose I have a matrix of n cross m dimension my array will have a dimension of 1 cross n*m. When I create  array I am getting error. The array contains only last element of matrix. The expected answer is given in attachment.

sigma.mw

## How to input "exprseq" type in Maplet?...

im trying to input this variable with value structure

```> xxx := x[2, 0], x[2, 1], x[2, 2], x[1, 0], x[1, 1]

```

check the type

```> whattype(xxx);
exprseq
```

but when i try to use Get tools from maplets package, its give me error

```> xxx:=Get`('xxx1'::exprseq)
invalid argument(s): xxx1::exprseq
```

is it possible to passing exprseq from maplet input into procedure?
or is there another way to input it (xxx) ?

You are please to check maple file:    robust_rev1.mw

case close, many thanks @tomleslie and @vv

## guess vector in fsolve...

Hello.

Can you please tell how the guess vector is defined in Newton's method in "fsolve" if not set initial interval for unknowns? Maybe someone knows what "norm of errors", "new norm" and "incr" in "infolevel[fsolve]" are?

Thanks!

## Killing vectors problem...

Could anyone explain why Maple doesn't calculate the Killing vectors for the metric below?

## The one way of rolling surface. Rolling without...

by: Maple 17

On the convex part of the surface we place a curve (not necessarily flat, as in this case). We divide this curve into segments of equal length (in the text Ls [i]) and divide the path that our surface will roll (in the text L [i]) into segments of the same length as segments of curve. Take the next segment of the trajectory L [i] and the corresponding segment on the curve Ls [i], calculate the angles between them. After that, we perform well-known transformations that place the curve in the space so that the segment Ls [i] coincides with the segment L [i]. At the same time, we perform exactly the same transformations with the equation of surface.

For example, the ellipsoid rolls on the oX1 axis, and each position of the ellipsoid in space corresponds to the equation in the figure.
Rolling_of_surface.mw

And similar examples:

## parametric algebraic equation involving more than ...

Hi

I want to solve quadratic eqution involving more than 2 parameters...want to analize unique soltuions and real roots also want to plot the real and unique region on graphs ....thanx

the equation is -delta*(Q*S*alpha*b-a*alpha^2+M*c+b*delta) where alpha is the varible and rest are paramters

## Get the "union" of a list of "intervals"...

Hello,

Assume we have the following "intervals" (I am not sure what is its formal name in Maple)

C :=[0,1/11],[1/11,1/9],[1/9, 1/7],[1/3,1/2],[1/2,1]

How can we get the "union" of these intervals? That is to say, obtain  [0,1/7],[1/3,1]

## Choose a number according to a probability distrib...

Hello!

Assume we have the first N positive integres, 1,..,N, and we assing to these numbers a (discrete) probability distribution p1,...,pN. Of course, p1+...+pN=1.

Then, How can we select a number in {1,..,N} according to the given probability distribution? That is, the number 1 can be chosen with probability p1, 2 with a probability p2, etc.

## How to save Maple variables from worksheet...

Hello everyone, i've a problem working with Maple because i have a really big system of equations and for everything that i have to do with them, for example, collect terms, coefficients, take a lot of time from me. The problem it is when, for example, i wait 30 minutes to take the coefficients from a equation and in the next command Maple might stop, then i have to close and start all over again... My question it is if have anyway to save my file in a way that if i close and re open i dont have to compile all again. Maybe this is pretty obvious but i really dont know how to do it, because if i close my work and open again, i have to compile everything again.

## How to build this model to solve in maple?...

I need to build this model:
We consider a population of female salmon, they live 4 years. Survival for first three years respectively: 0.5%,7%,15%. Each salmon has female kids only in 4 year and produces 5000 female offspring

## How to remove zeros from output?...

Hello

If 0 occurs in the first element, I want to remove the list containing zero and the associated number.

example

p := [[[0, 5], [3, 10], [1, 20], [0, 50]], [[2, 5], [0, 10], [2, 20], [0, 50]]]

after processing:

[[[3, 10], [1, 20]], [[2, 5], [2, 20]]]

I tried in vain...

select(i -> (subs(p,p[1,i,1])>0), [\$1..nops(p)]);

## Do not have a working activation code for Maple17....

Do not have a working activation code for Maple17.  Have these 2, but neither works.
Y3KKTP32PLF9PXFU

 ZJLL59SMMXQSE8MU

I am running Ubuntu 18 (linux).

Thanks

Tom Vawter

(John Vawter)

## Rolling of cube without slipping.

by: Maple 17

We produce only one rotation of the cube by the angle Pi/2, and then repeat it at the following points, changing the colors of the faces in turn. And so the illusion is created that the cube is rolling along a straight line without slipping.
(Just a picture without any sense.) cube_without_slipping.mw

## Problem to solve an ODE (probably a singularity)...

Hello,

I am trying to plot 2 equations divided in 3 intervals (tini..tr, tr..te, te..tfin1), but when i try to solve the first equation it appears:

"Warning, cannot evaluate the solution further left of .66099564e18, probably a singularity"

Is it possible avoid this point?

About the second equation, when i try to solve between "te and tr" the program says that the argument is invalid.

Can someone help me?

Here is the program:

restart;

Digits := 20;

M := 0.122e20*0.152e25;
kappa := evalf(sqrt(8*Pi/M^2));
rrhoCC := 0.769e-41*(0.1e-28*0.561e24)*0.152e25^4;

rrhoM0 := 0.1e51;
rrhoR0 := 0;
rrhoM := proc (t) options operator, arrow; rrhoM0/a(t)^3 end proc;
rrhoR := proc (t) options operator, arrow; rrhoR0/a(t)^4 end proc;
pM := proc (t) options operator, arrow; 0 end proc;
eq1 := diff(a(t), t) = a(t)*kappa*sqrt(rrhoM(t)+rrhoCC)/sqrt(3);
eq2 := 2*(diff(a(t), t, t)) = -(1/3)*kappa^2*(rrhoM(t)+3*pM(t)-2*rrhoCC)*a(t);
tini := 0.1e19;
sys1 := {eq1, a(tini) = 1.0};
sys2 := {eq2, a(tini) = 1.0, (D(a))(tini) = 0.284e-17};
with(DEtools);
with(plots);
tfin1 := 0;
te := 10^(-32);
tr := 10^12;
singularities(eq1, a(t));
singularities(eq2, a(t));
p1a := dsolve(sys1, type = numeric, abserr = 10^(-15), relerr = 10^(-15), range = tini .. tr);
p1b := dsolve(sys1, type = numeric, abserr = 10^(-10), relerr = 10^(-10), range = tr .. te);
p1c := dsolve(sys1, type = numeric, abserr = 10^(-10), relerr = 10^(-10), range = te .. tfin1);
fig1a := odeplot(p1a, [t, a(t)]);
fig1b := odeplot(p1b, [t, a(t)]);
fig1c := odeplot(p1c, [t, a(t)], color = red);
display(fig1a, fig1b, fig1c);
p2a := dsolve(sys2, type = numeric, abserr = 1.*10^(-12), relerr = 1.*10^(-12), range = tfin1 .. te);
p2b := dsolve(sys2, type = numeric, abserr = 1.*10^(-12), relerr = 1.*10^(-12), te .. tr);
p2c := dsolve(sys2, type = numeric, abserr = 1.*10^(-12), relerr = 1.*10^(-12), range = tr .. tini);
fig2a := odeplot(p2a, [t, a(t)], color = green);
fig2b := odeplot(p2b, [t, a(t)], color = green);
fig2c := odeplot(p2c, [t, a(t)], color = green);
display(fig2a, fig2b, fig2c);
display(fig1a,fig2a,fig1b,fig2b,fig1c,fig2c);

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