## Summation procedure involving multiplication and l...

Hi everyone again

This one is linked to my previous 2 question.

Essentially I am trying to use a procedure to reproduce the formula:

S(j) = (1 + sum(H_j*T_j,j=1..n))/(1 + sum(1/(H_j*T_j),j=1..n))

BigProc:= proc(H::list,T::list)
local Form, i;
Form:=[];
for i from 1 to nops(H) do
Form := [op(Form),(1 + [sum(H[1..i]*~T[1..i],i=1..5)])/~(1 + [sum(1/~(H[1..i]*~T[1..i]),i=1..5)])]
end do:
end proc:
MainProc([1,3,5],[3,6,8])

Error, (in sum) summation variable previously assigned, second argument evaluates to 1 = 1 .. 5

The actual answer should be (3, 396/25,22320/509)

ie

S(1) = (1+ 3)/(1+(1/3)) = 3

S(2) = (1 +(3+18))/(1+1/3 + 1/18)) = 396/25

S(3) = (1 +(3+18+40))/(1+1/3 + 1/18 +1/40) = 22320/509

I feel like I am missing a few things to my procedure. Any help would be greatly appreciated!

## Sorting a list based on another list...

Hi

This question may have been asked before but I cannot find it!

I am currently have 3 lists:

L:= [1,3,5,2,3]

M:=[4,2,4,6,2]

R:= [5,3,2,1,4]

I would like to be able to come up with a way (I assume a procedure) where I can order L and M based on the numerical order of R. So in this case that would be:

R:=[1,2,3,4,5]

L:=[2,5,3,3,1]

M:=[6,4,2,2,4]

I hope this makes sense? Any help would be greatly appreciated!

## How can I improve this use of DirectSearch?...

The uploaded worksheet animates a cam formed of two Archimedean spirals as the cam rotates, creating vertical motion in a circular cam follower.

DirectSearch is used to locate the centre of the follower, however I experience two problems with this use.

First: DirectSearch places the follower centre sometimes above and sometimes below the cam surface, seemingly at random.

Second: seemingly at random, DirectSearch produces completely wrong values for the follower centre unless its SolveEquations command is executed with the initialpoint values stated in the worksheet. I arrived at these by extensive trial and error.

Why does the first problem occur and is there a way to code SolveEquations to avoid it?

Is there a writeup anywhere which can guide me to correct initialpoint values for a particular SolveEquations attempt?

Archimedian_spiral_cam_follower.mw

## maple can not integrat an expression...

I can not integrate the following integral using maple 2016. Please guide me how to do it. I am a new user.

int(12.*x^3*c[2]+6.*x^2*c[1]+x^2*exp(x^3*c[2])*exp(x^2*c[1]), x = 0. .. 1.)

## Why Maple does not simplify...

Why Maple does not simplify to 1

beta^(1/2)*(1+beta^(1/2))/(beta+beta^(1/2))

## How do I collect & match polynomial coefficients f...

I have several functional equations in equally many unknown functions of at least two variables, plus parameters.  ("collect" works just for single equations, right?)

I know that for certain parameter ranges, all the functions involved will be quadratic, and I know some coefficients are zero.  That gives me some  coefficients to determine.  I want to

1. specify the functional equations [done in a very primitive low-tech way in the attachment, using atomic variables rather than indices ... have I done correctly?!?]
2. get Maple to collect coefficients (the K's and the L's in the attachment; the variables are (y,z))
3. get Maple to state an equation system these coefficients have to satisfy (these will unfortunately be coupled quadratics)
4. get Maple to solve that equation system if possible, and if not: to tell me when (= for what parameter values, parameters being the "remaining letters" in the attachment) I have specified enough coefficients
5. in case of a solution, get Maple to tell me which coefficients are real and positive (for those that are solution of quadratic eq's: whether a positive solution exists)

Phew. I am still a complete newbie. Edit: Attachment link: STcoeff2match.mw where the equations themselves are EQ0, EQ1 and EQ2 at the bottom. Copying and pasting them, they look like this (download STcoeff2pastedEQs.mw)

 >

 >

## How I can plot a square ...

Dear All, If I have a square with lenght b and width 2a

.The question is how can I make Maple plot this square as points

.I want to define a function f(x_[i],y_[i]) for all sides.

Thanks

## How to substitute this transformation in the given...

restart;
with(PDEtools);
assume(k::real, x::real, omega::real, t::real, theta::real, c::real);
tr0 := c*(t*upsilon+x) = xi;
tr1 := I*(k*x+omega*t+theta);
tr2 := phi(lhs(tr0))*exp(tr1);
PDE := proc (u) options operator, arrow; I*(diff(u, t))+diff(u, x, x)-I*sigma*u*(conjugate(u)*(diff(u, x))-u*(diff(conjugate(u), x))) end proc;
Eq1 := PDE(tr2);
Eq2 := simplify(convert(expand(subs(tr0, Eq1)), diff));

for_maple_prime.mw

## How do i solve a partial differential equation wit...

restart;
with(PDEtools);
assume(k::real, x::real, omega::real, t::real, theta::real, c::real);
u := phi(c*(t*upsilon+x))*exp(I*(k*x+omega*t+theta));
PDE := proc (u) options operator, arrow; I*(diff(u, t))+diff(u, x, x)-I*sigma*u*(conjugate(u)*(diff(u, x))-u*conjugate(diff(u, x))) end proc;
Eq1 := PDE(u)

## Building a Package Error...

Hi everyone.

I am trying to build a package in Maple out of a bunch of procedures that I have. To create the procedures, I write them on a Vim editor, than copy and paste into the Maple worksheet to test. In this way, it works (I end the procedure with ; and then I see all the text in blue and I afterwords test it).

I then gathered these procedures to a module, option package, and I do the same: edit on Vim, copy paste it to Maple worksheet and press enter to see a blue message "module() ... end module" in blue, and then I start playing.

However, I decided to add some more procedures to the module that was working. I have a new procedure that works (meaning when I copy to the worksheet it gives the blue text and I can call normally), but when I copy the contents of this new procedure inside the package, with all the others, and I copy everything to the worksheet, the package now fails to work. It gives a message "Error," in pink, no more text, and that is it. Does this sort of error sound familiar to anyone? Thanks in Advance,

Marcelo

## Where is my error ???...

I wrote this simple set of instructions  (Maple 2015 and Maple 2016)

restart:
p := x -> sum('a__||k' * x^k, k=0..5):
p(x);    # returns a0+ a1x +  ... + a5x5

p(1);   # returns a0+ ... + a5

p(0);   # returns 0 ...  not a0

Probably so huge a mistake that I can't see it !?!?!?

TIA

## Error, index out of bounds...

I have a problem with writing this equation in maple.

the equation is:

I want to write this equation in maple, so I write it in this way:

for k from 1 to 7 do tau[k] := add*(d(k, j)*(diff(theta[j](t), t, t)), j = 1 .. 7)+add(add(c[i, j, k]*(diff(theta[i](t), t))*(diff(theta[j](t), t)), j = 1 .. 7), i = 1 .. 7)+phi[k] end do:

but I see this error: Error, index out of bounds

I appriciate if you help me find the problem.

## How do I reduce this in Maple?...

Good day. Please can someone kindly help to reduce the result of this code. Thank you and kind regards

```restart:
s:=(sum(a[j]*x^j,j=0..3)+sum(a[j]*exp(-(j-3)*x),j=4..7)):
F:=diff(s,x):
p1:=simplify(eval(s,x=q))=y[n]:
p2:=simplify(eval(F,x=q))=f[n]:
p3:=simplify(eval(F,x=q+h/3))=f[n+1/3]:
p4:=simplify(eval(F,x=q+h))=f[n+1]:
p5:=simplify(eval(F,x=q+5*h/3))=f[n+5/3]:
p6:=simplify(eval(F,x=q+2*h))=f[n+2]:
p7:=simplify(eval(F,x=q+7*h/3))=f[n+7/3]:
p8:=simplify(eval(F,x=q+3*h))=f[n+3]:

vars:= seq(a[i],i=0..7):
Cc:=eval(<vars>, solve({p||(1..8)}, {vars})):
for i from 1 to 8 do
a[i-1]:=Cc[i]:
end do:
Cf:=s:
L:=collect(simplify(simplify(expand(eval(Cf,x=q+3*h)),size)), [y[n],f[n],f[n+1/3],f[n+1],f[n+5/3],f[n+2],f[n+7/3],f[n+3]], factor):
length(L);
H := ee -> collect(numer(ee),[exp],h->simplify(simplify(h),size))/collect(denom(ee),[exp],h->simplify(simplify(h),size)):
M:=y[n+3]=(H@expand)(L);
length(M);```

## curious behavior, simplify vs. factor...

> S:=-1/2*((-30*sqrt(3)+81*I)^(2/3)+21+2*sqrt(3)*(-30*sqrt(3)+81*I)^(1/3)-6*(-30*sqrt(3)+81*I)^(1/3)+I*sqrt(3)*(-30*sqrt(3)+81*I)^(2/3)-21*I*sqrt(3))/(-30*sqrt(3)+81*I)^(1/3);

When I enter

simplify(S);

a not much simpler expression involving arctan is output
but when I enter

factor(S);

the expected simplification to the number

3

is output.

This is not a but report, just a report of curious behavior.

I am using Maple 2016 on a Windows 10 PC.

 First 12 13 14 15 16 17 18 Last Page 14 of 58
﻿