Consider the following matrix

Q := <cos(t), sin(t)>; sin(t), -cos(t)>

If I multiply the first column by the second column (at first glance this would see to be a 2x1 column multiplied by a 2x1 column, which isn't possible), I still get a result. 

(Q[1 .. 2, 1]) . (Q[1 .. 2, 2])

Now this isn't really that big a deal. Apparently, something like Q[1 .. 2, 1] is actually a Vector, so we're actually computing the dot product between two vectors. However, the result is the following

What is the bar over the variable t?

Hello

I wonder if there is a way to parallelize the function listed below.   It deals with a set of sets (dynamical systems).  As far as I can see the problem is with subs and simplify.  In some cases a division by zero shows up (the reason I added try..catch and had to use for). 

The procedure should remove the systems with imaginary coefficients and return the valid indices.  

Many thanks

Ed

Obs.:  The number of dynamical systems can easily be greater than 10,000.  Any speed improvement is welcome.

Example of one such a dynamical system is

[(-x*rho*xi[6]*(beta - 1)*sqrt(((rho + beta - 1)*sigma - beta + 1)^2*xi[8]^2/(beta - 1)^2) - xi[8]*(-2*y*sigma*xi[7]*xi[6]^2*(beta - 1)^2 + (sigma*rho + (sigma + 1)*(beta - 1))*x*rho*xi[6] + 2*sigma*z*rho^2*xi[8]))/(2*xi[6]*xi[8]*rho*(beta - 1)), (-(beta - 1)*(-y*sigma*xi[7]*xi[6]^2*(beta - 1)^2 + rho^2*(sigma*z*xi[8] + x^2))*xi[6]*sqrt(((rho + beta - 1)*sigma - beta + 1)^2*xi[8]^2/(beta - 1)^2) - (2*sigma*(beta - 1)^2*(y*xi[7]*(rho + beta - 1)*sigma/2 + x^2*rho + y*(beta - 1)*xi[7]/2)*xi[6]^3 + 2*x*z*rho*sigma*xi[8]*(beta - 1)^2*xi[6]^2 + (-z*xi[8]*(rho + beta - 1)*sigma^2 + ((2*beta^2*z - 3*beta*z + z)*xi[8] + x^2*rho - (beta - 1)*(-2*beta*y*xi[7] + x^2))*sigma + x^2*(beta - 1))*rho^2*xi[6] + 2*x*z*rho^3*sigma*xi[8])*xi[8])/(2*xi[8]*sigma*(beta - 1)*(rho^2 + (beta - 1)^2*xi[6]^2)*xi[6]*xi[7]), (-(-x*sigma*(beta - 1)^2*xi[6]^3 + (beta - 1)^2*(sigma*y*xi[7] + x^2)*xi[6]^2 - rho^2*sigma*x*xi[6] - sigma*z*rho^2*xi[8])*(beta - 1)*rho*sqrt(((rho + beta - 1)*sigma - beta + 1)^2*xi[8]^2/(beta - 1)^2) + xi[8]*(-2*y*sigma^2*xi[7]*(beta - 1)^4*xi[6]^4 + 2*(rho*(rho + beta - 1)*sigma/2 + (beta - 1)*((-beta + 1/2)*rho + y*(beta - 1)*xi[7]))*sigma*(beta - 1)^2*x*xi[6]^3 + (beta - 1)^2*(((-y*xi[7] + 2*z*xi[8])*rho + y*(beta - 1)*xi[7])*sigma^2 + (x^2*rho + (beta - 1)*(-2*beta*y*xi[7] - 2*beta*z*xi[8] + x^2 + y*xi[7]))*sigma - x^2*(beta - 1))*rho*xi[6]^2 + 2*(rho*(rho + beta - 1)*sigma/2 + (beta - 1)*((-beta + 1/2)*rho + y*(beta - 1)*xi[7]))*sigma*x*rho^2*xi[6] + xi[8]*sigma*z*((rho - beta + 1)*sigma - beta + 1)*rho^3))/(2*xi[8]^2*sigma*(beta - 1)*rho*(rho^2 + (beta - 1)^2*xi[6]^2))]

coefmodel

{beta = 8/3, rho = 28, sigma = 10}

and phi and coe equal to 

[[], [], []]

cleanSystems := proc(sys::list,phi::list,coe::list,coefmodel::{list,set})
description "This function applies coefficient values to a system and remove it if the coef is somehow imaginary":
local i,aaa:=table(),bbb:=table(),ccc:=table(),ind:=table():
for i from 1 to nops(sys) do
  try
   aaa[i]:=simplify(subs(coefmodel,sys[i])):
   if has(aaa[i],I) then
      aaa[i]:=NULL:
      bbb[i]:=NULL:
      ccc[i]:=NULL:
      ind[i]:=NULL:
   else
      bbb[i]:=simplify(subs(coefmodel,phi[i])):
      ccc[i]:=simplify(subs(coefmodel,coe[i])):
      ind[i]:=i:
   end if:
  catch:
   aaa[i]:=NULL:
   bbb[i]:=NULL:
   ccc[i]:=NULL:
   ind[i]:=NULL:
  end try:
end do:
aaa:=convert(aaa,list):print(nops(aaa)):
bbb:=convert(bbb,list):print(nops(bbb)):
ccc:=convert(ccc,list):print(nops(ccc)):
ind:=convert(ind,list):print(nops(ind)):
return(aaa,bbb,ccc,ind):
end proc:

How to plot Nabla Discrete Mittag - Leffler Function in Maple?

For the attached worksheet "insert contents" worked two month ago. My computer settings have not changed since.

The same happens with an empty worksheet (document mode) created with 2022.2

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Unit_of_t.mw .

Download Unit_of_t.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/empty.mw .

Download empty.mw

How can we unveil all the possible transformations that reduce the number of independent variables of a given pde? I tried it by using "InvarientSolutions" which gives eight possible transformations. But under those transformations, I got only two different odes. Is there any other method/command from which we can get other possible odes of a given pde?

pde_ode.mw

The transformed boundary conditions are

Please and please, I have been having this challenge for some time now and I would be so so happy if I can get a solution to my challenge. I have been worried on:

how do I use these definitions (Volterra Integral Equation and Caputo definition) to solve

Helper, please. You can use any definition you are familiar with also. Only I need a fractional definition.

Thanks

My question is about the physics package: when transforming the metric tensor to new coordinates, sometimes the new coordinate can be expressed easily as a variable inside the new matrix entries,  but the new matrix is still displayed completely in terms of the old variables. How can I force it to display everything in terms of the new ones?

I have in internal procedure ppp that has an input prjpsn:=3. This set a Vector positions of x,y,z to either if prjpsn=1 

zpsn=1,   xpsn=2,  ypsn=3

or if prjpsn =3   

xpsn=1,   ypsn=2, zpsn=3

This then are used in another procedure. I can't get the values to transfere.  prjpsn would default to 3 in the module but can be set externally to 1 if needed.
The relevant parts are highlighted in green text. Cant get the worksheet to display.

Maple Worksheet - Errorprjpsn:=3


Failed to load the worksheet /maplenet/convert/Q_14-12-22_Module_internal_settings.mw .

Download Q_14-12-22_Module_internal_settings.mw

How do I calculate the conformal killing vectors of a metric tensor in GRTensorIII?

Why I get "Error, invalid subscript selector" error in my code?

y1 := Grid:-Seq(UP1(s, U, V, W, Phi, Xi, N, a, b, II, JJ, A, B, Dd, M, Ns), s = 1 .. 7);
UKt := add(y1[i], i = 1 .. 7);

Error, invalid subscript selector

As you can see y1 is defined without any problem and have 7 seqments, but the next line warns invalid subscript selector.

I have, for example,

> x(t) := sin(a)*cos(t) + cos(a)*sin(t)
            x := t -> sin(a) cos(t) + cos(a) sin(t)
> y(t) := combine(x(t))
            y := t -> combine(x(t))

>y(t);
            sin(a + t)

> x(t);
            sin(a) cos(t) + cos(a) sin(t)

# wanted but cannot do this: x(t) := combine(x(t))

Any workaround?

Thanks.

why does the command Matrix(2, 2, undefined) create the following

Matrix(2, 2, [[undefined(1, 1), undefined(1, 2)], [undefined(2, 1), undefined(2, 2)]])

instead of simple undefined for each item?

There is a button at the top right corner that has an icon that seems to say 4pi/3. When I hover over it is says "Maple Math". I click on it, and insert an expression that I copy directly from Maple: a simple definition of a function. There is an error that says "You have entered an invalid Maple expression". Why? The function is defined as z__1 := (x,y) -> x+y. Perhaps the issue is the subscript. I don't know but the UI does not tell me.

Here is an example that does not give an error in the form when I click the aforementioned "Maple Math" button. However, what I see below is a broken icon and the equation f := (x,y) -> x + y (exactly like this).

I am bewildered by the brokenness of this UI. 

Example: After manipulating the following indefinite integral

Int(r^2, m)

I want to add ranges before evaluating the integral (for display purposes I keep the innert form). The op command or the IntegrationTools can be used for that (disassembling the expression and assembling it to new int expression) but require quite long code. Isn’t there a shorter  way to simply add ranges to the integration variable.

Update: Download Add_range.mw