dharr

Dr. David Harrington

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19 years, 186 days
University of Victoria
Professor or university staff
Victoria, British Columbia, Canada

Social Networks and Content at Maplesoft.com

I am a professor of chemistry at the University of Victoria, BC, Canada, where my research areas are electrochemistry and surface science. I have been a user of Maple since about 1990.

same algorithm...

I didn't attempt to understand the algorithm, so really don't understand what you want. You can leave the range 0..infinity and it will be slower. If you can make a narrower range estimate it might go faster.

interpretation of pwlist...

`[0,-1,x^3,0,sin(x), (1/2)*Pi,undefined,20,undefined,20,undefined,50,undefined,50,undefined]`

0 for less than -1

x^3 between -1 and 0

sin(x) between 0 and Pi/2

undefined between Pi/2 and 20

undefined between 20 and 20, i.e., at 20: the undefined for x>Pi/2 apparently wins over the 5 at x=20 to resolve the conflict

undefined between 20 and 50 (from the x>Pi/2)

undefined between 50 and 50, i.e., at 50

undefined above 50

This does highlight that keeping 5 on your list may not be right if you want to remove all the undefined parts since Maple thinks it is undefined at x=20 and not 5. I guess the message is to be careful not to have two possible values at a point.

or zip...

zip also works with different lengths, so zip(`+`,a,b,0) rather than a+~b

bitwise operations...

@sand15 See the Bits package for bitwise operations.

Resize within a table...

If you insert a table, for example 3x3, and put some math containers in the cells, then you (or the user) can select and drag to resize in a way in which the row heights automatically resize and there is some retention of the relative positions of the embedded components. Doesn't seem to resize column widths, though the user can move the cell boundaries to do this. I haven't played much with this, so there may be table/component options which help you with this. You can hide the table borders using table/properties/Interior (or Exterior) borders, so your user doesn't see them, but they still help with alignment.

or backward sum or ......

Using a for loop to sum the terms backwards (smallest to largest) gives essentially the same error as 'add', i.e., an error of 1e-15.

In general, I expect Maple to have some algorithm, specified or not, that gives an answer within 1 or 2 in the last digit consistent with Digits. Since we know summing forward is problematic, I would trust that Maple has thought of that.

KahanSum2.mw

one term...

@Markiyan Hirnyk My implication, as stated in my earlier comment and my use of the word "partly", is that this is one term of the "standard solution" given by the OP. This is Maple's standard response for product separation of variables solutions, and only in some cases does it go further to produce the sum. I guess the user is expected to work it up as required.

Agreed...

@Markiyan Hirnyk  I agree it is not the general solution, but is a solution for the bc given. I agree _C4 is superfluous and there is no _C3, but that is what is produced!

Version...

@nm  This was version 2017.3. kernelopts(version) reports `Maple 2017.3, X86 64 WINDOWS, Sep 27 2017, Build ID 1265877` and Physics:-Version() reports "C:\Program Files\Maple 2017\lib\update.mla", `2017, September 27, 12:53 hours`.

I was looking for the solution for the specific boundary condition you gave, and one term of the Fourier series works here. If you try pdsolve without the b.c. but with the hint, then you are given the two odes to solve, which I assume can be worked up to one term of the Fourier series; the general solution is a sum of these which I think you won't get without more bc/ic conditions. The "What's new" help under PDEs suggests general series solutions can be obtained for some pdes.

remove sqrt...

it has the form sqrt(a^2+b^2), so there isn't an obvious answer here, If you think about a and b as the adjacent and opposite sides of a right triangle, then the sqrt is the length of the hypotenuse, which could be written a/cos(theta), where theta = arctan(b/a), but this is hardly a simple form.

Confusing...

@_Maxim_ I agree - it is very confusing. At least I can now understand how to make it work it all cases, for lists. I agree also that is doesn't seem to be documented. I had only ever used the multiple range notation for rtables, so had never attempted it for lists before.

Basically, a[1..3] being equivalent to a[[1,2,3]] rather than a[1,2,3] is already strange.

A consistent interpretation...

@_Maxim_  Took me a while to figure this out, since I at first couldn't explain m[1..2,2].

 > restart;

Consider first selecting multiple non-sequential elements from a list

 > a:=[q,w,e,r,t];
 (1)

We cannot select elements 1,2 and 4 by 1,2,4 becuase that is reserved for nesting.

 > a[1,2,4];

But we can do this by

 > a[[1,2,4]];
 (2)

Now the case in point

 > m := [[1, 2], [3, 4]];
 (3)

m[[1,2]][2] first finds m[[1,2]], which is elements 1 and 2 in the list (the whole list) and then takes its second element

 > m[[1,2]]; m[[1,2]][2];
 (4)

Accessing nested ones can be done by

 > m[1][2]; m[2][2];
 (5)

or by the equivalent notation

 > m[1,2]; m[2,2];
 (6)

And the range is 1..2 as the first selector means both of these

 > m[1..2,2];
 (7)

Similarly for the second selector

 > m[1,1..2]; m[1][1]; m[1][2];
 (8)
 >

Download indices.mw

Four operands for Array...

@David1 An Array has 4 operands: indexing function, dimension ranges, contents, options, which you can see by

op(sols)  or individually by op(1,sols) etc,

though there is no indexing function in this case.

local minimum...

@David1 If it fails to find the global minimum, it has found the lowest local minimum that it can.

The solutions are in an Array, so ArrayDim(sols) will return 1..31, 1..3. To get the 31 use rhs(ArrayDim(sols)[1])

diverse...

@David1 Your worksheet runs for me. DirectSearch is not a build-in package, so has to be downloaded from the cloud (for Maple 2017) or  installed from the applications centre, then I think it will run. For a general optimization problem, you could add a very sharp negative spike to the surface that was a global minimum and might be missed (see the DirectSearch:-GlobalOptima examples), but in real life you may know that your surface has some nice properties or is sufficiently smooth or is convex.

fsolve uses many different algorithms, and is likely using a more efficient method that only works for polynomials when that is the case.

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