Carl Love

## 26852 Reputation

11 years, 303 days
Himself
Wayland, Massachusetts, United States
My name was formerly Carl Devore.

## replace unapply with op@unapply...

@Adri van der Meer I had considered the one-to-many situation. I was thinking that solve should detect the one-to-one case and remove the brackets. But maybe not; perhaps they should remain because they will be expected. So here's a way to remove the brackets that can deal with either situation: just replace unapply with op@unapply.

`f:= x-> piecewise(x<1, x, x-1): solve(f(x)=y, x): g:= op@unapply(%, y):g(2);                               3g(1/2);                              3  1                              -, -                              2  2`

## replace unapply with op@unapply...

@Adri van der Meer I had considered the one-to-many situation. I was thinking that solve should detect the one-to-one case and remove the brackets. But maybe not; perhaps they should remain because they will be expected. So here's a way to remove the brackets that can deal with either situation: just replace unapply with op@unapply.

`f:= x-> piecewise(x<1, x, x-1): solve(f(x)=y, x): g:= op@unapply(%, y):g(2);                               3g(1/2);                              3  1                              -, -                              2  2`

## Long titles...

Please don't make the titles of your Questions so long. A fine title for your Question would've been "How to neglect 1/c^n terms, n > 2?". You tend to put the entire body of your Question in the title.

## Incomplete Question...

Your Question seems incomplete. Did you mean to say more?

How about some commentary to accompany your solution? What is the significance of the 0.64 and 73? Why do the solutions only have 2 or 3 digits?

Your C is essentially -infinity, putting the sum to 0 and thereby making B irrelevant. So the solution curve is essentially a straight line through the origin, which looks like a decent fit on a plot.

I be interested to see how DataFit performs with sample data actually produced by the function.

How about some commentary to accompany your solution? What is the significance of the 0.64 and 73? Why do the solutions only have 2 or 3 digits?

Your C is essentially -infinity, putting the sum to 0 and thereby making B irrelevant. So the solution curve is essentially a straight line through the origin, which looks like a decent fit on a plot.

I be interested to see how DataFit performs with sample data actually produced by the function.

## So what?...

So what? That's just a basic mathematical fact.

## By solve...

`solve(% = 0, alpha0);                           1           1                       0, - ----------, ----------                            (1/2)       (1/2)                       (-k2)       (-k2)     `

## By solve...

`solve(% = 0, alpha0);                           1           1                       0, - ----------, ----------                            (1/2)       (1/2)                       (-k2)       (-k2)     `

## Yes. Note the C in particular....

@Markiyan Hirnyk Yes, I noticed. I also notice that your C is exactly 1.0, whereas mine is 0.99997. The smallest value of x is 1.0, so it makes sense that it would be 1.0. The reason that mine is 0.99997 is that z = 0.00003 is nearly the smallest positive z for which Maple will numerically evaluate the infinite sum. Unfortunately, `evalf/Sum` does not have any option equivalent to the digits or epsilon option of `evalf/Int`, so there's no way to get extra guard digits and changing Digits won't help that. This is a drawback of my method.

`evalf(Sum(exp(-.00003*n^2)/n^2, n= 1..infinity));                        1.63524093728545evalf(Sum(exp(-.00002*n^2)/n^2, n= 1..infinity));                    infinity                                     -----                                        \        /          2\                       )    exp\-0.00002 n /                      /     ----------------                     -----          2                            n = 1         n        evalf(%% - Pi^2/6);                       -0.00969312956278`

## Yes. Note the C in particular....

@Markiyan Hirnyk Yes, I noticed. I also notice that your C is exactly 1.0, whereas mine is 0.99997. The smallest value of x is 1.0, so it makes sense that it would be 1.0. The reason that mine is 0.99997 is that z = 0.00003 is nearly the smallest positive z for which Maple will numerically evaluate the infinite sum. Unfortunately, `evalf/Sum` does not have any option equivalent to the digits or epsilon option of `evalf/Int`, so there's no way to get extra guard digits and changing Digits won't help that. This is a drawback of my method.

`evalf(Sum(exp(-.00003*n^2)/n^2, n= 1..infinity));                        1.63524093728545evalf(Sum(exp(-.00002*n^2)/n^2, n= 1..infinity));                    infinity                                     -----                                        \        /          2\                       )    exp\-0.00002 n /                      /     ----------------                     -----          2                            n = 1         n        evalf(%% - Pi^2/6);                       -0.00969312956278`

## How to format mono-spaced...

@mriedel To cut-and-paste mono-spaced content, first place your text cursor at the beginning of a blank line where you want the content to start. Then use the pull-down menu labelled "Paragraph" from the top toolbar of the MaplePrimes editor. Select the third item, "Preformatted". Then paste the content. The content will looked messed up in the editor, but Preview will show it properly spaced.

This process will automatically convert a "cut" of Maple 2d output (prettyprint=2) to mono-spaced 2d form (prettyprint=1).

## Problem doesn't seem fully specified...

The problem doesn't seem fully specified. Perhaps other details were given in the class notes? maybe a diagram?

If I were to write code for this I'd need to know

1. Is the reactor considered a single point? Can we think of all the neutrons as emanating from the origin (0,0) with an initial direction up the y-axis? or all four axial directions?
2. Where is the shield? I see that its size is specified, but not its location. Is the shield immediately surrounding the reactor? Or is there empty space in between?
3. What shape is the shield? Is it a circle around the reactor?
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