9 years, 93 days

## Definition of roll is not necessary...

@petit loup    @acer

Sample(Normal(0, 1), [n, n])

## @Jamie128  So do you say that z = ...

@Jamie128

So do you say that z = -2*M^2*sin(theta)^2 - 2*k*r^2?
What you need, I repeat myself, is a function r(theta, z) plot3d(r(theta, z), theta = a .. b, z = c .. d, coords = cylindrical)
and this expression of z doesn't make r uniquely defined:

```restart
z = -2*M^2*sin(theta)^2 - 2*k*r^2;
r =~ [solve(%, r)]
```

## plot3d, coords (cylindrical) help page:...

it is said that

For alternate coordinate systems this is interpreted differently. For example, when using cylindrical coordinates, Maple expects the command to be of the following form: plot3d(r(theta, z), theta = a .. b, z = c .. d, coords = cylindrical)

What are r(theta, z) and z in your expression -2*M^2*sin(theta)^2 - 2*k*r^2?

Do you mean z = -2*M^2*sin(theta)^2 - 2*k*r^2?

What does your claim "where the function is greater than zero and where it is less that zero" mean given that ehe radius (r?) is to be always greater or equal to 0.

To complete @Christian Wolinski 's reply: f can be integrated provided alpha is an integer <= 1.
I guess that the reason why the WhittakerM function

In the attached file you will see that the integration can be done only (that's my hunch, not a mathematical proof) when
WhittakerM(a, b, 3/2*t) can be converted into elementary functions.
(
Maybe there exist some recurrence relation to integrate int(h(t)*WhittakerM(a, b, 3/2*t) , t), but I wasn't capable to find any.
More precisely I thought that one could take advantage that

```diff(WhittakerW(p, q, 3/2*t), t);
/          3  \
WhittakerW |p + 1, q, - t|
3 /1   2 p\             /      3  \              \          2  /
- |- - ---|  WhittakerW |p, q, - t| - -------------------------
2 \2   3 t/             \      2  /               t

```

).

When alpha is an integer > 1, the denominator GAMMA(2-alpha)=0 and f is undefined.

Whittaker.mw

## @mz6687 I'm sorry, but I don...

@mz6687

I'm sorry, but I don't understand a single word of what you're saying.
What is this 8x8 matrix you are now talking about?

BTW: is it you who deleted your last question or was it moved by someone else?

Whatever, is this new thread isrelated to this one https://www.mapleprimes.com/questions/237066-Determinant-The-System-Hangs, you would better keep this discussion goin in this latter thread.

## Are you ok with that?...

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 (1)
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 (2)
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 > para_0 := [H__14 =0.3, H__33 = 1.5, H__38 = 0.15, H__44 = 1.5]; print(): para_1 := remove((x -> is(x in lhs~(para_0))), [entries(H, nolist)]) =~ 0; print(): para := [para_0[], para_1[], c__1 = 0.5, nu = 1, alpha__1 = 1.5, alpha__2 = 1, lambda__1 = 0.58*I, lambda__2 = 0.68*I]
 (3)
 > B1_para    := eval(B1, para); detB1_para := Determinant(B1_para)
 (4)
 > H_para := eval(H, para): # Given that B_para := 'H_para . B1_para'; # one gets: detH_para := Determinant(H_para); detB_para := detB1_para . detH_para:
 (5)
 > # One possible simplification whynot := simplify(combine(detB_para, exp)) assuming real; whynot := convert(whynot, trig)
 (6)
 >

## @mz6687  Sorry, I don't unders...

@mz6687

Sorry, I don't understand what you say

## Other question......

@mz6687

Your initial question was "Can Maple solve the determinant of the 9x9 matrix? "
I showed you the answer was YES.

Now you are talking about something else.
But you missed a point: in the reference you mention the matrix had a particular shape and depended only on 6 quantities

`{v__11, v__12, v__21, v__22, lambda__1, lambda__2}`

So the expression of its determinant was potentially simplifiable (and indeed was).

Your matrix B is dense and depends on 81 indeterminates (not only 6) meaning  there is no possible simplification between terms.
Using simplify or collect, for instance, will be a dead end.

Things could be completely different if all the m[i, j] were expressions involving a few number of independent quantities.

BTW: what does "solve the determinant" mean to you?

## @acer You're right, I edited by...

@acer

You're right, I edited my answer consequently.

## @Traruh Synred I know how to use Hi...

I know how to use Histogram, but I want to plot binned data!

Can you please give an example of those binned data and of the original data instead of speaking in the void?

For one thing, a Histogram requires a large list of each data point and is thus a memory hog, and each time you make a histogram Histogram loops through the data for the quantity, and if you make it for a related quantity you have to loop again.

That is totally unclear, can you provide an example?

## @AHSAN Your claim that "each c...

@AHSAN

Your claim that "each curve have their maximum point at some vale of x" is obviously wrong (last figure on my last file on forst figure in For_reference.mw ... soom around the peaks).
and not consistent with your need "to obsrvse that difference in percentage at the maximum value of x
" at the same time (if x is a constant as you before claimed it was it' difference in percentage is 0).

I hope you'll find someone better able than me to understand the subtleties of your question.
For my part, I'm done with you.

## @AHSAN  I still don't underst...

@AHSAN

I still don't understand what is your criterion to assess this relative increase/decrease:

• Is this criterion the height of the peak?

• You taught before of "enlargement"; is your criterion the peak width at some conventional height?

• Is this criterion one of those I use in my first file?

Whatever, the case here is an example based on the peak height
Could_It_Be_This_2.mw

## @AHSAN My mistake, this phrase abou...

My mistake, this phrase about "a loop" is indeed an error.

It's likely  I didn't understand correctelyyour question.
I understood you wanted to compite the decrease/increase of the eights of the peaks.

What do you mean by "the decrease or incease in percentage between curves" ?
If you this

```A_ref := eval(A, lambda = 1.3015):
data_1 := [beta=0.1, Q=1.3015, lambda=0.9986];
B_1    := eval(B, data_1):
plot((B_1-A_ref)/A_ref*100, x=-4..0)```

you get a curve which represents the relative variation of B_1 wrt A_ref, but this is a function x.
So do you want a number or an algebraic expression or a curve

Could_It_Be_This.mw

## @dharr Right, I didn't pay atte...

Right, I didn't pay attention to that.

## In ths Search window...

type "SIR  model" and click on Search

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