Ronan

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10 years, 107 days
East Grinstead, United Kingdom

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These are replies submitted by Ronan

@Carl Love Can you explain what index means in relation to solve? 

@Carl Love You are correct.  It took me a while to remenber the syntax to use.

 Interesting problem.  So I gather there are "s" nested summation loops. I asked a question a few months ago that required with a variable number of summation loops. @Carl Love answered it.

Is it possible to Add/sum by mapping multiple values from a list - MaplePrimes

So just to clarify can t[j] and t[i]  be replaced with T[j] , T[i] to totaly distinguish them from t?

I presume the inputs are M and s.

 Edit:-On problems like this a I start with small values for s and M and build the nested summations/products to handle them before trying for the total solution. I attach  document to see if my begining intrepertations are correct.


 

restart

NULL

`#mover(mi("l"),mo("˜"))` := proc (t) options operator, arrow; sum(beta[j, s]*t^(M-1-s), s = 0 .. M-1) end proc

proc (t) options operator, arrow; sum(beta[j, s]*t^(M-1-s), s = 0 .. M-1) end proc

(1)

eval(`#mover(mi("l"),mo("˜"))`(t), M = 5)

t^4*beta[j, 0]+t^3*beta[j, 1]+t^2*beta[j, 2]+t*beta[j, 3]+beta[j, 4]

(2)

T[j], T[i] := j/(M-1), i/(M-1)

j/(M-1), i/(M-1)

(3)

beta[j, 0] := 1/((product(T[j]-T[i], i = 0 .. j-1))*(product(T[j]-T[i], i = j+1 .. M-1)))

(-1)^(j+1)*(1/(M-1))^(j+1)/(GAMMA(j+1)*(M-1)^(-j)*(-1)^M*GAMMA(-j+M)*(1/(M-1))^M)

(4)

eval(beta[j, 0], [M = 5, j = 3])

-128/3

(5)

``

eval(`#mover(mi("l"),mo("˜"))`(t), [M = 5, j = 3])

t^4*beta[3, 0]+t^3*beta[3, 1]+t^2*beta[3, 2]+t*beta[3, 3]+beta[3, 4]

(6)

``


 

Download 28-3-22_A_repetative_summation.mw

 

@Ali2020 The document stated "I do not know how you achieved your resuls". As they are listed vertically they could come from a loop. That is all.

@max125 Opps.. I post my revised answer here. Makes the answer simpler.

restart

with(RealDomain)

[Im, Re, `^`, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctanh, cos, cosh, cot, coth, csc, csch, eval, exp, expand, limit, ln, log, sec, sech, signum, simplify, sin, sinh, solve, sqrt, surd, tan, tanh]

(1)

f := proc (x) options operator, arrow; 6-sqrt(-x^2+8*x+9) end proc

proc (x) options operator, arrow; 6-RealDomain:-sqrt(-RealDomain:-`^`(x, 2)+8*x+9) end proc

(2)

g := unapply(diff(f(x), x), x)

proc (x) options operator, arrow; -(1/2)*(-2*x+8)/(-x^2+8*x+9)^(1/2) end proc

(3)

plot([f(x), g(x)])

 

``

 

 

L := int(f(x), x = 0 .. l)

-6-(25/2)*arcsin(4/5)+6*l-(1/2)*(-l^2+8*l+9)^(1/2)*l+2*(-l^2+8*l+9)^(1/2)-(25/2)*arcsin((1/5)*l-4/5)

(4)

l := fsolve(L = 10)

6.810993081

(5)

L

21.59119024-(25/2)*arcsin(4/5)

(6)

evalf(%)

10.00000002

(7)

NULL

Download 23-3-22_A1_integration.mw

@nm I would just install over it.  Only when I have a big problem do I "clean" a program out of a computer.

@dharr Oh.  I didn't realist that about view. Very simple.

@vv Yes I hit that. Couldnt fix it so I copied and pasted the answer.

@Carl Love Answer is much neater.

@dharr , @tomleslie   Thanks. I had tried Null. Forgot about the all caps.

 

@Carl Love That is good. My old attempt cripples the graphics on the computer.

@acer Excellent diagnosis That looks like what happened.  I will fix it during the week and let you know.

So, in this case ooes the "DirectSearch.mla" now contain the DirectSearch, RationalTrigonometry and RonanRoutines packages?

@Joe Riel  Thank you. I don't understand whay this result is returned. The screen shot shows what is in the returned location.

See attached file on what I did.  AFIK. the mla files are in different locations; based on what I could find. I gave the different folders' locations in the question. 
 

restart

LibraryTools:-FindLibrary(RationalTrigonometry)

"C:\Users\Ronan\maple\toolbox\personal\lib\DirectSearch.mla"

(1)

LibraryTools:-FindLibrary(RonanRoutines)

"C:\Users\Ronan\maple\toolbox\personal\lib\DirectSearch.mla"

(2)

NULL

NULL


 

Download Find_Library.mw

 

@mmcdara Thank you. Very detailed.  The matrix is built of 3 projective points [x,y,z]. Well I was trying to see if the determinalt =0. That would imply the points are colinear. I was trying last night to normailse them to [x/z,y/z,1], but even that was to much. If I could that would reduce the determinant multiplication greatly. e.g 

det=a_11*(a22-a23)-a12*(a21-a23)+a13*(a21-a22)

I will check tonight and see if the z points have a common factor.

I totally understand your point about unreadable hugh expressions.

Don't know if this is another variant of the problem but the other night was trying to upload and display a document with a 3D plot and  it just wouldn't happen. 4 attempts. Eventually just gave up on displaying the document to get answer posted. How to plot this complex function? - MaplePrimes 

@acer Yes. that is true. I just left the borders turned on to highlight to bounded area. 

Edit:- I just put the document as a url link on my start page. I don't use it all the time..

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