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Ronan

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12 years, 194 days
East Grinstead, United Kingdom
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Maple 2022.1...

Ronan 1197
July 31 2022
0 0

@Christian Wolinski I have hilighted what I thing look odd to me

(add@map)(proc(E) ``(lcoeff(E))*normal(E/lcoeff(E)) end@add, [Q(expand(pn))]);

Very efficient....

Ronan 1197
July 31 2022
0 0

@Carl Love Thank you.

I noticed the '' what does it do...

Ronan 1197
July 31 2022
0 0

@Christian Wolinski  Thank you.. Idid notice the '' no idea what they do.
I had tried end proc but it is the @dd I don't get either.

 

Works! Can you Explain?...

Ronan 1197
July 30 2022
0 0

@Christian Wolinski Thank you. That produces the lists nicely. I admit I don't understand the ListTools part of the code. Could you please explain it? I did look in the Help on it but right now don't quite get it.
  There is some error  in the last line of the code.  I presume it is intended to maintain the order of the lists under addition.


 

restart

pn := expand((a[1]+a[2]+a[3]+a[4])^5)

a[1]^5+5*a[1]^4*a[2]+5*a[1]^4*a[3]+5*a[1]^4*a[4]+10*a[1]^3*a[2]^2+20*a[1]^3*a[2]*a[3]+20*a[1]^3*a[2]*a[4]+10*a[1]^3*a[3]^2+20*a[1]^3*a[3]*a[4]+10*a[1]^3*a[4]^2+10*a[1]^2*a[2]^3+30*a[1]^2*a[2]^2*a[3]+30*a[1]^2*a[2]^2*a[4]+30*a[1]^2*a[2]*a[3]^2+60*a[1]^2*a[2]*a[3]*a[4]+30*a[1]^2*a[2]*a[4]^2+10*a[1]^2*a[3]^3+30*a[1]^2*a[3]^2*a[4]+30*a[1]^2*a[3]*a[4]^2+10*a[1]^2*a[4]^3+5*a[1]*a[2]^4+20*a[1]*a[2]^3*a[3]+20*a[1]*a[2]^3*a[4]+30*a[1]*a[2]^2*a[3]^2+60*a[1]*a[2]^2*a[3]*a[4]+30*a[1]*a[2]^2*a[4]^2+20*a[1]*a[2]*a[3]^3+60*a[1]*a[2]*a[3]^2*a[4]+60*a[1]*a[2]*a[3]*a[4]^2+20*a[1]*a[2]*a[4]^3+5*a[1]*a[3]^4+20*a[1]*a[3]^3*a[4]+30*a[1]*a[3]^2*a[4]^2+20*a[1]*a[3]*a[4]^3+5*a[1]*a[4]^4+a[2]^5+5*a[2]^4*a[3]+5*a[2]^4*a[4]+10*a[2]^3*a[3]^2+20*a[2]^3*a[3]*a[4]+10*a[2]^3*a[4]^2+10*a[2]^2*a[3]^3+30*a[2]^2*a[3]^2*a[4]+30*a[2]^2*a[3]*a[4]^2+10*a[2]^2*a[4]^3+5*a[2]*a[3]^4+20*a[2]*a[3]^3*a[4]+30*a[2]*a[3]^2*a[4]^2+20*a[2]*a[3]*a[4]^3+5*a[2]*a[4]^4+a[3]^5+5*a[3]^4*a[4]+10*a[3]^3*a[4]^2+10*a[3]^2*a[4]^3+5*a[3]*a[4]^4+a[4]^5

Q := proc (E) local X; if type(E, `+`) then X := ([op])('E') else X := ['E'] end if; ListTools:-Categorize(proc (x, y) lcoeff(x) = lcoeff(y) end proc, X) end proc

proc (E) local X; if type(E, `+`) then X := ([op])('E') else X := ['E'] end if; ListTools:-Categorize(proc (x, y) lcoeff(x) = lcoeff(y) end proc, X) end proc

Q(pn)

[a[1]^5, a[2]^5, a[3]^5, a[4]^5], [5*a[1]^4*a[2], 5*a[1]^4*a[3], 5*a[1]^4*a[4], 5*a[1]*a[2]^4, 5*a[1]*a[3]^4, 5*a[1]*a[4]^4, 5*a[2]^4*a[3], 5*a[2]^4*a[4], 5*a[2]*a[3]^4, 5*a[2]*a[4]^4, 5*a[3]^4*a[4], 5*a[3]*a[4]^4], [10*a[1]^3*a[2]^2, 10*a[1]^3*a[3]^2, 10*a[1]^3*a[4]^2, 10*a[1]^2*a[2]^3, 10*a[1]^2*a[3]^3, 10*a[1]^2*a[4]^3, 10*a[2]^3*a[3]^2, 10*a[2]^3*a[4]^2, 10*a[2]^2*a[3]^3, 10*a[2]^2*a[4]^3, 10*a[3]^3*a[4]^2, 10*a[3]^2*a[4]^3], [20*a[1]^3*a[2]*a[3], 20*a[1]^3*a[2]*a[4], 20*a[1]^3*a[3]*a[4], 20*a[1]*a[2]^3*a[3], 20*a[1]*a[2]^3*a[4], 20*a[1]*a[2]*a[3]^3, 20*a[1]*a[2]*a[4]^3, 20*a[1]*a[3]^3*a[4], 20*a[1]*a[3]*a[4]^3, 20*a[2]^3*a[3]*a[4], 20*a[2]*a[3]^3*a[4], 20*a[2]*a[3]*a[4]^3], [30*a[1]^2*a[2]^2*a[3], 30*a[1]^2*a[2]^2*a[4], 30*a[1]^2*a[2]*a[3]^2, 30*a[1]^2*a[2]*a[4]^2, 30*a[1]^2*a[3]^2*a[4], 30*a[1]^2*a[3]*a[4]^2, 30*a[1]*a[2]^2*a[3]^2, 30*a[1]*a[2]^2*a[4]^2, 30*a[1]*a[3]^2*a[4]^2, 30*a[2]^2*a[3]^2*a[4], 30*a[2]^2*a[3]*a[4]^2, 30*a[2]*a[3]^2*a[4]^2], [60*a[1]^2*a[2]*a[3]*a[4], 60*a[1]*a[2]^2*a[3]*a[4], 60*a[1]*a[2]*a[3]^2*a[4], 60*a[1]*a[2]*a[3]*a[4]^2]

map(add, [Q(expand(pn))])

[a[1]^5+a[2]^5+a[3]^5+a[4]^5, 5*a[1]^4*a[2]+5*a[1]^4*a[3]+5*a[1]^4*a[4]+5*a[1]*a[2]^4+5*a[1]*a[3]^4+5*a[1]*a[4]^4+5*a[2]^4*a[3]+5*a[2]^4*a[4]+5*a[2]*a[3]^4+5*a[2]*a[4]^4+5*a[3]^4*a[4]+5*a[3]*a[4]^4, 10*a[1]^3*a[2]^2+10*a[1]^3*a[3]^2+10*a[1]^3*a[4]^2+10*a[1]^2*a[2]^3+10*a[1]^2*a[3]^3+10*a[1]^2*a[4]^3+10*a[2]^3*a[3]^2+10*a[2]^3*a[4]^2+10*a[2]^2*a[3]^3+10*a[2]^2*a[4]^3+10*a[3]^3*a[4]^2+10*a[3]^2*a[4]^3, 20*a[1]^3*a[2]*a[3]+20*a[1]^3*a[2]*a[4]+20*a[1]^3*a[3]*a[4]+20*a[1]*a[2]^3*a[3]+20*a[1]*a[2]^3*a[4]+20*a[1]*a[2]*a[3]^3+20*a[1]*a[2]*a[4]^3+20*a[1]*a[3]^3*a[4]+20*a[1]*a[3]*a[4]^3+20*a[2]^3*a[3]*a[4]+20*a[2]*a[3]^3*a[4]+20*a[2]*a[3]*a[4]^3, 30*a[1]^2*a[2]^2*a[3]+30*a[1]^2*a[2]^2*a[4]+30*a[1]^2*a[2]*a[3]^2+30*a[1]^2*a[2]*a[4]^2+30*a[1]^2*a[3]^2*a[4]+30*a[1]^2*a[3]*a[4]^2+30*a[1]*a[2]^2*a[3]^2+30*a[1]*a[2]^2*a[4]^2+30*a[1]*a[3]^2*a[4]^2+30*a[2]^2*a[3]^2*a[4]+30*a[2]^2*a[3]*a[4]^2+30*a[2]*a[3]^2*a[4]^2, 60*a[1]^2*a[2]*a[3]*a[4]+60*a[1]*a[2]^2*a[3]*a[4]+60*a[1]*a[2]*a[3]^2*a[4]+60*a[1]*a[2]*a[3]*a[4]^2]

(`@`(add, map))(add, [Q(expand(pn))])

a[1]^5+5*a[1]^4*a[2]+5*a[1]^4*a[3]+5*a[1]^4*a[4]+10*a[1]^3*a[2]^2+20*a[1]^3*a[2]*a[3]+20*a[1]^3*a[2]*a[4]+10*a[1]^3*a[3]^2+20*a[1]^3*a[3]*a[4]+10*a[1]^3*a[4]^2+10*a[1]^2*a[2]^3+30*a[1]^2*a[2]^2*a[3]+30*a[1]^2*a[2]^2*a[4]+30*a[1]^2*a[2]*a[3]^2+60*a[1]^2*a[2]*a[3]*a[4]+30*a[1]^2*a[2]*a[4]^2+10*a[1]^2*a[3]^3+30*a[1]^2*a[3]^2*a[4]+30*a[1]^2*a[3]*a[4]^2+10*a[1]^2*a[4]^3+5*a[1]*a[2]^4+20*a[1]*a[2]^3*a[3]+20*a[1]*a[2]^3*a[4]+30*a[1]*a[2]^2*a[3]^2+60*a[1]*a[2]^2*a[3]*a[4]+30*a[1]*a[2]^2*a[4]^2+20*a[1]*a[2]*a[3]^3+60*a[1]*a[2]*a[3]^2*a[4]+60*a[1]*a[2]*a[3]*a[4]^2+20*a[1]*a[2]*a[4]^3+5*a[1]*a[3]^4+20*a[1]*a[3]^3*a[4]+30*a[1]*a[3]^2*a[4]^2+20*a[1]*a[3]*a[4]^3+5*a[1]*a[4]^4+a[2]^5+5*a[2]^4*a[3]+5*a[2]^4*a[4]+10*a[2]^3*a[3]^2+20*a[2]^3*a[3]*a[4]+10*a[2]^3*a[4]^2+10*a[2]^2*a[3]^3+30*a[2]^2*a[3]^2*a[4]+30*a[2]^2*a[3]*a[4]^2+10*a[2]^2*a[4]^3+5*a[2]*a[3]^4+20*a[2]*a[3]^3*a[4]+30*a[2]*a[3]^2*a[4]^2+20*a[2]*a[3]*a[4]^3+5*a[2]*a[4]^4+a[3]^5+5*a[3]^4*a[4]+10*a[3]^3*a[4]^2+10*a[3]^2*a[4]^3+5*a[3]*a[4]^4+a[4]^5

" (add@map)(proc(E) (lcoeff(E))*normal(E/lcoeff(E)) end@add, [Q(expand(pn))]); #`some typo here end@add, Don't know how to correct at present`"

Error, invalid proc termination

" (add@map)(proc(E) (lcoeff(E))*normal(E/lcoeff(E)) end@add, [Q(expand(pn))]); #`some typo here end@add, Don't know how to correct at present`"

Just my experimentation

([op])(pn)

[a[1]^5, 5*a[1]^4*a[2], 5*a[1]^4*a[3], 5*a[1]^4*a[4], 10*a[1]^3*a[2]^2, 20*a[1]^3*a[2]*a[3], 20*a[1]^3*a[2]*a[4], 10*a[1]^3*a[3]^2, 20*a[1]^3*a[3]*a[4], 10*a[1]^3*a[4]^2, 10*a[1]^2*a[2]^3, 30*a[1]^2*a[2]^2*a[3], 30*a[1]^2*a[2]^2*a[4], 30*a[1]^2*a[2]*a[3]^2, 60*a[1]^2*a[2]*a[3]*a[4], 30*a[1]^2*a[2]*a[4]^2, 10*a[1]^2*a[3]^3, 30*a[1]^2*a[3]^2*a[4], 30*a[1]^2*a[3]*a[4]^2, 10*a[1]^2*a[4]^3, 5*a[1]*a[2]^4, 20*a[1]*a[2]^3*a[3], 20*a[1]*a[2]^3*a[4], 30*a[1]*a[2]^2*a[3]^2, 60*a[1]*a[2]^2*a[3]*a[4], 30*a[1]*a[2]^2*a[4]^2, 20*a[1]*a[2]*a[3]^3, 60*a[1]*a[2]*a[3]^2*a[4], 60*a[1]*a[2]*a[3]*a[4]^2, 20*a[1]*a[2]*a[4]^3, 5*a[1]*a[3]^4, 20*a[1]*a[3]^3*a[4], 30*a[1]*a[3]^2*a[4]^2, 20*a[1]*a[3]*a[4]^3, 5*a[1]*a[4]^4, a[2]^5, 5*a[2]^4*a[3], 5*a[2]^4*a[4], 10*a[2]^3*a[3]^2, 20*a[2]^3*a[3]*a[4], 10*a[2]^3*a[4]^2, 10*a[2]^2*a[3]^3, 30*a[2]^2*a[3]^2*a[4], 30*a[2]^2*a[3]*a[4]^2, 10*a[2]^2*a[4]^3, 5*a[2]*a[3]^4, 20*a[2]*a[3]^3*a[4], 30*a[2]*a[3]^2*a[4]^2, 20*a[2]*a[3]*a[4]^3, 5*a[2]*a[4]^4, a[3]^5, 5*a[3]^4*a[4], 10*a[3]^3*a[4]^2, 10*a[3]^2*a[4]^3, 5*a[3]*a[4]^4, a[4]^5]

[op(pn)]

[a[1]^5, 5*a[1]^4*a[2], 5*a[1]^4*a[3], 5*a[1]^4*a[4], 10*a[1]^3*a[2]^2, 20*a[1]^3*a[2]*a[3], 20*a[1]^3*a[2]*a[4], 10*a[1]^3*a[3]^2, 20*a[1]^3*a[3]*a[4], 10*a[1]^3*a[4]^2, 10*a[1]^2*a[2]^3, 30*a[1]^2*a[2]^2*a[3], 30*a[1]^2*a[2]^2*a[4], 30*a[1]^2*a[2]*a[3]^2, 60*a[1]^2*a[2]*a[3]*a[4], 30*a[1]^2*a[2]*a[4]^2, 10*a[1]^2*a[3]^3, 30*a[1]^2*a[3]^2*a[4], 30*a[1]^2*a[3]*a[4]^2, 10*a[1]^2*a[4]^3, 5*a[1]*a[2]^4, 20*a[1]*a[2]^3*a[3], 20*a[1]*a[2]^3*a[4], 30*a[1]*a[2]^2*a[3]^2, 60*a[1]*a[2]^2*a[3]*a[4], 30*a[1]*a[2]^2*a[4]^2, 20*a[1]*a[2]*a[3]^3, 60*a[1]*a[2]*a[3]^2*a[4], 60*a[1]*a[2]*a[3]*a[4]^2, 20*a[1]*a[2]*a[4]^3, 5*a[1]*a[3]^4, 20*a[1]*a[3]^3*a[4], 30*a[1]*a[3]^2*a[4]^2, 20*a[1]*a[3]*a[4]^3, 5*a[1]*a[4]^4, a[2]^5, 5*a[2]^4*a[3], 5*a[2]^4*a[4], 10*a[2]^3*a[3]^2, 20*a[2]^3*a[3]*a[4], 10*a[2]^3*a[4]^2, 10*a[2]^2*a[3]^3, 30*a[2]^2*a[3]^2*a[4], 30*a[2]^2*a[3]*a[4]^2, 10*a[2]^2*a[4]^3, 5*a[2]*a[3]^4, 20*a[2]*a[3]^3*a[4], 30*a[2]*a[3]^2*a[4]^2, 20*a[2]*a[3]*a[4]^3, 5*a[2]*a[4]^4, a[3]^5, 5*a[3]^4*a[4], 10*a[3]^3*a[4]^2, 10*a[3]^2*a[4]^3, 5*a[3]*a[4]^4, a[4]^5]

({op})(pn)

{a[1]^5, a[2]^5, a[3]^5, a[4]^5, 5*a[1]*a[2]^4, 5*a[1]*a[3]^4, 5*a[1]*a[4]^4, 10*a[1]^2*a[2]^3, 10*a[1]^2*a[3]^3, 10*a[1]^2*a[4]^3, 10*a[1]^3*a[2]^2, 10*a[1]^3*a[3]^2, 10*a[1]^3*a[4]^2, 5*a[1]^4*a[2], 5*a[1]^4*a[3], 5*a[1]^4*a[4], 5*a[2]*a[3]^4, 5*a[2]*a[4]^4, 10*a[2]^2*a[3]^3, 10*a[2]^2*a[4]^3, 10*a[2]^3*a[3]^2, 10*a[2]^3*a[4]^2, 5*a[2]^4*a[3], 5*a[2]^4*a[4], 5*a[3]*a[4]^4, 10*a[3]^2*a[4]^3, 10*a[3]^3*a[4]^2, 5*a[3]^4*a[4], 20*a[1]*a[2]*a[3]^3, 20*a[1]*a[2]*a[4]^3, 30*a[1]*a[2]^2*a[3]^2, 30*a[1]*a[2]^2*a[4]^2, 20*a[1]*a[2]^3*a[3], 20*a[1]*a[2]^3*a[4], 20*a[1]*a[3]*a[4]^3, 30*a[1]*a[3]^2*a[4]^2, 20*a[1]*a[3]^3*a[4], 30*a[1]^2*a[2]*a[3]^2, 30*a[1]^2*a[2]*a[4]^2, 30*a[1]^2*a[2]^2*a[3], 30*a[1]^2*a[2]^2*a[4], 30*a[1]^2*a[3]*a[4]^2, 30*a[1]^2*a[3]^2*a[4], 20*a[1]^3*a[2]*a[3], 20*a[1]^3*a[2]*a[4], 20*a[1]^3*a[3]*a[4], 20*a[2]*a[3]*a[4]^3, 30*a[2]*a[3]^2*a[4]^2, 20*a[2]*a[3]^3*a[4], 30*a[2]^2*a[3]*a[4]^2, 30*a[2]^2*a[3]^2*a[4], 20*a[2]^3*a[3]*a[4], 60*a[1]*a[2]*a[3]*a[4]^2, 60*a[1]*a[2]*a[3]^2*a[4], 60*a[1]*a[2]^2*a[3]*a[4], 60*a[1]^2*a[2]*a[3]*a[4]}

NULL


 

Download 30-7-22_Q_sort_equation_by_numerical_coeffs_ver_2.mw

Clearly I misinterpreted the question....

Ronan 1197
July 22 2022
0 0

@Ronan Sorry about that! 

Thank You...

Ronan 1197
July 13 2022
0 0

@Carl Love Ok so I see now.  Just tested it this way

(f, (E, V) -> V)(expand(A), exp(T))  gives  f(A, exp(T)), exp(T)

 

Can you explain......

Ronan 1197
July 12 2022
0 0

@Christian Wolinski Very nice solution. I don't quite get the technicality of the (E,V)->V So E=expand(A) and V =exp(T) in this case and somehow (solve,((E,V)->V))(expand(A),exp(T))  includes exp(T) in the answer.   I notice the " , " after solve and the enclosing (....) are necessary.  I did check through help but didn't see an explination. Of course maybe I missed that.

Edit:- I see that (E,V)->V))(expand(A),exp(T)   is eqivalent to 

f := (E, V) -> V;

f(expand(A), exp(T));

Solve Index Meaning?...

Ronan 1197
June 13 2022
0 0

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

True...

Ronan 1197
May 28 2022
0 0

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

This might help you....

Ronan 1197
March 28 2022
0 0

 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

 

not serious, an example...

Ronan 1197
March 26 2022
0 0

@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.

Thank you....

Ronan 1197
March 23 2022
0 0

@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

shouldn't need to uninstall...

Ronan 1197
March 16 2022
0 0

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

Nice....

Ronan 1197
March 14 2022
0 0

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

I Know...

Ronan 1197
March 14 2022
0 0

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

@Carl Love Answer is much neater.

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