@Carl Love 

Dear Sir,

I tested well with deg=12 and like you I have a factor 4.

But to use your very delicate formula in capital letters, i specify again, as you ignored it, that by excessively increasing the degree of the polynomial and the number of data processed, we will inevitably end up with a discrepancy. But what is the operational benefit of going from 31 ms to 120 ms ?

So academically you are right. It's likely that with older processors Horner was very useful. But today, allow me to express doubts.

Have a nice day.

@Carl Love 

Thank you. Thats ok with a polynom with degree=64 and nData=2^12. But are such degrees so often manipulated ?

If there are no operational examples in number, with polynomials of degrees around 100, Horner's method remains in my eyes of rather academic interest.

@Carl Love 

Thank you for your response as well as to all the other contributors.

With your example I don't have the same results as you.

Rh := CodeTools:-Usage(map(Ph, Data));
memory used=33.38KiB, alloc change=0 bytes, cpu time=0ns, real time=0ns, gc time=0ns

gc(); R := CodeTools:-Usage(map(P, Data));
memory used=33.23KiB, alloc change=0 bytes, cpu time=0ns, real time=0ns, gc time=0ns

I still think the performance gap is not very significant, unless you take very, very high degree polynomials. And again, with degrees at 200 the difference is around 10^-2.

@C_R 

Thanks for your answer and all the others.
I note that there is no simple solution and that finally a re-writing by hand of the factorization is also fast.

@acer 

Thank you very much for your help. I thought that the use of a dedicated command could be enough !

Best regards.

@vv 

Thank you for your answer but it was not the question. The question was how to transform the initial expression with 5/3 in factor and (1/3)^k in the sum ?

@TechnicalSupport 

With the 2021.1 update, the problem is solved for me.

However, there is still a display problem. Some icons in the menu bar disappear. It is necessary to hover over the area with the mouse to make them appear. (Resolution : 3840x2160).

Hello,

I also have the same type of problem. The drawing bar does not always appear when clicking on a figure. Sometimes even, when it is present, it is impossible to return to drawing a line without an arrow if we had previously drawn an arrow.

Finally, this display issue also occurs with menu icons. You have to hover with the mouse to make them appear again.

All these display problems were not present in the 2020 version.

@Aliocha 

Hello Mr Richard,

This is not a Maple error but an error for my part. I ended up finding this to be the wrong choice of vectors. We must calculate :

A1 := LineInt(VectorField(<f, -g>), Arc(Circle(<0, 0>, r), 0, Pi)); and

A2 := LineInt(VectorField(<g, f>), Arc(Circle(<0, 0>, r), 0, Pi));

Indeed we have : f(z)*dz=(f+i*g)(dx+i*dy)=(f*dx-g*dy)+i*(g*dx+f*dy) so

@vv 

Yes, absolutely, this is the easiest method. But I am preparing an educational sheet to show how we can calculate the Dirichlet integral (sin(z)/z) using the residue theorem and the function exp(iz)/z. We calculate the curvilinear integral on the large circle; passage to the limit in infinity. Ditto for the small circle with crossing the limit at zero.

@vv 

It is indeed about the direct computation by the curvilinear interval. But I thought that the LineInt function offered an alternative by following the proposed lace.

Dirichlet_et_LineInt.mw@Thomas Richard 

Thank you for your answer. I made the changes you suggested to me. But that doesn't change anything.