@Carl Love Your two answers was didactic for me. The second one was moreover very intersting. But because I am intersted in providing a view from the supremum of the plots, fixing its color with e.g. "color = green" improves my requirement.

However, the @Kitonum 's answer has the facility of avoiding an extra function (display). So, we may improve your answer and Kitonum's to have:

plotter:=(ab::range, n::posint)->plot([seq(sin(m*x), m = 1 .. 2, (op(1, ab)-`-`(op(ab)))/(n-1))], x = -Pi .. Pi):

plotter(1 .. 2, 20)

Thanks so much to both of you!

@Kitonum Tnx! It is exactly what I need! However, the modified version of your 3D idea (modified orientation) proposed by @Carle_Love is the most interesting one that by fixing the color will be like your recent answer (without having the step option).

Moreover, I have provided a mixture of your and Carle_Love's answer as a comment under his reply.

@Kitonum Thanks for your answer. However, unfortunately it does not fit my current requirement. However, I fortunately found the answer.

@Christopher2222 Thanks!

Dear @Markiyan Hirnyk 

I had experienced the rational one before posting; but, I posted this for requesting Maple to upgrade the simplification code so that when a simple short float is used, it converts the formula to rational automatically. The completely exact results is a special feature that I have seen only in Maple. So, I suggest your team to upgrade. But as you say I think that Maple 18 has upgraded the simplification.

maple 

ali := (1/3)*c[1]*x/(x+1)+.1

is a smaller example for which simplify(ali-simplify(ali)) is not zero but if we replace ali by

ali := (1/3)*c[1]*x/(x+1)+1/10

the result of simplify(ali-simplify(ali)) would be zero.

Dear @Markiyan Hirnyk,

Thanks for submitting the SCR.

Best regards

Sorry, this was my problem for several days. But, just as I asked I found the answer. I should set partition for this method and not iteration because this method is not iterative.

Best,

In the name of God,

Dear Markiyan Hirnyk,

Thanks for your answer.

About your post scriptum(P.S): please see my comments for dear Mac Dude:

http://www.mapleprimes.com/questions/139159-Summerized-Diefinition

Best wishes

In the name of God,

Dear Markiyan Hirnyk,

Thanks for your answer.

About your post scriptum(P.S): please see my comments for dear Mac Dude:

http://www.mapleprimes.com/questions/139159-Summerized-Diefinition

Best wishes

In the name of God

Dear Carl,

Thanks for your reply. It doesn't solve even for Digits=15 and also for fulldigits option.

It may interests you, Accidently I removed this instruction

wiht(Student[NumericalAnalysis]);

And, ran the code again, there was no problem remained!

Again thank you for the reply

Hossayni

In the name of God

Dear Carl,

Thanks for your reply. It doesn't solve even for Digits=15 and also for fulldigits option.

It may interests you, Accidently I removed this instruction

wiht(Student[NumericalAnalysis]);

And, ran the code again, there was no problem remained!

Again thank you for the reply

Hossayni

Dear @Mac Dude ,

Really Thanks for your useful answer

I tested and debugged what you suggest and it satisfied my need successfully.

The debugged and changed code is this:

assign(seq(cat('v', convert(i, 'string')) = Vector(i), i = 1 .. 5));

Again thank you very much for your responds.

Sincerely yours

Hossayni

Dear @Mac Dude ,

Really Thanks for your useful answer

I tested and debugged what you suggest and it satisfied my need successfully.

The debugged and changed code is this:

assign(seq(cat('v', convert(i, 'string')) = Vector(i), i = 1 .. 5));

Again thank you very much for your responds.

Sincerely yours

Hossayni

In the name God

Dear Mac,

I want to define numerous distinct vectors using one command.

In some programmin language it may be so:

v1,v2,v3,...,v10:=Vector(3):

Or:

v1:=v2:=...:=v10:=Vector(3):

Thanks for your useful command. But the +~ operator does not do this.

Sincerely yours

Hossayni