achreftabet

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@Kitonum 

please 

how  Classification of equilibrium points in R^3

@Scot Gould 

i did not understand this step

@Kitonum 

hi

What is the difference between Maple 18 and Maple 2018

@Scot Gould 

thank you for answering my questions about the sum
I have another problem in the compilations

Sum_vs_Add_(1).mw
 

restart; randomize():

Define S and test it:

 

S := n -> sum( sum( a[i, j]*x^i*y^j, j = 0..n-i), i=0..n);

proc (n) options operator, arrow; sum(sum(a[i, j]*x^i*y^j, j = 0 .. n-i), i = 0 .. n) end proc

(1)

S(2);

x^2*a[2, 0]+x*y*a[1, 1]+y^2*a[0, 2]+x*a[1, 0]+y*a[0, 1]+a[0, 0]

(2)

Define A and test it:

A := n -> add( add( a[i,j]*x^i*y^j, j=0..n-i), i=0..n);

proc (n) options operator, arrow; add(add(a[i, j]*x^i*y^j, j = 0 .. n-i), i = 0 .. n) end proc

(3)

A(2);

x^2*a[2, 0]+x*y*a[1, 1]+y^2*a[0, 2]+x*a[1, 0]+y*a[0, 1]+a[0, 0]

(4)


Assign values random values to the elements  in the array `a`. (i have problem)

N := 10:
a := Array(0..N, 0..N, (i,j)->rand(-1.0..1.0)())

Warning, inserted missing semicolon at end of statement

 

Error, invalid input: rand expects its 1st argument, r, to be of type {posint, integer .. integer}, but received -1.0 .. 1.0

 

 

Problem: te

sting S with n = 2.

S(2);

x^2*a[2, 0]+x*y*a[1, 1]+y^2*a[0, 2]+x*a[1, 0]+y*a[0, 1]+a[0, 0]

(5)

Hmm, no longer symbolic.

 

As opposed to A:

A(2);

x^2*a[2, 0]+x*y*a[1, 1]+y^2*a[0, 2]+x*a[1, 0]+y*a[0, 1]+a[0, 0]

(6)

S can't be plotted even if the function is delayed:

plot3d( 'S(10)', x=0..1, y=0..1)

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

 

 

But this does work.

newS := (x,y,n) -> sum( sum( a[i, j]*x^i*y^j, j = 0..n-i), i=0..n);

proc (x, y, n) options operator, arrow; sum(sum(a[i, j]*x^i*y^j, j = 0 .. n-i), i = 0 .. n) end proc

(7)

plot3d('newS(x,y,10)', x=0..1, y=0..1);

 

A behaves as a I would expect.

plot3d(A(10), x=0..1, y=0..1)

 

 


 you can calculate this sum by this program

-2 + x - xy + x2 + 2 y2
 

Download Sum_vs_Add_(1).mw

 

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