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These are replies submitted by Kitonum

@Stretto   I did not study all these options in detail, but I just offered you another way in which you first find all these points, and then consciously delete them. Of course, you yourself must choose the approach that you like best.

As for me, I always try to choose an approach where I clearly understand what is happening and it is easy for me to manage what is happening.

@Carl Love  Your code does not work in Maple 2018.2 and in older versions, at least since Maple 2015.

@Carl Love  Have you checked if this works?

r:= t->[t, t^2, t^3];


@ActiveUser  If I understand correctly, then you can just take the arithmetic mean of any neighboring numbers.
For your example:

sourcesamples :=[evalf(-1-sqrt(7)), -2, 1, evalf(-1 + sqrt(7)), 2];
samples:=sort(convert({ceil(sourcesamples[1])-1, seq(op([sourcesamples[i],(sourcesamples[i]+sourcesamples[i+1])/2,sourcesamples[i+1]]), i=1..n-1),floor(sourcesamples[n])+1},list),(x,y)->evalf(x)<evalf(y));



@ActiveUser  I am not familiar with all this issue.


1. You can use the  op  command for this: 

Sol:=solve(a*x^2 + b*x + c=0, x, parametric=true, real);

2. I do not know the commands from this package and have never used it.

@Carl Love I do not understand what your doubts are based on. As for the work of the value procedure, I would call it not an error, but simply an unsuccessful design. The essence of the problem is that this procedure does not calculate any derivatives (but only the values of the functions themselves from the system), and returns  0  for any derivatives. Of course, it would be better if in the case of derivatives, it returns the input unevaluated or returns an error message. I believe that spacestep and timestep options are not connected in any way with this problem.

Compare the angular coefficients of the tangents at  y = 0  with the numerical results (this to some extent confirms the correctness of the results):

a := 0.7: L := 8: HAA := [0, 2, 5, 10]: h:=0.001:
PDE1 := diff(u(y, t), t) = diff(u(y, t), y, y)+diff(diff(u(y, t), y, y), t)-b*u(y, t)+T(y, t):
PDE2 := diff(T(y, t), t) = (1+(1+(a-1)*T(y, t))^3)*(diff(T(y, t), y, y))+(a-1)*(1+(a-1)*T(y, t))^2*(diff(T(y, t), y))^2+T(y, t)*(diff(T(y, t), y, y))+(diff(T(y, t), y))^2:
ICandBC := {T(L, t) = 0, T(y, 0) = 0, u(0, t) = t, u(L, t) = 0, u(y, 0) = 0, (D[1](T))(0, t) = -1}:
for i from 1 to nops(HAA) do
b := HAA[i];
pds[i] := pdsolve({PDE1,PDE2}, ICandBC, numeric);
end do:
seq(A[i], i=1..4);
plots:-display(< `<|>`(seq(pds[i]:-plot(u(y,t), y=0..3, t=1, scaling=constrained),i=1..4))>);



If you need a procedure, then do so (I just rewrote vv's code as a procedure):

Squares:=(M,N)->plots:-display(seq(seq(plottools:-polygon([[m,n],[m+1/2,n+1/2],[m+1,n],[m+1/2,n-1/2]], color=`if`(m::odd,red,blue)), m=0..M),n=0..N), axes=none, scaling=constrained):

Examples of use:


sys := [x^2 + y^2 - x*y - 1 = 0, y^2 + z^2 - y*z - a^2 = 0, z^2 + x^2 - x*z - b^2 = 0]:
solve(eval(sys,ab), explicit):

           {x = 6.676479229-2.966007548*I, y = 5.939434090+4.226624806*I, z = 12.50085790+.1379423560*I}, {x = -6.676479229+2.966007548*I, y = -5.939434090-4.226624806*I, z = -12.50085790-.1379423560*I}, {x = 6.676479229+2.966007548*I, y = 5.939434090-4.226624806*I, z = 12.50085790-.1379423560*I}, {x = -6.676479229-2.966007548*I, y = -5.939434090+4.226624806*I, z = -12.50085790+.1379423560*I}, {x = .1989718373, y = 1.084528494, z = 10.49807685}, {x = -.1989718373, y = -1.084528494, z = -10.49807685}, {x = 1.141952419, y = .4227976407, z = -9.781889234}, {x = -1.141952419, y = -.4227976407, z = 9.781889234}

Or even simpler:

sys := [x^2 + y^2 - x*y - 1 = 0, y^2 + z^2 - y*z - a^2 = 0, z^2 + x^2 - x*z - b^2 = 0]:

Output is the same.

@abdgafartunde  Instead of column matrices, it is better to use vectors.

See the toy example:

N:= 5:
A:=<1,2; 3,4>;
b:=<1, 2>;  C:=<1, 1>;

for i from 0 to N do
      x[i+1] := A%.((i^2+1)*b) + C;


@abdgafartunde  I meant that in the same way, you can assign a name to each output, and then refer to these names when necessary.

@Ahmed111  See update to my answer above. The commands  diff  and  Physics:-diff  calculate any derivatives, both ordinary and partial. See help on these commands.

@Carl Love  See update to my answer. Compare my result with yours. 

@Scot Gould  Thank you for this!  I did not know that Maple solves systems written in vector form.

@amirhadiz  The  Interpolation  package appeared only in the latest versions of Maple. You have an older version, but you can use the code from my answer.

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