[Edit: a general procedure based on these ideas is given below.]

Maple's isolve can solve some but not all of the quadratic equations in two variables describing the conic sections. Here I show that by transforming the equations, Maple can then solve these missing cases.

Download DiophantineConics2.mw

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How can I use an if statement inside a do - loop in maple and then plot a figure based on the conditional results? I need help with the correct syntax for combining the do-loop, `if` condition, and plotting command.

Sheet attached below:
Algorithmm.mw

Hi,
I want to have a colorbar aside the curve, but I can't. (My Maple version is 2018).

restart:
with(plots):

# --- constants ---
qc := 0.4:
qh := 0.64:
alpha := 0.8:

# --- parameter ranges ---
deltac_min := 0.01: deltac_max := 0.99:
Tch_min := 0.1:     Tch_max := 1.1:

# --- numerical safety ---
epsDen := 1e-12:
Mcap := 3.0: # cap to avoid infinity

# --- denominator ---
Den := (deltac, Tch) ->
       -2*Tch*deltac*qh - 2*Tch*deltac + 2*Tch*qh
       + 2*deltac*qc + 2*Tch + 2*deltac:

# --- safe functions ---
M1safe := (deltac, Tch) ->
    piecewise(Den(deltac,Tch) > epsDen,
              min(2/sqrt(Den(deltac,Tch)), Mcap),
              Mcap):

M0safe := (deltac, Tch) ->
    piecewise(Den(deltac,Tch) > epsDen,
              min(2*alpha/sqrt(Den(deltac,Tch)), Mcap),
              Mcap):

# --- density plots ---
p1 := densityplot(
       M1safe(deltac,Tch),
       deltac = deltac_min .. deltac_max,
       Tch   = Tch_min .. Tch_max,
       grid  = [200,200],
       style = patchnogrid,
       colorstyle = HUE,
       axes = boxed,
       labels = ["δ_c", "T_ch"],
       title = sprintf("M1(δ_c, T_ch)  (capped at %.2f)", Mcap)
     ):

p2 := densityplot(
       M0safe(deltac,Tch),
       deltac = deltac_min .. deltac_max,
       Tch   = Tch_min .. Tch_max,
       grid  = [200,200],
       style = patchnogrid,
       colorstyle = HUE,
       axes = boxed,
       labels = ["δ_c", "T_ch"],
       title = sprintf("M0(δ_c, T_ch)  (capped at %.2f)", Mcap)
     ):

# --- Contour Den = 0 (to mark physical boundary) ---
cont := contourplot(
          Den(deltac,Tch),
          deltac = deltac_min .. deltac_max,
          Tch   = Tch_min .. Tch_max,
          contours = [0],
          color = black,
          thickness = 2
        ):

# --- Overlay contour ---
p1_final := display(p1, cont):
p2_final := display(p2, cont):

# --- Display side by side ---
display(array([p1_final, p2_final]), scaling = constrained);

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

restart;
with(plots):

# === Constants ===
qc := 0.4:
qh := 0.64:
alpha := 0.8:

# === Denominator ===
Den := (deltac, Tch) ->
     -2*Tch*deltac*qh - 2*Tch*deltac + 2*Tch*qh
     + 2*deltac*qc + 2*Tch + 2*deltac:

# === M1 and M0 ===
M1 := (deltac, Tch) -> piecewise(Den(deltac,Tch)>0, 2/sqrt(Den(deltac,Tch)), undefined):
M0 := (deltac, Tch) -> piecewise(Den(deltac,Tch)>0, 2*alpha/sqrt(Den(deltac,Tch)), undefined):

# === Domain ===
deltac_min := 0.05:  deltac_max := 0.95:
Tch_min := 0.01:     Tch_max := 1.10:   # Physically realistic range

# === 3D Plots ===
p1 := plot3d(M1(deltac,Tch),
             deltac=deltac_min..deltac_max,
             Tch=Tch_min..Tch_max,
             grid=[80,80],
             axes=boxed,
             orientation=[-130,45],
             scaling=constrained,
             style=surfacecontour,
             color=green,
             labels=["δ_c", "T_ch", "M1"],
             labelfont=[TIMES,12],
             title="M1(δ_c, T_ch) for qc=0.4, qh=0.64"):

p2 := plot3d(M0(deltac,Tch),
             deltac=deltac_min..deltac_max,
             Tch=Tch_min..Tch_max,
             grid=[80,80],
             axes=boxed,
             orientation=[-130,45],
             scaling=constrained,
             style=surfacecontour,
             color=blue,
             labels=["δ_c", "T_ch", "M0"],
             labelfont=[TIMES,12],
             title="M0(δ_c, T_ch) for α=0.8, qc=0.4, qh=0.64"):

# === Display vertically (M1 above M0) ===
display(Array(1..2, [p1, p2]), insequence=true, scaling=constrained);
display(Array([[p1], [p2]]));

I am using S := sort([sqrt(x2), sqrt(y2), sqrt(z2)]);

restart;
n := 0:
L := []:

for a from 3 to 100 do
    for b from 3 to a do
        c2 := a^2 - a*b + b^2;
        c := isqrt(c2);
        if c^2 = c2 then
            if c < a + b and a < b + c and b < c + a then
                if igcd(a, b, c) = 1 then
                    x2 := (-a^2 + b^2 + c^2)/2;
                    y2 := (a^2 - b^2 + c^2)/2;
                    z2 := (a^2 + b^2 - c^2)/2;
                    if 0 < x2 and 0 < y2 and 0 < z2 then
                        S := sort([sqrt(x2), sqrt(y2), sqrt(z2)]);
                        x := S[1]; 
                        y := S[2]; 
                        z := S[3];
                        n := n + 1;
                        L := [op(L), [x, y, z, sqrt(x^2 + y^2), sqrt(y^2 + z^2), sqrt(x^2 + z^2)]];
                    end if;
                end if;
            end if;
        end if;
    end do;
end do;

n;
L;
 

But I get the result. How can I get the correct result of sort? 

After Maple 2025 start-up (with disabled start-up page) and closing the blank worksheet (note the dark grey workspace) there is still one mserver running (highlighted in yellow).

I have not seen a difference when I kill this process and open a new worksheet which starts a new mserver.exe task (and run Maple code).

The task seems to be inactive (no processor load and memory allocation visible).

Is it a task only used by the interface task (javaw.exe)?
What might be the purpose of this mserver.exe? 

Update: The task is inactive in a sense that it does not show immetiate activity when annother mserver.exe task runs (i.e. exceuting a worksheet). However, after a day memory allocation shows changes. When exactly these changes happend is unclear.

Has anyone had any success in turning off the scrollable matrix feature on Mac? I found the post

 https://www.mapleprimes.com/questions/238061-How-To-Disable-The-New-Scrollable-Matrices

and tried to follow the steps outlined by Acer, but I cannot get it to work. Specifically, I greated a preference file at the location:

 //Users/$USER/Library/Preferences/Maple/<version>/Maple preferences which has the statement 

ScrollableMathTableOutput=false

Any success stories, or tips, will be greatly appreciated. 

Thanks. 

I want to ask a question, but I cannot submit it using the link below. I tried several times, but it didn’t work. I wrote it like this, but I didn’t get the desired answer.

http://www.mapleprimes.com/questions/231499-Changing-The-Variables-

Download 963.mw

Hi,

I want to solve the equation shown in the image, along with its given conditions, using Maple and obtain the same results as in the image, but it does not work. Could you please help me?

Download 852.mw

Although several similar problems were asked many years ago (see, e.g., the section “Formal linear algebra” here), there appears to be no new progress so far. It is said that such functionalities exists in the Physics package, but I cannot find any corresponding examples. 
In short, can Maple at present calculate these examples in terms of symbolic array constructs completely automatically?

residue(z^3*cos(1/(z - 2)), z = 2);

                  3       1
         residue(z  cos(-----), z = 2)
                        z - 2

l notice the help document  asks me to increse the n，but the n of essential singularity is infinity

I wrote a simple expand command in Maple - expand(cos((u - 2*k)*x))

only to get the result

2*cos(x*u)*cos(x*k)^2 + 2*sin(x*u)*sin(x*k)*cos(x*k) - cos(x*u)

The presence of a squared term seems to indicate a bug??

I need to compute complicated numerical integral, and my Maple integration does not produce very stable results. Is the a way to do that on line? 

In the below I had to add the assumption x>=0 to get simplifications. Am I wrong with my interpretation that the other assumptions should have been sufficient?

We are looking for the smallest natural number n with the property that both the digit sum Q(n) of the number n and the digit sum Q(n + 1) of the successor of n are divisible by 5.