30 Reputation

0 years, 319 days

Message : "Error, (in assuming) when cal...

Maple 2023

Hi, maybe someone knows how to fix this:

"Error, (in assuming) when calling 'assume'. Received: 'question.mw'"

I am attaching the corresponding maple file. I've never met such an error message, and unfortunately the Maplesoft help does not contain any information about such an issue :

 >
 (1)
 >
 (2)
 >
 (3)
 >
 (4)
 >
 (5)
 >
 (6)
 >
 (7)
 >
 (8)
 >
 (9)
 >
 (10)
 >
 >

Question command "implicitplot" inside a...

Maple

Hi,

The procedure below returns the plots of 3 matrices whose eigenvalues are given and fixed (but chosen randomly). Plots are returned simultaneously via the command display. When I run the procedure 2-3 times, I realize that the drawings are not directly comparable. I have to say that I have naively used the command (three times, i.e. for each plot):

implicitplot("function", -2 .. 2, -2 .. 2, axes = boxed, color = blue, gridrefine = 3, scaling = constrained, resolution = 1000);

Is there a way to "force" maple to return -- each time I run the procedure -- plots of the same size, same scaling and so on ? I would like also to put names on the axis with consistent writings and fonts. Is it possible ?

Many thanks,

Best,

Rachid

-----

with(plots);
with(LinearAlgebra);
P0 := proc(n, epsilon)
local m, N, D1, Modu, fs, f1, f2, f, q, s, r, t, eps, pp, k;
eps := epsilon;
m := n;
N := eval(RandomMatrix(m, m));
N := N/evalf(Norm(evalf(N), 2));
D1 := DiagonalMatrix(Eigenvalues(N));
pp := pointplot({seq([Re(D1[k, k]), Im(D1[k, k])], k = 1 .. m)});
f := (i, j) -> if i = j then D1[i, i]; elif i = j + 1 then (1 - abs(D1[i, i])^2)^(1/2)*(1 - abs(D1[j, j])^2)^(1/2); elif j + 1 < i then (1 - abs(D1[i, i])^2)^(1/2)*(1 - abs(D1[j, j])^2)^(1/2)*mul(-conjugate(D1[t, t]), t = j + 1 .. i - 1); else 0; end if;
Modu := Matrix(m, (i, j) -> f(i, j)); fs := (x, y) -> Norm(1/((x + y*I)*IdentityMatrix(m) - N), 2) - 1/eps;
f1 := (x, y) -> Norm(1/((x + y*I)*IdentityMatrix(m) - D1), 2) - 1/eps;
f2 := (x, y) -> Norm(1/((x + y*I)*IdentityMatrix(m) - Modu), 2) - 1/eps;
s := implicitplot(fs, -2 .. 2, -2 .. 2, axes = boxed, color = blue, gridrefine = 3, scaling = constrained, resolution = 1000);
q := implicitplot(f1, -2 .. 2, -2 .. 2, axes = boxed, gridrefine = 3, scaling = constrained, resolution = 1000);
r := implicitplot(f2, -2 .. 2, -2 .. 2, axes = boxed, color = green, gridrefine = 3, scaling = constrained, resolution = 1000); RETURN(display({q, s, r, pp}));
end proc;

definition of a matrix by using a functi...

Maple

Hi,

In the code below I do not understand why f(3,1) cannot be computed : it returns the conjugate of D1[2,2] although I have defined it as a random number. Maybe you understand this ? Actually I first got an error message of the type "bad index into matrix". Thus I wrote ''D1''[t, t] instead of D1[t, t] to fix the issue in the product.

with(LinearAlgebra);
D1 := evalf(RandomMatrix(3));
f := (i, j) -> if i = j then D1[i, i]; elif i = j + 1 then (1 - abs(D1[i, i])^2)^(1/2)*(1 - abs(D1[j, j])^2)^(1/2); elif j + 1 < i then (1 - abs(D1[i, i])^2)^(1/2)*(1 - abs(D1[j, j])^2)^(1/2)*product(-conjugate(''D1''[t, t]), t = j + 1 .. i - 1); else 0; end if;
f(1, 1);
f(1, 2), f(1, 3);
f(2, 2);
f(2, 3);
f(3, 3);
f(2, 1);
f(3, 2);
f(3, 1);
Modu := evalf(Matrix(3, (i, j) -> f(i, j)));

f(3,1) is given by 3222.984487*conjugate(D1[2, 2]): I do not get why the value of D1[2,2] is ignored.

Plotting pseudospectra...

Maple

Hi everyone,

Do you know if there are some known codes for plotting pseudospectra of squared (and finite) matrices with given spectrum ?