Is this form more acceptable:

Your expression is always a root (in lambda) of one of these:

3*lambda^2+(l^4+36)*lambda+3*l^4+108
-3*lambda^4+((3/2)*l^4+18)*lambda^3+(l^8+(141/4)*l^4+81)*lambda^2+(3/2)*(l^4-12)*(l^4+18)*lambda+81*l^4-972
162+2*lambda^4+(l^4+24)*lambda^3+((7/2)*l^4+108)*lambda^2+(3*l^4+216)*lambda
l^4*lambda+3*l^4-3*lambda^2

Thumb if You like.

How about this:

sys := {w = -2*Pi*i*k_2*v + 2*Pi*i*k_2*(4*K^2)/(5*Pi)*u, z = -2*Pi*i*k_1*v + 2*Pi*i*k_1*(4*K^2)/(5*Pi)*u, p*s*x = -2*Pi*i*k_1*u - 4*Pi^2*(k_1^2 + k_2^2)*x + a_1, p*s*y = -2*Pi*i*k_2*u - 4*Pi^2*(k_1^2 + k_2^2)*y + a_2, k_1*z + k_2*w = 0, k_1*x + k_2*y = 0};
sys union {-RootOf(_Z^2+1)*z-w, RootOf(_Z^2+1)*x+y};
solve(% union {w<>0});
map2(remove, evalb, [%]);
eliminate(%[1], {x, y, z, u, v, w});
collect(%, [Pi, K], factor);

In the title.
                                 

First look at this:

(() -> solve({args}, indets({args}, name) minus {t}))(eq || (`$`(1 .. 4)));
subs(t = 0, %);
allvalues(%);

Clearly your equations are incomplete.

Could it be that you need a registered version of Maple?

How about:
plot(floor(x/3)*3, x=-5..5);
 

Simply compare these two codes:

restart;
P1 := 1007;
P2 := 1014;
P3 := 1014.1;
evalf(P2 - P1, 2);
evalf(P3 - P1, 2);

restart;
P1 := 1007.;
P2 := 1014.;
P3 := 1014.1;
evalf(P2 - P1, 2);
evalf(P3 - P1, 2);

The difference is obvious. No bugs here.

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For Your matrix you can use this:

F := (n, f) -> LinearAlgebra:-BandMatrix(map(f, [$1 .. n]), 0, n);
F(4, (n) -> d[n]);

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for i from 1 to n do proc(i, a, b) a[i]:=b[i] end(i, a ,b) od;

also

for i from 1 to n do proc(i) a[i]:=b[i] end(i) od;

provided a, b are not declared local.

Your formula appears to be:

fgP,fgQ:=unapply(gP,x,y), unapply(gQ,x,y);
(fgP(QS1,QS2)*fgQ(S1,-S2)/(fgP(PS1,PS2)*fgQ(S1,-S2))) mod p;

Notice the cancellation.

e_n_1b := n_1 = (-w^(2*sigma)*tau + w^sigma)*s*nsp_1/(w^sigma*tau^2 - w^(2*sigma)*tau + w^sigma - tau) + tau*(w^(sigma - 1)*tau - w^(2*sigma - 1))*s*nsp_2/(w^sigma*tau^2 - w^(2*sigma)*tau + w^sigma - tau);

wpowers := (A, e) -> frontend(convert, [subsindets(A, dependent(w)^anything, expand), parfrac, e], [{Non}(identical(w^sigma)), {}]);
wpowers(e_n_1b, w);
wpowers(e_n_1b, w^sigma);

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Edit: There was an error in my response, just like there was one in your code.
Correction:

PlotGraph := proc(func::anything, opts::(seq({identical(zoom) = [range, range]})))
   plots:-display(plot(func), ifelse(membertype(identical(zoom) = [range, range], [opts]), view = subs([opts], zoom), 'NULL'))
end proc;;
PlotGraph(x^2, zoom = [0 .. 1, -5 .. 5]);

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One variable, constant bounds:

a := solve({-1 < x, 0 < (2*x)/(x^2 - 1), x < 1}, {x});
solve(`and`(op(a)));

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See this example:

A := map((x -> ifelse( x<1/3 or x>2/3, x, 0)), LinearAlgebra:-RandomMatrix(25, 25, generator = rand(0 .. 1.0))):
P := plots[matrixplot](A, heights = histogram, transparency = 0.3, style = patchnogrid, shading = zhue, orientation=[30, 30, 0]):
subsindets(P, [[anything, anything, 0.]$4], (x -> NULL));

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