This is how to step through the basis, setting each basic variable to 1 and the others to 0, and evaluating your Zs in light of this. If you post an actual example, I'll show you how to apply this to it.

Sol:= solve(sys, vars):
Basic,NonBasic:= selectremove(evalb, Sol):
Basic:= op~(Basic):
for v in Basic do
     Evals:= {v= 1} union (Basic minus {v} =~ 0);
     eval(Zs, eval(NonBasic, Evals) union Evals)
od:

Eq:= (x^2+y^2)^2=(x^2-y^2):
subs(x= r*cos(theta), y= r*sin(theta), Eq);

combine(%);

%/r^2;

Change the return line to

return convert(orbit, list)

The result needs to be a string (or a name), because an integer can't have the leading zeros. Here's how to make the string:

b:= cat("", op~(convert(a, listlist))[]);

TypeTools:-AddType(Point, [realcons,realcons]):
~set:= x-> convert(x, set):
~list:= x-> convert(x, list):

ThreeIneqs:= proc(A::Point, B::Point, C::Point, XY::[name,name])
uses G= geometry;
local p, a, b, c, L, S:= {A,B,C};
     seq(
          (Eq-> `if`(eval(Eq, XY=~p) < 0, 1, -1)*Eq <= 0)
          (lhs(G:-Equation(
               G:-line(L, (P-> [G:-point(a, P[1][]), G:-point(b, P[2][])])(S minus {p})),
               XY
          ))),
          p= S
     )
end proc:

NumbTrue:= proc(S::~list(boolean), Evals::{set,list}(name=anything))
local r;
     r:= is~(eval(S,Evals));
     `if`(has(r, FAIL), FAIL, numboccur(r, true))
end proc:

TwoOrMore:= proc(Tri::~set(Point), P::Point)
local x,y;
     evalb(NumbTrue([ThreeIneqs(Tri[], [x,y])], [x,y]=~P) > 1)
end proc:

Example:
   
TwoOrMore([[2,3], [4,5], [8,2]], [4,4]);

                                          true

You have two errors:

1. Pi must be spelled with capital P and lowercase i,
2. polarplot should be plots:-polarplot.

It can be done with geom3d:-intersection. In particular, if the result of this command is not NULL, then the input objects intersect.

It can be done in two steps:

convert(s, trig);
combine(%);

f:= 3+2*x+y+2*x^2+2*x*y+3*y^2 = 0:
d1:= implicitdiff(f, y, x);

d2:= implicitdiff(f, y, x$2);

This can be simplified substantially using the original expression and simplify with side relations:

simplify(d2, {f});

diff(f(x,y)=exp(2*x+cos(y)), y$3, x$5);

Edit menu => Split or Join => Split Execution Group (F3)

Simply apply command factor to the result returned by intsolve:

intEq:= 2*cosh(x)-sinh(x)-(2-x)= 1 + int( (2-x+t)* phi(t),t=0..x):
Sol:= intsolve(intEq,phi(x)):
factor(Sol);

Try adding the following option to the plot commands:

xtickmarks= [38320= "11/29", 38330= "12/09", 38340= "12/19", 38350="12/29"]

If you have a lot of such plots to do, it may be worthwhile to write a procedure that translates dates from this "Excel format" to a standard format. This can be done with Finance:-AdvanceDate using any known match (such as 38320 = "11/29/2004") as a reference point. The date can be formatted into a string with Finance:-FormatDate.

A search at the Maple Applications Center turned up one hit: here .

Use Zoom factor from the View menu.