I've been working on my master's project and am at (at least I hope I've got it) the final stage of making Maple do everything that I want it to. I have the flow chart here which is a little hard to see while looking at the module I have set up.
The difficulty I'm having is getting it to run as a whole. I just do not know what I need to do to get the thing started. The way I have it set up is that each procedure references another until they are done - a loop structure. Which may be more appropriate but I humbly submit it to you.
I do not completely understand the module pieces. I do know that each procedure I have inside of here should work (and if not, that's why it's a master's problem :D)
Thank you again for looking!
(I know the local and export may not be correct, and sorry for the matrix multiplication looking so ugly here)
> LocSubAlg:=module()
description "the local subcase algorithm";
option package;
local Start, DegCk, Step1, Step2, UnitCk, Step3, Step4;
export a, b, c, d, g, h, k, l, m, n, p, z, A, alpha, alpha1, beta, beta1, beta2, Print;
Start:= proc()
a:=readstat("Please enter the polynomial a: ");
b:=readstat("Please enter the polynomial b: ");
c:=readstat("Please enter the polynomial c: ");
d:=readstat("Please enter the polynomial d: ");
with(linalg):
A:= Matrix(3,3);
A[1,1]:= a;
A[1,2]:= b;
A[2,1]:= c;
A[2,2]:= d;
alpha:= Matrix(3, 3, shape = identity);
beta:= Matrix(3, 3, shape = identity);
DegCk;
end proc;
DegCk := proc ()
m := degree(a, t);
if m = 0 then
Step4
elif m>degree(b, t) then
UnitCk
elif m <= degree(b, t) then
Step1
end if;
end proc;
Step1:= proc()
quo(b, a, t, 'q');
with(linalg):
A:=A*(Matrix([[1, -q, 0], [0, 1, 0], [0, 0, 1]]));
beta:=beta*(Matrix([[1, -q, 0], [0, 1, 0], [0, 0, 1]]));
UnitCk;
end proc;
UnitCk:= proc()
z:=eval(b, t=0);
if type(z, complex)=true and z<>0 then
Step2
else Step3
end if;
end proc;
Step2:= proc()
g:=eval(a, t=0);
h:=eval(b, t=0);
k:=(-g/h);
l:=((h-b)/t);
m:=(t*h);
n:=((-c*(h-b)-a*d*t)/m);
with(linalg):
A:=A*(Matrix([[1, 0, 0], [k, 1, 0], [0, 0, 1]]));
beta:=beta*(Matrix([[1, 0, 0], [k, 1, 0], [0, 0, 1]]));
a:=a/t;
alpha1:=(Matrix([[1, 0, 0], [0, 0, 1], [0, -1, 0]])) *(Matrix([[1, 0, 0], [0, 1, -a*d], [0, 0, 1]])) *(Matrix([[1, 0, 0], [c*d, 1, 0], [0, 0, 1]]));
beta1:=(Matrix([[1, 0, 0], [0, 1, 0], [t*c, 0, 1]])) *(Matrix([[1, 0, 0], [0, 1, 0], [0, t*d, 1]])) *(Matrix([[1, 0, 0], [0, 1, -a], [0, 0, 1]])) *(Matrix([[1, 0, 0], [0, 0, 1], [0, -1, 0]]));
beta2:=(Matrix([[1, l, 0], [0, 1, 0], [0, 0, 1]])) *(Matrix([[g, 0, 0], [0, g^(-1), 0],[0, 0, 1]])) *(Matrix([[0, -1, 0], [1, 0, 0], [0, 0, 1]])) *(Matrix([[1, m, 0], [0, 1, 0], [0, 0, 1]]))
*(Matrix([[1, 0, 0], [n, 1, 0], [0, 0, 1]])) *(Matrix([[1, 0, 0], [0, 0, -1], [0, 1, 0]]));
alpha:=alpha1*alpha;
beta:=beta*beta1;
A:=alpha1*A*beta1*beta2;
DegCk;
end proc;
Step3:= proc()
gcdex(a, b, resultant(a,b,t), t, 'v', 'w');
p:=(w*d-v*c);
with(linalg):
alpha1:=(Matrix([[1, 1, 0], [0, 1, 0], [0, 0, 1]])) *(Matrix([[1, 0, 0], [p, 1, 0], [0, 0, 1]]));
alpha:=alpha1*alpha;
A:=alpha1*A;
Step2;
end proc;
Step4:= proc()
with(linalg):
alpha1:=(Matrix([[1, -b, 0], [0, 1, 0], [0, 0, 1]]));
beta1:=(Matrix([[1, 0, 0], [-c, 1, 0], [0, 0, 1]]));
alpha:=alpha1*alpha;
beta:=beta*beta1;
A:=alpha1*A*beta1;
Print;
end proc;
Print:=proc()
print(A);
end proc;
end module;
