read `GFMatrix.txt`:

M:=1000:
L:=5:
print(`Rational Generating functions for determinants of Almost diagonal matrices`):

c0:=0:

print(``):
print(`By Yukun Yao's Computer`):
print(``):

for m1 from 2 to L do
for n1 from m1 to L do

ra:=rand(1..M):
A:=ra():
mu:=[A,seq(ra(),i=2..m1)],[A,seq(ra(),i=2..n1)]:

 gu:=GFMatrixL([20,mu],  t):
 c0:=c0+1:
  print(`Fact Number`, c0):
  print(``):
 print(`Let M(n) be an almost diagonal matrix n by n matrix that is zero except for the diagonals near the main diagonal`):
 print(`and whose top row is`):
 print(``):
 print(mu[1]):
 print(``):
 print(`and whose leftmost column is`):
 print(``):
 print(mu[2]):
 print(``):
 print(`Let m(n) be the determinant of M(n)`):
 print(``):
 print(`The generating function`):
  print(``):
  print(Sum(m(n)*t^n,n=0..infinity)):
 print(``):
 print(`equals`):
  
 print(``):
  print(gu):
 print(``):
  print(`and in Maple format`):
 print(``):
lprint(gu);
 print(``):
print(`------------------------------------`):
  print(``):
 od:
od:

print(`This took`, time(), `seconds. `):


quit: