read `ALG.txt`:
gu:=DimerData(z,x):
print(`The characteristic polynomial for the Dimer problem for a 4 by infinity strip is, where z is the activation parameter is`):
print(`the degree 4 polynomial in x`):
print(gu[4]):
print(`Let's see whether it is the tensor product of two degree-two polynomials`):
print(TestFact(gu[4],x,[2,2])):
print(``):
print(`------------------`):
print(``):
print(`The characteristic polynomial for the Dimer problem for a 6 by infinity strip is, where z is the activation parameter is`):
print(`the degree 8 polynomial in x`):
print(gu[6]):
print(`Let's see whether it is the tensor product of three degree-two polynomials`):
print(TestFact(gu[6],x,[2,2,2])):
print(``):
print(`------------------`):
print(``):
print(`The characteristic polynomial for the Dimer problem for a 8 by infinity strip is, where z is the activation parameter is`):
print(`the degree 16 polynomial in x`):
print(gu[8]):
print(`Let's see whether it is the tensor product of four degree-two polynomials`):
print(`To speed things up, let's make z=5`):
print(TestFact(subs(z=5,gu[8]),x,[2,2,2,2])):
print(`and to be on the safe side, also z=17 `):
print(TestFact(subs(z=17,gu[8]),x,[2,2,2,2])):
print(``):
print(`------------------`):
print(``):
print(`The characteristic polynomial for the Dimer problem for a 10 by infinity strip is, where z is the activation parameter is`):
print(`the degree 32 polynomial in x`):
print(gu[10]):
print(`Let's see whether it is the tensor product of five degree-two polynomials`):
print(`To speed things up, let's make z=5`):
print(TestFact(subs(z=5,gu[10]),x,[2,2,2,2,2])):
print(`and to be on the safe side, also z=17 `):
print(TestFact(subs(z=17,gu[10]),x,[2,2,2,2,2])):
print(``):
print(`------------------`):
print(``):
print(`This took`, time(), `seconds. `):
quit: