[Verse 1]
When chains collide in perfect rows
Zero leads to A then flows
Through B and into C it goes
Back to zero, sequence closed
But homology breaks the spell
What was exact won't translate well
The functor scrambles perfect form
Now we need to track the storm
[Chorus]
Long exact sequence tells the tale
Delta connects when mappings fail
H sub n of A to B to C
Then delta drops the degree
Connecting homomorphism's the key
Links the levels, sets them free
When exactness falls apart
Delta mends the broken heart
[Verse 2]
Short exact feeds the machine
Homology reveals the scene
Degree by degree it shows
Exactly where the breakdown goes
From H sub n down to n minus one
Delta's work is never done
Threading through each graded space
Cataloguing every trace
[Chorus]
Long exact sequence tells the tale
Delta connects when mappings fail
H sub n of A to B to C
Then delta drops the degree
Connecting homomorphism's the key
Links the levels, sets them free
When exactness falls apart
Delta mends the broken heart
[Bridge]
It's an error report in disguise
Shows us where precision dies
Functor couldn't keep it straight
Long exact compensates
Boundary maps and cycles dance
Delta gives them second chance
[Chorus]
Long exact sequence tells the tale
Delta connects when mappings fail
H sub n of A to B to C
Then delta drops the degree
Connecting homomorphism's the key
Links the levels, sets them free
When exactness falls apart
Delta mends the broken heart
[Outro]
From short to long the story grows
Delta's magic always knows
How to fix what can't be saved
Homology's perfectly paved