You forgot to mention, is this a Li-ion or NiCd battery
For the OLD ni-cad batterries, you are correct about memory. For these batteries you should discharge complettly before charging (complete discharge is when Battery voltage equals 1 volt Per cell, ie a 10 cell battery, Eout equals 10volt when discharged, and 12.5 V when fully charged- CAUTION do NOT let these batteries drop below 1 volt/cell.
Ni metal Hydroxide simular to NiCd, but less of a memory problem, same charge and discharge as above.
Most laptops (past several years) us the Newer Li-ion Battery. These DO NOT have the memorry problem and you do NOT need to let them discharge completely. For one of my laptops I have two batterries. What I do leave one battery in for 2 weeks to a Month, then swap batteries. You can leave the battery in or leave it out - but put back in at least every 2-3 wks and top up the charge. My second laptop I just leave it in.
My Old Laptop (5 yrs or more old) use the old NiCd batteries which I remove when not in use and periodically put in, run battery down until it says low batterry then I recharge - DO NOT do this for Li-ion batteries.