Financial Instruments - Effects of Derivative Instruments on Condensed Consolidated Statements of Operations (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Jan. 31, 2021	Oct. 31, 2020	Jul. 31, 2020	Apr. 30, 2020	Jan. 31, 2020	Oct. 31, 2019	Jul. 31, 2019	Apr. 30, 2019	Jan. 31, 2021	Jan. 31, 2020	Jan. 31, 2019
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue	$ 1,039.2	$ 952.4	$ 913.1	$ 885.7	$ 899.3	$ 842.7	$ 796.8	$ 735.5	$ 3,790.4	$ 3,274.3	$ 2,569.8
Marketing and sales									1,440.3	1,310.3	1,183.9
Research and development									932.5	851.1	725.0
General and administrative									413.9	405.6	340.1
Designated as hedging instrument | Foreign Exchange Contracts
Derivative Instruments, Gain (Loss) [Line Items]
Amount of (loss) gain reclassified from accumulated other comprehensive income into income									4.4	9.6	(12.1)
Designated as hedging instrument | Foreign Exchange Contracts | Subscription revenue
Derivative Instruments, Gain (Loss) [Line Items]
Amount of (loss) gain reclassified from accumulated other comprehensive income into income									(0.4)	11.7
Designated as hedging instrument | Foreign Exchange Contracts | Maintenance revenue
Derivative Instruments, Gain (Loss) [Line Items]
Amount of (loss) gain reclassified from accumulated other comprehensive income into income									0.1	5.9
Designated as hedging instrument | Foreign Exchange Contracts | Cost of subscription and maintenance revenue
Derivative Instruments, Gain (Loss) [Line Items]
Amount of (loss) gain reclassified from accumulated other comprehensive income into income									0.6	(0.9)
Designated as hedging instrument | Foreign Exchange Contracts | Marketing and sales
Derivative Instruments, Gain (Loss) [Line Items]
Amount of (loss) gain reclassified from accumulated other comprehensive income into income									2.4	(4.3)
Designated as hedging instrument | Foreign Exchange Contracts | Research and development
Derivative Instruments, Gain (Loss) [Line Items]
Amount of (loss) gain reclassified from accumulated other comprehensive income into income									0.5	(0.7)
Designated as hedging instrument | Foreign Exchange Contracts | General and administrative
Derivative Instruments, Gain (Loss) [Line Items]
Amount of (loss) gain reclassified from accumulated other comprehensive income into income									1.2	(2.1)
Subscription
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue									3,478.9	2,751.9	1,802.3
Maintenance
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue									183.3	386.6	635.1
Subscription and Maintenance
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue									3,662.2	3,138.5	2,437.4
Cost of revenue									$ 242.1	$ 223.9	$ 216.0