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Financial Instruments - Effects of Derivative Instruments on Condensed Consolidated Statements of Operations (Detail) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Jan. 31, 2020	Oct. 31, 2019	Jul. 31, 2019	Apr. 30, 2019	Jan. 31, 2019	Oct. 31, 2018	Jul. 31, 2018	Apr. 30, 2018	Jan. 31, 2020	Jan. 31, 2019	Jan. 31, 2018
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue	$ 899.3	$ 842.7	$ 796.8	$ 735.5	$ 737.3	$ 660.9	$ 611.7	$ 559.9	$ 3,274.3	$ 2,569.8	$ 2,056.6
Marketing and sales									1,310.3	1,183.9	1,087.3
Research and development									851.1	725.0	755.5
General and administrative									405.6	340.1	305.2
Designated as Hedging Instrument \| Foreign Exchange Contracts
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) recognized in accumulated other comprehensive loss on derivatives (effective portion)									3.0
Amount of gain (loss) recognized in accumulated other comprehensive loss on derivatives (effective portion)										19.6	(21.3)
Amount of gain (loss) reclassified from accumulated other comprehensive income into income									9.6
Amount and location of gain (loss) reclassified from accumulated other comprehensive loss into income (loss) (effective portion)										(12.1)	9.9
Designated as Hedging Instrument \| Foreign Exchange Contracts \| Subscription revenue
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income									11.7
Designated as Hedging Instrument \| Foreign Exchange Contracts \| Maintenance revenue
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income									5.9
Designated as Hedging Instrument \| Foreign Exchange Contracts \| Cost of subscription and maintenance revenue
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income									(0.9)
Designated as Hedging Instrument \| Foreign Exchange Contracts \| Marketing and sales
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income									(4.3)
Designated as Hedging Instrument \| Foreign Exchange Contracts \| Research and development
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income									(0.7)
Designated as Hedging Instrument \| Foreign Exchange Contracts \| General and administrative
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income									(2.1)
Designated as Hedging Instrument \| Foreign Exchange Contracts \| Net revenue
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income									17.6
Amount and location of gain (loss) reclassified from accumulated other comprehensive loss into income (loss) (effective portion)										(8.5)	8.0
Designated as Hedging Instrument \| Foreign Exchange Contracts \| Cost of other revenue
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income									(0.9)
Amount and location of gain (loss) reclassified from accumulated other comprehensive loss into income (loss) (effective portion)										0.0	0.0
Designated as Hedging Instrument \| Foreign Exchange Contracts \| Operating expenses
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income									(7.1)
Amount and location of gain (loss) reclassified from accumulated other comprehensive loss into income (loss) (effective portion)										(3.6)	1.9
Not Designated as Hedging Instrument \| Foreign Exchange Contracts \| Interest and other expense, net
Derivative Instruments, Gain (Loss) [Line Items]
Amount and location of gain (loss) recognized on derivatives in net income (loss)									6.0	6.6	(19.1)
Subscription
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue									2,751.9	1,802.3	894.3
Maintenance
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue									386.6	635.1	989.6
Subscription and Maintenance
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue									3,138.5	2,437.4	1,883.9
Cost of revenue									$ 223.9	$ 216.0	$ 214.4