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Financial Instruments (Effects of Derivative Instruments on Condensed Consolidated Statements of Operations) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Jul. 31, 2019	Jul. 31, 2018	Jul. 31, 2019	Jul. 31, 2018
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue	$ 796.8	$ 611.7	$ 1,532.3	$ 1,171.6
Marketing and sales	316.8	289.1	630.1	565.5
Research and development	215.4	180.8	421.0	353.6
General and administrative	101.4	79.1	200.5	152.0
Foreign currency contracts \| Designated as hedging instrument
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income	3.4		4.1
Foreign currency contracts \| Designated as hedging instrument \| Subscription Revenue
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income	3.2		5.4
Foreign currency contracts \| Designated as hedging instrument \| Maintenance Revenue
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income	1.8		3.1
Foreign currency contracts \| Designated as hedging instrument \| Cost of subscription and maintenance revenue
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income	(0.2)		(0.3)
Foreign currency contracts \| Designated as hedging instrument \| Marketing and sales
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income	(0.8)		(2.4)
Foreign currency contracts \| Designated as hedging instrument \| Research and development
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income	(0.2)		(0.5)
Foreign currency contracts \| Designated as hedging instrument \| General and administrative
Derivative Instruments, Gain (Loss) [Line Items]
Amount of gain (loss) reclassified from accumulated other comprehensive income into income	(0.4)		(1.2)
Subscription
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue	663.7	420.6	1,259.5	771.0
Maintenance
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue	103.5	166.4	215.5	347.6
Subscription and Maintenance
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue	767.2	587.0	1,475.0	1,118.6
Cost of revenue	$ 53.0	$ 54.1	$ 112.7	$ 104.5