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Financial Instruments (Effects of Derivative Instruments on Condensed Consolidated Statements of Operations) (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 31, 2019	Oct. 31, 2018	Oct. 31, 2019	Oct. 31, 2018
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue	$ 842.7	$ 660.9	$ 2,375.0	$ 1,832.5
Marketing and sales	330.7	297.6	960.8	863.1
Research and development	213.0	181.0	634.0	534.6
General and administrative	99.1	87.4	299.6	239.4
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	2.9		7.0
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	3.3		8.7
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	1.6		4.7
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	(0.4)		(0.7)
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	(1.0)		(3.4)
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	(0.1)		(0.6)
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	(0.5)		(1.7)
Subscription
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue	715.0	481.3	1,974.5	1,252.3
Maintenance
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue	91.2	150.1	306.7	497.7
Subscription and Maintenance
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue	806.2	631.4	2,281.2	1,750.0
Cost of revenue	$ 54.2	$ 54.8	$ 166.9	$ 159.3