Financial Instruments (Effects of Derivative Instruments on Condensed Consolidated Statements of Operations) (Details) - USD ($) $ in Millions	3 Months Ended	6 Months Ended
Jul. 31, 2020	Jul. 31, 2019	Jul. 31, 2020	Jul. 31, 2019
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue	$ 913.1	$ 796.8	$ 1,798.8	$ 1,532.3
Marketing and sales	350.9	316.8	692.2	630.1
Research and development	232.5	215.4	449.9	421.0
General and administrative	93.2	101.4	198.0	200.5
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	0.8	3.4	2.0	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	1.6	3.2	3.7	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	0.0	1.8	0.6	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	(0.1)	(0.2)	(0.3)	(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	(0.5)	(0.8)	(1.3)	(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	0.0	(0.2)	(0.1)	(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	(0.2)	(0.4)	(0.6)	(1.2)
Subscription
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue	841.2	663.7	1,644.2	1,259.5
Maintenance
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue	51.2	103.5	113.3	215.5
Subscription and Maintenance
Derivative Instruments, Gain (Loss) [Line Items]
Total net revenue	892.4	767.2	1,757.5	1,475.0
Cost of revenue	$ 58.5	$ 53.0	$ 115.9	$ 112.7

The aggregate costs related to goods produced and sold and services rendered by an entity during the reporting period. This excludes costs incurred during the reporting period related to financial services rendered and other revenue generating activities.

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The aggregate costs incurred (1) in a planned search or critical investigation aimed at discovery of new knowledge with the hope that such knowledge will be useful in developing a new product or service, a new process or technique, or in bringing about a significant improvement to an existing product or process; or (2) to translate research findings or other knowledge into a plan or design for a new product or process or for a significant improvement to an existing product or process whether intended for sale or the entity's use, during the reporting period charged to research and development projects, including the costs of developing computer software up to the point in time of achieving technological feasibility, and costs allocated in accounting for a business combination to in-process projects deemed to have no alternative future use.

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