Leases (Lease Costs and Cash Flow Information) (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 31, 2020	Oct. 31, 2019	Oct. 31, 2020	Oct. 31, 2019
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	$ 25.9	$ 21.7	$ 76.1	$ 63.7
Variable lease cost	3.2	2.5	8.9	8.9
Cash paid for operating leases included in operating cash flows			74.7	66.4
Non-cash operating lease liabilities arising from obtaining operating lease right-of-use assets			50.8	55.2
Variable lease payments			8.9	8.9
Cost of subscription and maintenance revenue
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	1.9	1.7	5.6	4.9
Variable lease cost	0.2	0.2	0.6	0.7
Cost of other revenue
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	0.6	0.6	1.7	1.7
Variable lease cost	0.1	0.1	0.2	0.2
Marketing and sales
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	11.9	9.6	34.0	28.0
Variable lease cost	1.5	1.1	4.0	3.9
Research and development
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	8.6	6.6	24.3	20.1
Variable lease cost	1.0	0.7	2.8	2.8
General and administrative
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	2.9	3.2	10.5	9.0
Variable lease cost	$ 0.4	$ 0.4	$ 1.3	$ 1.3