Leases - Lease Costs and Cash Flow Information (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 31, 2021	Oct. 31, 2020	Oct. 31, 2021	Oct. 31, 2020
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	$ 24.8	$ 25.9	$ 74.3	$ 76.1
Variable lease cost	6.7	3.2	16.5	8.9
Cash paid for operating leases included in operating cash flows			84.4	74.7
Non-cash operating lease liabilities arising from obtaining operating lease right-of-use assets			12.2	50.8
Variable lease payments			16.5	8.9
Cost of subscription and maintenance revenue
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	2.1	1.9	6.1	5.6
Variable lease cost	0.5	0.2	1.3	0.6
Cost of other revenue
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	0.6	0.6	1.6	1.7
Variable lease cost	0.1	0.1	0.4	0.2
Marketing and sales
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	11.0	11.9	32.5	34.0
Variable lease cost	3.0	1.5	7.2	4.0
Research and development
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	7.4	8.6	23.1	24.3
Variable lease cost	2.1	1.0	5.2	2.8
General and administrative
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	3.7	2.9	11.0	10.5
Variable lease cost	$ 1.0	$ 0.4	$ 2.4	$ 1.3