Leases - Lease Costs and Cash Flow Information (Details) - USD ($) $ in Millions	3 Months Ended
	Apr. 30, 2021	Apr. 30, 2020
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	$ 24.9	$ 25.5
Variable lease cost	5.3	3.4
Cash paid for operating leases included in operating cash flows	29.9	24.9
Non-cash operating lease liabilities arising from obtaining operating lease right-of-use assets	4.5	8.5
Variable lease payments	5.3	3.4
Cost of subscription and maintenance revenue
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	1.9	2.0
Variable lease cost	0.4	0.3
Cost of other revenue
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	0.5	0.7
Variable lease cost	0.1	0.1
Marketing and sales
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	10.8	11.5
Variable lease cost	2.3	1.5
Research and development
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	8.0	7.9
Variable lease cost	1.7	1.1
General and administrative
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	3.7	3.4
Variable lease cost	$ 0.8	$ 0.4