Leases (Lease Costs and Cash Flow Information) (Details) - USD ($) $ in Millions	3 Months Ended
	Apr. 30, 2020	Apr. 30, 2019
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	$ 25.5	$ 20.3
Variable lease cost	3.4	3.0
Cash paid for operating leases included in operating cash flows	24.9	23.6
Non-cash operating lease liabilities arising from obtaining operating lease right-of-use assets	8.5	44.0
Variable lease payments	3.4	3.0
Cost of subscription and maintenance revenue
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	2.0	1.6
Variable lease cost	0.3	0.2
Cost of other revenue
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	0.7	0.4
Variable lease cost	0.1	0.1
Marketing and sales
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	11.5	8.8
Variable lease cost	1.5	1.3
Research and development
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	7.9	6.7
Variable lease cost	1.1	1.0
General and administrative
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	3.4	2.8
Variable lease cost	$ 0.4	$ 0.4