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