Leases (Lease Costs and Cash Flow Information) (Details) - USD ($) $ in Millions	3 Months Ended	6 Months Ended
	Jul. 31, 2019	Jul. 31, 2019
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	$ 21.7	$ 42.0
Variable lease cost	3.4	6.4
Cash paid for operating leases included in operating cash flows		45.9
Non-cash operating lease liabilities arising from obtaining operating lease right-of-use assets		53.0
Cost of subscription and maintenance revenue
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	1.6	3.2
Variable lease cost	0.3	0.5
Cost of other revenue
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	0.7	1.1
Variable lease cost	0.0	0.1
Marketing and sales
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	9.6	18.4
Variable lease cost	1.5	2.8
Research and development
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	6.8	13.5
Variable lease cost	1.1	2.1
General and administrative
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	3.0	5.8
Variable lease cost	$ 0.5	$ 0.9