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