Leases (Lease Costs and Cash Flow Information) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Jul. 31, 2020	Jul. 31, 2019	Jul. 31, 2020	Jul. 31, 2019
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	$ 24.7	$ 21.7	$ 50.2	$ 42.0
Variable lease cost	2.3	3.4	5.7	6.4
Cash paid for operating leases included in operating cash flows			47.6	45.9
Non-cash operating lease liabilities arising from obtaining operating lease right-of-use assets			18.4	53.0
Variable lease payments			5.7	6.4
Cost of subscription and maintenance revenue
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	1.7	1.6	3.7	3.2
Variable lease cost	0.1	0.3	0.4	0.5
Cost of other revenue
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	0.4	0.7	1.1	1.1
Variable lease cost	0.0	0.0	0.1	0.1
Marketing and sales
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	10.6	9.6	22.1	18.4
Variable lease cost	1.0	1.5	2.5	2.8
Research and development
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	7.8	6.8	15.7	13.5
Variable lease cost	0.7	1.1	1.8	2.1
General and administrative
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Operating lease cost	4.2	3.0	7.6	5.8
Variable lease cost	$ 0.5	$ 0.5	$ 0.9	$ 0.9