Revenue Recognition Adoption of New Accounting Standard - Income Statement (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended								12 Months Ended
	Jan. 31, 2020	Oct. 31, 2019	Jul. 31, 2019	Apr. 30, 2019	Jan. 31, 2019	Oct. 31, 2018	Jul. 31, 2018	Apr. 30, 2018	Jan. 31, 2020	Jan. 31, 2019	Jan. 31, 2018
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net revenue	$ 899.3	$ 842.7	$ 796.8	$ 735.5	$ 737.3	$ 660.9	$ 611.7	$ 559.9	$ 3,274.3	$ 2,569.8	$ 2,056.6
Cost of revenue									324.9	285.9	303.4
Marketing and sales									1,310.3	1,183.9	1,087.3
Provision for income taxes	8.5	(29.7)	(26.3)	(32.8)	31.7	(35.2)	(16.0)	(18.6)	(80.3)	(38.1)	(9.6)
Net income (loss)	$ 131.8	$ 66.7	$ 40.2	$ (24.2)	$ 64.7	$ (23.7)	$ (39.4)	$ (82.4)	$ 214.5	$ (80.8)	$ (566.9)
Basic net (loss) income per share (in dollars per share)	$ 0.60	$ 0.30	$ 0.18	$ (0.11)	$ 0.30	$ (0.11)	$ (0.18)	$ (0.38)	$ 0.98	$ (0.37)	$ (2.58)
Diluted net (loss) income per share (in dollars per share)	$ 0.59	$ 0.30	$ 0.18	$ (0.11)	$ 0.29	$ (0.11)	$ (0.18)	$ (0.38)	$ 0.96	$ (0.37)	$ (2.58)
As reported
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Marketing and sales										$ 1,183.9
Provision for income taxes										(38.1)
Net income (loss)										$ (80.8)
Basic net (loss) income per share (in dollars per share)										$ (0.37)
Diluted net (loss) income per share (in dollars per share)										$ (0.37)
Impact from the adoption of ASC 606 and 340-40
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Marketing and sales										$ 1,166.0
Provision for income taxes										(42.9)
Net income (loss)										$ (90.9)
Basic net (loss) income per share (in dollars per share)										$ (0.42)
Diluted net (loss) income per share (in dollars per share)										$ (0.42)
Impact from the adoption of ASC 606 and 340-40 | Restatement Adjustment
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Marketing and sales										$ (17.9)
Provision for income taxes										(4.8)
Net income (loss)										$ (10.1)
Basic net (loss) income per share (in dollars per share)										$ (0.05)
Diluted net (loss) income per share (in dollars per share)										$ (0.05)
Subscription | As reported
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net revenue										$ 1,802.3
Subscription | Impact from the adoption of ASC 606 and 340-40
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net revenue										1,785.7
Subscription | Impact from the adoption of ASC 606 and 340-40 | Restatement Adjustment
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net revenue										(16.6)
Maintenance | As reported
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net revenue										635.1
Maintenance | Impact from the adoption of ASC 606 and 340-40
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net revenue										640.8
Maintenance | Impact from the adoption of ASC 606 and 340-40 | Restatement Adjustment
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net revenue										5.7
Other
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net revenue									$ 23.7	18.2	$ 26.8
Other | As reported
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net revenue										132.4
Cost of revenue										54.4
Other | Impact from the adoption of ASC 606 and 340-40
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net revenue										121.1
Cost of revenue										55.5
Other | Impact from the adoption of ASC 606 and 340-40 | Restatement Adjustment
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net revenue										(11.3)
Cost of revenue										1.1
Cost of subscription and maintenance revenue
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net revenue									$ 3,138.5	2,437.4	$ 1,883.9
Cost of subscription and maintenance revenue | As reported
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Cost of revenue										216.0
Cost of subscription and maintenance revenue | Impact from the adoption of ASC 606 and 340-40
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Cost of revenue										215.9
Cost of subscription and maintenance revenue | Impact from the adoption of ASC 606 and 340-40 | Restatement Adjustment
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Cost of revenue										$ (0.1)