Income Taxes - Differences between the U.S. statutory rate and the aggregate income tax provision (Details) - USD ($)	3 Months Ended								12 Months Ended
	Jan. 31, 2019	Oct. 31, 2018	Jul. 31, 2018	Apr. 30, 2018	Jan. 31, 2018	Oct. 31, 2017	Jul. 31, 2017	Apr. 30, 2017	Jan. 31, 2019	Jan. 31, 2018	Jan. 31, 2017
Income Tax Disclosure [Abstract]
First $1M of officer compensation									$ 1,000,000
Income tax provision (benefit) at U.S. Federal statutory rate									(9,000,000.0)	$ (188,400,000)	$ (177,000,000.0)
State income tax benefit, net of the U.S. Federal benefit									(11,400,000)	(21,900,000)	(17,300,000)
Foreign income taxed at rates different from the U.S. statutory rate									117,800,000	(53,300,000)	22,300,000
U.S. valuation allowance									18,800,000	(82,500,000)	233,000,000.0
Transition tax									(16,000,000.0)	408,400,000	0
Increase in attributes due to ASU 2016-9 adoption									0	0	(119,400,000)
Change in valuation allowance from ASU 2016-9 adoption									0	0	119,400,000
Tax effect of non-deductible stock-based compensation									7,600,000	20,700,000	18,800,000
Stock compensation windfall / shortfall									(39,400,000)	(67,700,000)	(23,000,000.0)
Research and development tax credit benefit									(23,500,000)	(11,300,000)	(10,300,000)
Closure of income tax audits and changes in uncertain tax positions									(12,700,000)	1,200,000	8,200,000
Tax effect of officer compensation in excess of $1.0 million									5,000,000.0	2,200,000	2,200,000
Non-deductible expenses									1,500,000	2,100,000	2,000,000.0
Other									(600,000)	100,000	(600,000)
Income tax expense	$ 31,700,000	$ 35,200,000	$ 16,000,000.0	$ 18,600,000	$ (24,800,000)	$ 8,600,000	$ 17,600,000	$ 8,200,000	$ 38,100,000	$ 9,600,000	$ 58,300,000