Income Taxes - Differences between the U.S. statutory rate and the aggregate income tax provision (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Jan. 31, 2021	Oct. 31, 2020	Jul. 31, 2020	Apr. 30, 2020	Jan. 31, 2020	Oct. 31, 2019	Jul. 31, 2019	Apr. 30, 2019	Jan. 31, 2021	Jan. 31, 2020	Jan. 31, 2019
Income Tax Disclosure [Abstract]
Income tax provision (benefit) at U.S. Federal statutory rate									$ 114.8	$ 61.9	$ (9.0)
State income tax benefit, net of the U.S. Federal benefit									(7.9)	(5.3)	(11.4)
Foreign income taxed at rates different from the U.S. statutory rate									(15.7)	(41.2)	117.8
Valuation allowance adjustment									(661.7)	65.3	18.8
Transition tax and revisions due to subsequent regulations										9.6	(16.0)
Tax effect of non-deductible stock-based compensation									20.4	24.9	7.6
Stock compensation windfall / shortfall									(35.4)	(22.4)	(39.4)
Research and development tax credit benefit									(22.1)	(19.8)	(23.5)
Closure of income tax audits and changes in uncertain tax positions									0.0	(2.0)	(12.7)
Tax effect of officer compensation in excess of $1.0 million									4.6	3.4	5.0
Non-deductible expenses									2.3	5.4	1.5
Global intangible low-taxed income, foreign derived intangible income									(65.0)	0.0	0.0
Other									4.2	0.5	(0.6)
Income tax provision (benefit)	$ (740.2)	$ 23.9	$ 30.8	$ 24.0	$ (8.5)	$ 29.7	$ 26.3	$ 32.8	(661.5)	$ 80.3	$ 38.1
First $1M of officer compensation									$ 1.0