Income Taxes - Differences between the U.S. statutory rate and the aggregate income tax provision (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 31, 2022	Jan. 31, 2021	Jan. 31, 2020
Income Tax Disclosure [Abstract]
Income tax provision at U.S. Federal statutory rate	$ 118.6	$ 114.8	$ 61.9
State income tax benefit, net of the U.S. Federal benefit	2.2	(43.0)	1.8
Foreign income taxed at rates different from the U.S. statutory rate	(25.4)	(11.5)	(81.0)
Valuation allowance adjustment	(0.2)	(637.4)	93.9
Transition tax and revisions due to subsequent regulations	0.0	0.0	9.6
Tax effect of non-deductible stock-based compensation	32.3	24.8	29.2
Stock compensation (windfall) / shortfall	(43.2)	(35.1)	(22.5)
Research and development tax credit benefit	(18.5)	(15.5)	(19.8)
Closure of income tax audits and changes in uncertain tax positions	(0.4)	0.1	(2.1)
Tax effect of officer compensation in excess of $1.0 million	7.0	4.6	3.4
Non-deductible expenses	4.5	2.3	5.4
Global intangible low-taxed income, foreign derived intangible income	24.1	(65.0)	0.0
India withholding tax refund	(43.8)	0.0	0.0
Acquisition-related integrations	9.0	0.0	0.0
Other	1.5	(0.6)	0.5
Income tax provision (benefit)	67.7	$ (661.5)	$ 80.3
First $1M of officer compensation	$ 1.0