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Income Taxes - Differences between the U.S. statutory rate and the aggregate income tax provision (Details) - USD ($) | 3 Months Ended | 12 Months Ended
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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
Income Tax Disclosure [Abstract] |  |  |  |  |  |  |  |  |  |  |
First $1M of officer compensation |  |  |  |  |  |  |  |  | $ 1,000,000 |  |
Income tax provision (benefit) at U.S. Federal statutory rate |  |  |  |  |  |  |  |  | 61,900,000 | $ (9,000,000.0) | $ (188,400,000)
State income tax benefit, net of the U.S. Federal benefit |  |  |  |  |  |  |  |  | (5,300,000) | (11,400,000) | (21,900,000)
Foreign income taxed at rates different from the U.S. statutory rate including GILTI |  |  |  |  |  |  |  |  | (41,200,000) | 117,800,000 | (53,300,000)
Valuation allowance adjustment |  |  |  |  |  |  |  |  | 65,300,000 | 18,800,000 | (82,500,000)
Transition tax and revisions due to subsequent regulations |  |  |  |  |  |  |  |  | 9,600,000 | (16,000,000.0) | 408,400,000
Tax effect of non-deductible stock-based compensation |  |  |  |  |  |  |  |  | 24,900,000 | 7,600,000 | 20,700,000
Stock compensation windfall / shortfall |  |  |  |  |  |  |  |  | (22,400,000) | (39,400,000) | (67,700,000)
Research and development tax credit benefit |  |  |  |  |  |  |  |  | (19,800,000) | (23,500,000) | (11,300,000)
Closure of income tax audits and changes in uncertain tax positions |  |  |  |  |  |  |  |  | (2,000,000.0) | (12,700,000) | 1,200,000
Tax effect of officer compensation in excess of $1.0 million |  |  |  |  |  |  |  |  | 3,400,000 | 5,000,000.0 | 2,200,000
Non-deductible expenses |  |  |  |  |  |  |  |  | 5,400,000 | 1,500,000 | 2,100,000
Other |  |  |  |  |  |  |  |  | 500,000 | (600,000) | 100,000
Income tax expense | $ (8,500,000) | $ 29,700,000 | $ 26,300,000 | $ 32,800,000 | $ (31,700,000) | $ 35,200,000 | $ 16,000,000.0 | $ 18,600,000 | $ 80,300,000 | $ 38,100,000 | $ 9,600,000

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- Definition Effective Income Tax Rate Reconciliation, Tax Cuts and Jobs Act, Transition Tax on Accumulated Foreign Earnings, Amount + References No definition available. + Details
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- Definition The portion of the difference between total income tax expense (benefit) as reported in the Income Statement and the expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income from continuing operations attributable to closure of income tax audits and changes in uncertain tax positions. + References No definition available. + Details
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- Definition The amount of income tax expense or benefit for the period computed by applying the domestic federal statutory tax rates to pretax income from continuing operations. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 13 -URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32698-109319 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 12 -URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319 Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 235 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SX 210.4-08(h)(2)) -URI http://asc.fasb.org/extlink&oid=26873400&loc=d3e23780-122690 + Details
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- Definition Amount of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to other nondeductible expenses. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 12 -URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 13 -URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32698-109319 + Details
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- Definition Amount of reported income tax expense (benefit) in excess of (less than) expected income tax expense (benefit) computed by applying domestic federal statutory income tax rate to pretax income (loss) from continuing operation, attributable to nondeductible expense for award under share-based payment arrangement. Includes, but is not limited to, expense determined to be nondeductible upon grant or after for award under share-based payment arrangement. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 13 -URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32698-109319 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 12 -URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319 + Details
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- Definition Amount of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to other adjustments. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 12 -URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319 + Details
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