Income Taxes - Reconciliation of Income Taxes Calculated at U.S. Federal Statutory Income Tax Rate (Detail) - USD ($) $ in Thousands	12 Months Ended
Dec. 31, 2023	Dec. 31, 2022	Dec. 31, 2021
Income Tax Disclosure [Abstract]
U.S. federal statutory rate	21.00%	21.00%	21.00%
Income taxes at U.S. federal statutory rate	$ 2,650	$ (5,925)	$ (60)
Foreign income taxes at rates other than the federal statutory rate	1,733	2,249	2,950
U.S. state and local income taxes, net of U.S. federal tax benefit	(1,952)	(5,976)	(4,826)
U.S. effect of foreign operations	(9,931)	15,827	1,827
Change in valuation allowance	29,849	7,830	20,212
Foreign withholding taxes	7,444	6,738	(4,545)
U.S. foreign tax credit and deduction	(17,522)	(12,315)	(288)
Research and development tax credit	391	(326)	(784)
Stock-based compensation	1,361	8,649	(12,791)
Other	123	1,250	753
Uncertain tax positions	6,370	472	6,058
FDII deduction	(169)	(5,245)	0
Mark-to-market adjustment of contingent consideration	1,198	(1,502)	0
Repurchase of convertible senior notes	0	3,490	0
Income tax expense	$ 21,545	$ 15,216	$ 8,506

Effective income tax rate reconciliation foreign income tax withholding amount.

No definition available.

Name:	altr_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxWithholdingAmount
Namespace Prefix:	altr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- 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 repurchase of convertible senior notes.

+ References

No definition available.