Debt - Schedule of Convertible Notes (Detail) - USD ($)	Mar. 31, 2023	Dec. 31, 2022
Debt Instrument [Line Items]
Net carrying amount	$ 81,004,000	$ 0
Net carrying amount	225,039,000	305,604
Convertible Senior Notes Due in 2024 [Member]
Debt Instrument [Line Items]
Principal	81,754,000	81,754,000
Less: unamortized debt issuance costs	750,000	903,000
Net carrying amount	81,004,000
Net carrying amount		80,851,000
Convertible senior notes due in 2027 [Member]
Debt Instrument [Line Items]
Principal	230,000,000	230,000,000
Less: unamortized debt issuance costs	4,961,000	5,247,000
Net carrying amount	$ 225,039,000	$ 224,753,000

Carrying value as of the balance sheet date of long-term debt (with maturities initially due after one year or beyond the operating cycle if longer) identified as Convertible Notes Payable, excluding current portion. Convertible Notes Payable is a written promise to pay a note which can be exchanged for a specified amount of another, related security, at the option of the issuer and the holder.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22)
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_ConvertibleLongTermNotesPayable
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Carrying value as of the balance sheet date of the portion of long-term debt due within one year or the operating cycle if longer identified as Convertible Notes Payable. Convertible Notes Payable is a written promise to pay a note which can be exchanged for a specified amount of another, related security, at the option of the issuer and the holder.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.20)
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_ConvertibleNotesPayableCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount, before unamortized (discount) premium and debt issuance costs, of long-term debt. Includes, but is not limited to, notes payable, bonds payable, commercial loans, mortgage loans, convertible debt, subordinated debt and other types of debt.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (b)(1)
-URI https://asc.fasb.org/extlink&oid=123466204&loc=SL6031897-161870

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(16))
-URI https://asc.fasb.org/extlink&oid=126734703&loc=d3e572229-122910

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(16))
-URI https://asc.fasb.org/extlink&oid=126897435&loc=d3e534808-122878

+ Details

Name:	us-gaap_DebtInstrumentCarryingAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount, after accumulated amortization, of debt issuance costs. Includes, but is not limited to, legal, accounting, underwriting, printing, and registration costs.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 1D
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=123466505&loc=SL123495340-112611

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 3
-URI https://asc.fasb.org/extlink&oid=124435984&loc=d3e28555-108399

+ Details

Name:	us-gaap_DeferredFinanceCostsNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_DebtInstrumentAxis=altr_ConvertibleSeniorNotesDueInTwoThousandTwentyFourMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=altr_ConvertibleSeniorNotesDueInTwoThousandTwentySevenMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: