Stock-based Compensation - Summary of Stock Option Activity under 2012 Plan (Detail) - 2012 Plan [Member] - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
Dec. 31, 2023	Dec. 31, 2022
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]
Number of options, Outstanding, Beginning Balance	374,574
Number of options, Exercised	(103,215)
Number of options, Outstanding and exercisable, Ending Balance	271,359
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]
Weighted average exercise price per share, Outstanding, Beginning Balance	$ 4.34
Weighted average exercise price per share, Exercised	4.03
Weighted average exercise price per share, Outstanding and exercisable, Ending Balance	$ 4.46
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]
Weighted average remaining contractual term (years), Outstanding		3 years 4 months 24 days
Weighted average remaining contractual term (years), Outstanding and exercisable	2 years 6 months
Aggregate intrinsic value, Outstanding and exercisable	$ 21.6

Share based compensation arrangement by share based payment award options outstanding and exercisable intrinsic value.

No definition available.

Name:	altr_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingAndExercisableIntrinsicValue
Namespace Prefix:	altr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Share based compensation arrangement by share based payment award options outstanding and exercisable number.

+ References

No definition available.

+ Details

Name:	altr_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingAndExercisableNumber
Namespace Prefix:	altr_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Share based compensation arrangement by share based payment award options outstanding and exercisable weighted average exercise price.

+ References

No definition available.

+ Details

Name:	altr_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingAndExercisableWeightedAverageExercisePrice
Namespace Prefix:	altr_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Share based compensation arrangement by share based payment award options outstanding and exercisable weighted average remaining contractual term.

+ References

No definition available.

+ Details

Name:	altr_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingAndExercisableWeightedAverageRemainingContractualTerm
Namespace Prefix:	altr_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- References

No definition available.

+ Details

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

- Definition

Number of options outstanding, including both vested and non-vested options.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(i)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(ii)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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

- Definition

Weighted average price at which grantees can acquire the shares reserved for issuance under the stock option plan.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- References

No definition available.

+ Details

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

- Definition

Weighted average price at which option holders acquired shares when converting their stock options into shares.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average remaining contractual term for option awards outstanding, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 718
-SubTopic 10
-Subparagraph (e)(1)
-Name Accounting Standards Codification
-Paragraph 2
-Section 50
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of share options (or share units) exercised during the current period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-SubTopic 10
-Topic 505
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481112/505-10-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(02)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(28))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480008/505-10-S99-1

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_PlanNameAxis=altr_TwoThousandAndTwelveIncentiveAndNonqualifiedStockOptionPlanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: