From mboxrd@z Thu Jan 1 00:00:00 1970 Received: from Hermes.metastack.local (172.16.0.8) by Hermes.metastack.local (172.16.0.8) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256) id 15.1.2507.17 via Mailbox Transport; Thu, 19 Jan 2023 08:37:59 +0000 Received: from Hermes.metastack.local (172.16.0.8) by Hermes.metastack.local (172.16.0.8) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256) id 15.1.2507.17; Thu, 19 Jan 2023 08:37:59 +0000 Received: from exchange.romulus.metastack.com (172.16.0.21) by Hermes.metastack.local (172.16.0.8) with Microsoft SMTP Server (version=TLS1_0, cipher=TLS_RSA_WITH_AES_256_CBC_SHA) id 15.1.2507.17 via Frontend Transport; Thu, 19 Jan 2023 08:37:59 +0000 Received: from romulus.metastack.com ([172.16.0.20]) by exchange.romulus.metastack.com (8.14.2/8.14.2) with ESMTP id 30J8bFeF015667 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO) for ; Thu, 19 Jan 2023 08:37:15 GMT Received: from mail2-relais-roc.national.inria.fr (mail2-relais-roc.national.inria.fr [192.134.164.83]) by romulus.metastack.com (8.14.2/8.14.2) with ESMTP id 30J8b8dl015647 for ; Thu, 19 Jan 2023 08:37:08 GMT Received: from prod-listesu18.inria.fr (HELO sympa.inria.fr) ([128.93.162.160]) by mail2-relais-roc.national.inria.fr with ESMTP; 19 Jan 2023 09:37:05 +0100 Received: by sympa.inria.fr (Postfix, from userid 20132) id E97FDE0395; Thu, 19 Jan 2023 09:37:06 +0100 (CET) Received: from mail2-relais-roc.national.inria.fr (mail2-relais-roc.national.inria.fr [192.134.164.83]) by sympa.inria.fr (Postfix) with ESMTPS id 920D7E0394 for ; Thu, 19 Jan 2023 09:37:02 +0100 (CET) Received: from mail-dbaeur03on2122.outbound.protection.outlook.com (HELO EUR03-DBA-obe.outbound.protection.outlook.com) ([40.107.104.122]) by mail2-smtp-roc.national.inria.fr with ESMTP/TLS/ECDHE-RSA-AES256-GCM-SHA384; 19 Jan 2023 09:36:59 +0100 Received: from AM6PR03MB5781.eurprd03.prod.outlook.com (2603:10a6:20b:f4::26) by GVXPR03MB8329.eurprd03.prod.outlook.com (2603:10a6:150:3e::22) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.6002.25; Thu, 19 Jan 2023 08:36:58 +0000 Received: from AM6PR03MB5781.eurprd03.prod.outlook.com ([fe80::cbdc:c6b6:3f81:5c1]) by AM6PR03MB5781.eurprd03.prod.outlook.com ([fe80::cbdc:c6b6:3f81:5c1%4]) with mapi id 15.20.6002.025; Thu, 19 Jan 2023 08:36:58 +0000 From: =?iso-8859-1?Q?Nicolas_H=F6ck?= To: "caml-list@inria.fr" Subject: [Caml-list] Unsubscribe - Re: Algorithmic integration Thread-Topic: [Caml-list] Unsubscribe - Re: Algorithmic integration Thread-Index: AQHZK+FWKDW5lQXX0U2aXelem3xamw== Sender: "caml-list-request@inria.fr" X-MS-Exchange-MessageSentRepresentingType: 2 Date: Thu, 19 Jan 2023 08:36:58 +0000 Message-ID: References: Keywords: Sent to dra-news@metastack.com,MetaStack - Lists,MetaStack List-Help: List-Subscribe: List-Unsubscribe: In-Reply-To: Reply-To: =?iso-8859-1?Q?Nicolas_H=F6ck?= Accept-Language: en-GB, en-US Content-Language: en-US X-MS-Exchange-Organization-AuthAs: Anonymous X-MS-Exchange-Organization-AuthSource: Hermes.metastack.local X-MS-Has-Attach: X-Auto-Response-Suppress: All X-MS-Exchange-Organization-Network-Message-Id: c13c6f09-aff5-4aa8-e367-08daf9f8788d X-MS-TNEF-Correlator: X-MS-Exchange-Organization-RecordReviewCfmType: 0 x-scanned-by: MIMEDefang 2.65 on 62.31.23.242 received-spf: None (mail2-relais-roc.national.inria.fr: no sender authenticity information available from domain of postmaster@sympa.inria.fr) identity=helo; client-ip=128.93.162.160; receiver=mail2-relais-roc.national.inria.fr; envelope-from="caml-list-owner@inria.fr"; x-sender="postmaster@sympa.inria.fr"; x-conformance=spf_only x-ironport-av: E=Sophos;i="5.97,228,1669071600"; d="scan'208,217";a="88408644" x-ironport-anti-spam-filtered: true x-loop: caml-list@inria.fr x-no-archive: yes x-ms-publictraffictype: Email Content-Type: text/html; charset="iso-8859-1" Content-ID: Content-Transfer-Encoding: quoted-printable MIME-Version: 1.0 Pls unsubscribe.

On 19 Jan 2023, at 07:13, Markus Mottl <markus.mottl@gmail.com> = wrote:

You don't often get email from markus.mottl@gmail.com. Learn why this is important
When it comes to integration, one way to use algorithmic differen= tiation (AD) is that if your program corresponds to an analytic function wi= thin the range of the integral, you could calculate a power series approxim= ation using AD.  The resulting polynomial can be trivially integrated.  The solution could be made exact if the= program corresponds to a finite power series, or could be approximated to = an arbitrary degree otherwise.

Most AD systems, including Owl, cannot feasibly do this, because they = would have to use repeated differentiation for higher order polynomials.&nb= sp; This takes exponential time.  But it can be done in quadratic time= using power series convolutions, or in some cases with Fourier transforms (e.g. matrix multiplication) even in O(D log= (D)), where D is the degree of the polynomial.

There are algorithms for exact real integration, but last time I check= ed, they are dog slow.

On Tue, Jan 17, 2023 at 5:05 PM Kenne= th Adam Miller <kennethadammiller@gmail.com> wrote:
Does anybody know how I could do symbolic integration with= OCaml? I see the owl package, but it appears that it only has differentiat= ion. Is there any way I could implement integration with this same library?=


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Markus Mottl        http://www.ocaml.info        markus.mottl@gmail.com