<!-- For best results, you should include the HTML-coded --> <!-- metadata that you find further down the page --> <!-- (below the line) in the <HEAD></HEAD>-tag of your --> <!-- page. This will simplify correct indexing by robots. --> <!-- ---------------------------------------------------- --> <META NAME="DC.Title" CONTENT="Mathematical Knowledge Representation"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#title"> <META NAME="DC.Creator" CONTENT="James H. Davenport"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#creator"> <META NAME="DC.Contributor.CorporateName" CONTENT="The OpenMath Society"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#contributor"> <META NAME="DC.Subject" CONTENT="OpenMath"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#subject"> <META NAME="DC.Subject" CONTENT="Knowledge"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#subject"> <META NAME="DC.Subject" CONTENT="Notation"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#subject"> <META NAME="DC.Subject" CONTENT="(SCHEME=LCSH) QA11"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#subject"> <META NAME="DC.Subject" CONTENT="(SCHEME=LCSH) T10.5"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#subject"> <META NAME="DC.Subject" CONTENT="(SCHEME=MSC) 00A20"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#subject"> <META NAME="DC.Subject" CONTENT="(SCHEME=MSC) 68P20"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#subject"> <META NAME="DC.Subject" CONTENT="(SCHEME=DDC) 5110.1"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#subject"> <META NAME="DC.Description" CONTENT="On the one hand, we all ``know'' that $\sqrt{z^2}=z$, but on the other hand we know that this is false when $z=-1$. We all know that $\ln e^x=x$, and we all know that this is false when $x=2\pi i$. How do we imbue a computer algebra system with this sort of ``knowledge''? Why is it that $\sqrt x\sqrt y =\sqrt{xy}$ is false in general ($x=y=-1$), but $\sqrt{1-z}\sqrt{1+z}=\sqrt{1-z^2}$ is true everywhere? It is the contention of this paper that, only by considering the geometry of $\C$ (or $\C^n$ if there are $n$ variables) induced by the various branch cuts can we hope to answer these questions even semi-algorithmically. This poses questions for geometry, and calls out for a more efficient form of cylindrical algebraic decomposition. "> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#description"> <META NAME="DC.Publisher" CONTENT="RISC, University of Linz"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#publisher"> <META NAME="DC.Date" CONTENT="(SCHEME=ISO8601) 2001-09-26"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#date"> <META NAME="DC.Type" CONTENT="Text.Article"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#type"> <META NAME="DC.Format" CONTENT="(SCHEME=IMT) application/pdf"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#format"> <LINK REL=SCHEMA.imt HREF="http://sunsite.auc.dk/RFC/rfc/rfc2046.html"> <META NAME="DC.Format.X-Carrier" CONTENT="file"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#format"> <META NAME="DC.Identifier" CONTENT="(SCHEME=URL) http://www.risc.uni-linz.ac.at/conferences/MKM2001/Proceedings"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#identifier"> <META NAME="DC.Language" CONTENT="(SCHEME=ISO639-1) en"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#language"> <META NAME="EULER.Event.Location" CONTENT="RISC, Universiy of Linz"> <LINK REL=SCHEMA.dc HREF="http://www.lub.lu.se/EULER/partners/april99-metadatacreator.html"> <META NAME="EULER.Event.Date" CONTENT="(SCHEME=ISO8601) 2001-09-26"> <LINK REL=SCHEMA.dc HREF="http://www.lub.lu.se/EULER/partners/april99-metadatacreator.html"> <META NAME="EULER.Event.Name" CONTENT="Mathematical Knowledge Management"> <LINK REL=SCHEMA.dc HREF="http://www.lub.lu.se/EULER/partners/april99-metadatacreator.html"> <META NAME="DC.Date.X-MetadataLastModified" CONTENT="(SCHEME=ISO8601) 2001-10-26"> <LINK REL=SCHEMA.dc HREF="http://purl.org/metadata/dublin_core_elements#date">