src/HOL/Complex/README.html
changeset 14634 ffb4099c316f
parent 14631 ec1e67f88f49
child 14641 79b7bd936264
--- a/src/HOL/Complex/README.html	Tue Apr 20 04:09:19 2004 +0200
+++ b/src/HOL/Complex/README.html	Wed Apr 21 13:18:37 2004 +0200
@@ -7,19 +7,52 @@
 with numeric constants and some complex analysis.  The development includes
 nonstandard analysis for the complex numbers.  Note that the image
 <KBD>HOL-Complex</KBD> includes theories from the directories 
-<KBD><a href="../Real/">HOL/Real</a></KBD>  and <KBD><a href="../Hyperreal/">HOL/Hyperreal</a></KBD>.
-
-
-		<ul>
+<KBD><a href="#Anchor-Real">HOL/Real</a></KBD>  and <KBD><a href="#Anchor-Hyperreal">HOL/Hyperreal</a></KBD>. They define other types including <kbd>real</kbd> (the real numbers) and <kbd>hypreal</kbd> (the hyperreal or non-standard reals).<ul>
 			<li><a href="CLim.html">CLim</a> Limits, continuous functions, and derivatives for the complex numbers
 			<li><a href="CSeries.html">CSeries</a> Finite summation and infinite series for the complex numbers
 			<li><a href="CStar.html">CStar</a> Star-transforms for the complex numbers, to form non-standard extensions of sets and functions
 			<li><a href="Complex.html">Complex</a> The complex numbers
 			<li><a href="NSCA.html">NSCA</a> Nonstandard complex analysis
 			<li><a href="NSComplex.html">NSComplex</a> Ultrapower construction of the nonstandard complex numbers
+			
 			<li><a href="NSInduct.html">NSInduct</a> Nonstandard induction for the hypernatural numbers
+		
+			
+		</ul>
+		<h2><a name="Anchor-Real" id="Anchor-Real"></a>Real: Dedekind Cut Construction of the Real Line</h2>
+		<ul>
+			<li><a href="Lubs.html">Lubs</a> Definition of upper bounds, lubs and so on, to support completeness proofs.
+			<li><a href="PReal.html">PReal</a> The positive reals constructed using Dedekind cuts
+			<li><a href="Rational.html">Rational</a> The rational numbers constructed as equivalence classes of integers
+			<li><a href="RComplete.html">RComplete</a> The reals are complete: they satisfy the supremum property. They also have the Archimedean property.
+			<li><a href="RealDef.html">RealDef</a> The real numbers, their ordering properties, and embedding of the integers and the natural numbers
+			<li><a href="RealPow.html">RealPow</a> Real numbers raised to natural number powers
+		</ul>
+		<h2><a name="Anchor-Hyperreal" id="Anchor-Hyperreal"></a>Hyperreal: Ultrafilter Construction of the Non-Standard Reals</h2>
+		See J. D. Fleuriot and L. C. Paulson. Mechanizing Nonstandard Real Analysis. LMS J. Computation and Mathematics 3 (2000), 140-190.
+		<ul>
+			<li><a href="Filter.html">Filter</a> Theory of Filters and Ultrafilters. Main result is a version of the Ultrafilter Theorem proved using Zorn's Lemma.
+			<li><a href="HLog.html">HLog</a> Non-standard logarithms
+			<li><a href="HSeries.html">HSeries</a> Non-standard theory of finite summation and infinite series
+			<li><a href="HTranscendental.html">HTranscendental</a> Non-standard extensions of transcendental functions
+			<li><a href="HyperDef.html">HyperDef</a> Ultrapower construction of the hyperreals
+			<li><a href="HyperNat.html">HyperNat</a> Ultrapower construction of the hypernaturals
+			<li><a href="HyperPow.html">HyperPow</a> Powers theory for the hyperreals
+			<li><a href="IntFloor.html">IntFloor</a> Floor and Ceiling functions relating the reals and integers
+			<li><a href="Integration.html">Integration</a> Gage integrals
+			<li><a href="Lim.html">Lim</a> Theory of limits, continuous functions, and derivatives
+			<li><a href="Log.html">Log</a> Logarithms for the reals
+			<li><a href="MacLaurin.html">MacLaurin</a> MacLaurin series
+			<li><a href="NatStar.html">NatStar</a> Star-transforms for the hypernaturals, to form non-standard extensions of sets and functions involving the naturals or reals
+			<li><a href="NthRoot.html">NthRoot</a> Existence of n-th roots of real numbers
+			<li><a href="NSA.html">NSA</a> Theory defining sets of infinite numbers, infinitesimals, the infinitely close relation, and their various algebraic properties.
+			<li><a href="Poly.html">Poly</a> Univariate real polynomials
+			<li><a href="SEQ.html">SEQ</a> Convergence of sequences and series using standard and nonstandard analysis
+			<li><a href="Series.html">Series</a> Finite summation and infinite series for the reals
+			<li><a href="Star.html">Star</a> Nonstandard extensions of real sets and real functions
+			<li><a href="Transcendental.html">Transcendental</a> Power series and transcendental functions
 		</ul>
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+		<P>Last modified $Date$
 
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