author paulson
Thu Jul 01 12:29:53 2004 +0200 (2004-07-01)
changeset 15013 34264f5e4691
parent 14641 79b7bd936264
child 15283 f21466450330
permissions -rw-r--r--
new treatment of binary numerals
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     5 <H1>Complex: The Complex Numbers</H1>
     6 		<P>This directory defines the type <KBD>complex</KBD> of the complex numbers,
     7 with numeric constants and some complex analysis.  The development includes
     8 nonstandard analysis for the complex numbers.  Note that the image
     9 <KBD>HOL-Complex</KBD> includes theories from the directories 
    10 <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).
    12 <ul>
    13 <li><a href="CLim.html">CLim</a> Limits, continuous functions, and derivatives for the complex numbers
    14 <li><a href="CSeries.html">CSeries</a> Finite summation and infinite series for the complex numbers
    15 <li><a href="CStar.html">CStar</a> Star-transforms for the complex numbers, to form non-standard extensions of sets and functions
    16 <li><a href="Complex.html">Complex</a> The complex numbers
    17 <li><a href="NSCA.html">NSCA</a> Nonstandard complex analysis
    18 <li><a href="NSComplex.html">NSComplex</a> Ultrapower construction of the nonstandard complex numbers
    19 </ul>
    21 <h2><a name="Anchor-Real" id="Anchor-Real"></a>Real: Dedekind Cut Construction of the Real Line</h2>
    23 <ul>
    24 <li><a href="Lubs.html">Lubs</a> Definition of upper bounds, lubs and so on, to support completeness proofs.
    25 <li><a href="PReal.html">PReal</a> The positive reals constructed using Dedekind cuts
    26 <li><a href="Rational.html">Rational</a> The rational numbers constructed as equivalence classes of integers
    27 <li><a href="RComplete.html">RComplete</a> The reals are complete: they satisfy the supremum property. They also have the Archimedean property.
    28 <li><a href="RealDef.html">RealDef</a> The real numbers, their ordering properties, and embedding of the integers and the natural numbers
    29 <li><a href="RealPow.html">RealPow</a> Real numbers raised to natural number powers
    30 </ul>
    31 <h2><a name="Anchor-Hyperreal" id="Anchor-Hyperreal"></a>Hyperreal: Ultrafilter Construction of the Non-Standard Reals</h2>
    32 See J. D. Fleuriot and L. C. Paulson. Mechanizing Nonstandard Real Analysis. LMS J. Computation and Mathematics 3 (2000), 140-190.
    33 <ul>
    34 <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.
    35 <li><a href="HLog.html">HLog</a> Non-standard logarithms
    36 <li><a href="HSeries.html">HSeries</a> Non-standard theory of finite summation and infinite series
    37 <li><a href="HTranscendental.html">HTranscendental</a> Non-standard extensions of transcendental functions
    38 <li><a href="HyperDef.html">HyperDef</a> Ultrapower construction of the hyperreals
    39 <li><a href="HyperNat.html">HyperNat</a> Ultrapower construction of the hypernaturals
    40 <li><a href="HyperPow.html">HyperPow</a> Powers theory for the hyperreals
    41 <li><a href="IntFloor.html">IntFloor</a> Floor and Ceiling functions relating the reals and integers
    42 <li><a href="Integration.html">Integration</a> Gage integrals
    43 <li><a href="Lim.html">Lim</a> Theory of limits, continuous functions, and derivatives
    44 <li><a href="Log.html">Log</a> Logarithms for the reals
    45 <li><a href="MacLaurin.html">MacLaurin</a> MacLaurin series
    46 <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
    47 <li><a href="NthRoot.html">NthRoot</a> Existence of n-th roots of real numbers
    48 <li><a href="NSA.html">NSA</a> Theory defining sets of infinite numbers, infinitesimals, the infinitely close relation, and their various algebraic properties.
    49 <li><a href="Poly.html">Poly</a> Univariate real polynomials
    50 <li><a href="SEQ.html">SEQ</a> Convergence of sequences and series using standard and nonstandard analysis
    51 <li><a href="Series.html">Series</a> Finite summation and infinite series for the reals
    52 <li><a href="Star.html">Star</a> Nonstandard extensions of real sets and real functions
    53 <li><a href="Transcendental.html">Transcendental</a> Power series and transcendental functions
    54 </ul>
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    56 <P>Last modified $Date$
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