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<h1>GAP 4 Package <strong class="pkg">Forms</strong></h1>
<h2>Sesquilinear and Quadratic</h2>
<p>
1.0</p>
<p>May 2007</p>
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<p><b>John Bamberg
</b>
<br />e-mail: <a href="mailto:bamberg@cage.ugent.be">bamberg@cage.ugent.be</a>
<br />WWW: <a href="http://cage.ugent.be/~bamberg">http://cage.ugent.be/~bamberg</a>
<br />Address: <br />Department of Pure Mathematics, Ghent University, Galglaan 2, 9000 Ghent, Belgium
</p><p><b>Jan De Beule
</b>
<br />e-mail: <a href="mailto:jdebeule@cage.ugent.be">jdebeule@cage.ugent.be</a>
<br />WWW: <a href="http://cage.ugent.be/~jdebeule">http://cage.ugent.be/~jdebeule</a>
<br />Address: <br />Department of Pure Mathematics, Ghent University, Galglaan 2, 9000 Ghent, Belgium
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<h3>Copyright</h3>
<p>(C) 2007 by the authors</p>
<p>This package may be distributed under the terms and conditions of the GNU Public License Version 2 or higher.</p>
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<h3>Contents</h3>
<a href="chap1.html#s0ss0">1. Introduction</a><br />
<a href="chap1.html#s1ss0">1.1 Philosophy</a><br />
<a href="chap1.html#s2ss0">1.2 Overview over this manual</a><br />
<a href="chap2.html#s0ss0">2. Examples</a><br />
<a href="chap2.html#s1ss0">2.1 A conic of PG(2,8)</a><br />
<a href="chap2.html#s2ss0">2.2 A form for W(5,3)</a><br />
<a href="chap3.html#s0ss0">3. Background Theory on Forms</a><br />
<a href="chap3.html#s1ss0">3.1 Sesquilinear forms, dualities, and polarities</a><br />
<a href="chap3.html#s1ss1">3.1-1 Example</a><br />
<a href="chap3.html#s2ss0">3.2 Quadratic forms</a><br />
<a href="chap3.html#s2ss1">3.2-1 Example</a><br />
<a href="chap3.html#s3ss0">3.3 Morphisms of forms</a><br />
<a href="chap3.html#s4ss0">3.4 An important convention</a><br />
<a href="chap3.html#s4ss1">3.4-1 Example</a><br />
<a href="chap3.html#s5ss0">3.5 Canonical forms</a><br />
<a href="chap4.html#s0ss0">4. Functionality</a><br />
<a href="chap4.html#s1ss0">4.1 Functions for creating forms</a><br />
<a href="chap4.html#s1ss1">4.1-1 BilinearFormByMatrix</a><br />
<a href="chap4.html#s1ss2">4.1-2 QuadraticFormByMatrix</a><br />
<a href="chap4.html#s1ss3">4.1-3 HermitianFormByMatrix</a><br />
<a href="chap4.html#s1ss4">4.1-4 BilinearFormByPolynomial</a><br />
<a href="chap4.html#s1ss5">4.1-5 QuadraticFormByPolynomial</a><br />
<a href="chap4.html#s1ss6">4.1-6 HermitianFormByPolynomial</a><br />
<a href="chap4.html#s2ss0">4.2 Attributes and properties of forms</a><br />
<a href="chap4.html#s2ss1">4.2-1 IsReflexiveForm</a><br />
<a href="chap4.html#s2ss2">4.2-2 IsAlternatingForm</a><br />
<a href="chap4.html#s2ss3">4.2-3 IsSymmetricForm</a><br />
<a href="chap4.html#s2ss4">4.2-4 IsDegenerateForm</a><br />
<a href="chap4.html#s2ss5">4.2-5 BaseField</a><br />
<a href="chap4.html#s2ss6">4.2-6 GramMatrix</a><br />
<a href="chap4.html#s2ss7">4.2-7 WittIndex</a><br />
<a href="chap4.html#s2ss8">4.2-8 RadicalOfForm</a><br />
<a href="chap4.html#s2ss9">4.2-9 PolynomialOfForm</a><br />
<a href="chap4.html#s2ss10">4.2-10 DiscriminantOfForm</a><br />
<a href="chap4.html#s3ss0">4.3 Functions for changing forms</a><br />
<a href="chap4.html#s3ss1">4.3-1 BaseChangeToCanonical</a><br />
<a href="chap4.html#s3ss2">4.3-2 IsometricCanonicalForm</a><br />
<a href="chap4.html#s4ss0">4.4 Operations on forms</a><br />
<a href="chap4.html#s4ss1">4.4-1 BaseChangeHomomorphism</a><br />
<a href="chap4.html#s4ss2">4.4-2 EvaluateForm</a><br />
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