forms/doc/forms.aux

22 \newlabel{intro}{{1}{4}{\textcolor {Chapter }{Introduction}}{chapter.1}{}}
24 \newlabel{philosophy}{{1.1}{4}{\textcolor {Chapter }{Philosophy}}{section.1.1}{}}
26 \newlabel{overview}{{1.2}{4}{\textcolor {Chapter }{Overview over this manual}}{section.1.2}{}}
28 \newlabel{howto}{{1.3}{4}{\textcolor {Chapter }{How to read this manual}}{section.1.3}{}}
30 \newlabel{web}{{1.4}{5}{\textcolor {Chapter }{Web resources}}{section.1.4}{}}
32 \newlabel{release_notes}{{1.5}{5}{\textcolor {Chapter }{Release notes}}{section.1.5}{}}
36 \newlabel{examples}{{2}{6}{\textcolor {Chapter }{Examples}}{chapter.2}{}}
51 \newlabel{theory}{{3}{10}{\textcolor {Chapter }{Background Theory on Forms}}{chapter.3}{}}
57 \newlabel{theory:sesquilinearforms}{{3.1}{10}{\textcolor {Chapter }{Sesquilinear forms}}{section.3.…
67 \newlabel{quadforms}{{3.2}{15}{\textcolor {Chapter }{Quadratic forms}}{section.3.2}{}}
73 \newlabel{functionality}{{4}{20}{\textcolor {Chapter }{Constructing forms and basic functionality}}…
75 \newlabel{sec:filters}{{4.1}{20}{\textcolor {Chapter }{Important filters}}{section.4.1}{}}
77 \newlabel{IsBilinearForm}{{4.1.1}{20}{\textcolor {Chapter }{Categories for forms}}{subsection.4.1.1…
78 \newlabel{IsHermitianForm}{{4.1.1}{20}{\textcolor {Chapter }{Categories for forms}}{subsection.4.1.…
79 \newlabel{IsSesquilinearForm}{{4.1.1}{20}{\textcolor {Chapter }{Categories for forms}}{subsection.4…
80 \newlabel{IsQuadraticForm}{{4.1.1}{20}{\textcolor {Chapter }{Categories for forms}}{subsection.4.1.…
81 \newlabel{IsForm}{{4.1.1}{20}{\textcolor {Chapter }{Categories for forms}}{subsection.4.1.1}{}}
82 \newlabel{IsForm}{{4.1.1}{20}{\textcolor {Chapter }{Categories for forms}}{subsection.4.1.1}{}}
83 \newlabel{IsTrivialForm}{{4.1.1}{20}{\textcolor {Chapter }{Categories for forms}}{subsection.4.1.1}…
85 \newlabel{IsFormRep}{{4.1.2}{20}{\textcolor {Chapter }{Representation for forms}}{subsection.4.1.2}…
87 \newlabel{sec:formsbymatrix}{{4.2}{21}{\textcolor {Chapter }{Constructing forms using a matrix}}{se…
89 \newlabel{BilinearFormByMatrix}{{4.2.1}{21}{\textcolor {Chapter }{BilinearFormByMatrix}}{subsection…
90 \newlabel{BilinearFormByMatrix}{{4.2.1}{21}{\textcolor {Chapter }{BilinearFormByMatrix}}{subsection…
92 \newlabel{QuadraticFormByMatrix}{{4.2.2}{22}{\textcolor {Chapter }{QuadraticFormByMatrix}}{subsecti…
93 \newlabel{QuadraticFormByMatrix}{{4.2.2}{22}{\textcolor {Chapter }{QuadraticFormByMatrix}}{subsecti…
95 \newlabel{HermitianFormByMatrix}{{4.2.3}{23}{\textcolor {Chapter }{HermitianFormByMatrix}}{subsecti…
97 \newlabel{sec:formsbypolynomial}{{4.3}{24}{\textcolor {Chapter }{Constructing forms using a polynom…
99 \newlabel{BilinearFormByPolynomial}{{4.3.1}{24}{\textcolor {Chapter }{BilinearFormByPolynomial}}{su…
100 \newlabel{BilinearFormByPolynomial}{{4.3.1}{24}{\textcolor {Chapter }{BilinearFormByPolynomial}}{su…
102 \newlabel{QuadraticFormByPolynomial}{{4.3.2}{25}{\textcolor {Chapter }{QuadraticFormByPolynomial}}{…
103 \newlabel{QuadraticFormByPolynomial}{{4.3.2}{25}{\textcolor {Chapter }{QuadraticFormByPolynomial}}{…
105 \newlabel{HermitianFormByPolynomial}{{4.3.3}{25}{\textcolor {Chapter }{HermitianFormByPolynomial}}{…
106 \newlabel{HermitianFormByPolynomial}{{4.3.3}{25}{\textcolor {Chapter }{HermitianFormByPolynomial}}{…
108 \newlabel{switch}{{4.4}{26}{\textcolor {Chapter }{Switching between bilinear and quadratic forms}}{…
110 \newlabel{QuadraticFormByBilinearForm}{{4.4.1}{26}{\textcolor {Chapter }{QuadraticFormByBilinearFor…
112 \newlabel{BilinearFormByQuadraticForm}{{4.4.2}{27}{\textcolor {Chapter }{BilinearFormByQuadraticFor…
114 \newlabel{AssociatedBilinearForm}{{4.4.3}{28}{\textcolor {Chapter }{AssociatedBilinearForm}}{subsec…
116 \newlabel{evaluate}{{4.5}{29}{\textcolor {Chapter }{Evaluating forms}}{section.4.5}{}}
118 \newlabel{EvaluateForm}{{4.5.1}{29}{\textcolor {Chapter }{EvaluateForm}}{subsection.4.5.1}{}}
119 \newlabel{EvaluateForm}{{4.5.1}{29}{\textcolor {Chapter }{EvaluateForm}}{subsection.4.5.1}{}}
121 \newlabel{ortho}{{4.6}{30}{\textcolor {Chapter }{Orthogonality, totally isotropic subspaces, and to…
123 \newlabel{OrthogonalSubspaceMat}{{4.6.1}{30}{\textcolor {Chapter }{OrthogonalSubspaceMat}}{subsecti…
124 \newlabel{OrthogonalSubspaceMat}{{4.6.1}{30}{\textcolor {Chapter }{OrthogonalSubspaceMat}}{subsecti…
126 \newlabel{IsIsotropicVector}{{4.6.2}{31}{\textcolor {Chapter }{IsIsotropicVector}}{subsection.4.6.2…
128 \newlabel{IsSingularVector}{{4.6.3}{31}{\textcolor {Chapter }{IsSingularVector}}{subsection.4.6.3}{…
130 \newlabel{IsTotallyIsotropicSubspace}{{4.6.4}{32}{\textcolor {Chapter }{IsTotallyIsotropicSubspace}…
132 \newlabel{IsTotallySingularSubspace}{{4.6.5}{33}{\textcolor {Chapter }{IsTotallySingularSubspace}}{…
134 \newlabel{properties}{{4.7}{33}{\textcolor {Chapter }{Attributes and properties of forms}}{section.…
136 \newlabel{IsReflexiveForm}{{4.7.1}{33}{\textcolor {Chapter }{IsReflexiveForm}}{subsection.4.7.1}{}}
138 \newlabel{IsAlternatingForm}{{4.7.2}{33}{\textcolor {Chapter }{IsAlternatingForm}}{subsection.4.7.2…
140 \newlabel{IsSymmetricForm}{{4.7.3}{34}{\textcolor {Chapter }{IsSymmetricForm}}{subsection.4.7.3}{}}
142 \newlabel{IsOrthogonalForm}{{4.7.4}{34}{\textcolor {Chapter }{IsOrthogonalForm}}{subsection.4.7.4}{…
144 \newlabel{IsPseudoForm}{{4.7.5}{34}{\textcolor {Chapter }{IsPseudoForm}}{subsection.4.7.5}{}}
146 \newlabel{IsSymplecticForm}{{4.7.6}{34}{\textcolor {Chapter }{IsSymplecticForm}}{subsection.4.7.6}{…
148 \newlabel{IsDegenerateForm}{{4.7.7}{34}{\textcolor {Chapter }{IsDegenerateForm}}{subsection.4.7.7}{…
150 \newlabel{IsSingularForm}{{4.7.8}{35}{\textcolor {Chapter }{IsSingularForm}}{subsection.4.7.8}{}}
152 \newlabel{BaseField}{{4.7.9}{35}{\textcolor {Chapter }{BaseField}}{subsection.4.7.9}{}}
154 \newlabel{GramMatrix}{{4.7.10}{35}{\textcolor {Chapter }{GramMatrix}}{subsection.4.7.10}{}}
156 \newlabel{RadicalOfForm}{{4.7.11}{35}{\textcolor {Chapter }{RadicalOfForm}}{subsection.4.7.11}{}}
160 \newlabel{PolynomialOfForm}{{4.7.12}{36}{\textcolor {Chapter }{PolynomialOfForm}}{subsection.4.7.12…
162 \newlabel{DiscriminantOfForm}{{4.7.13}{36}{\textcolor {Chapter }{DiscriminantOfForm}}{subsection.4.…
165 \newlabel{recognition}{{4.8}{36}{\textcolor {Chapter }{Recognition of forms preserved by a classica…
168 \newlabel{PreservedForms}{{4.8.1}{37}{\textcolor {Chapter }{PreservedForms}}{subsection.4.8.1}{}}
170 \newlabel{PreservedSesquilinearForms}{{4.8.2}{38}{\textcolor {Chapter }{PreservedSesquilinearForms}…
172 \newlabel{PreservedQuadraticForms}{{4.8.3}{39}{\textcolor {Chapter }{PreservedQuadraticForms}}{subs…
174 \newlabel{trivialform}{{4.9}{39}{\textcolor {Chapter }{The trivial form and some of its properties}…
183 \newlabel{morphisms}{{5}{42}{\textcolor {Chapter }{Morphisms of forms}}{chapter.5}{}}
189 \newlabel{morphisms:sesquilinear}{{5.1}{42}{\textcolor {Chapter }{Morphisms of sesquilinear forms}}…
195 \newlabel{morphisms:hermitian}{{5.1.1}{43}{\textcolor {Chapter }{Hermitian forms}}{subsection.5.1.1…
198 \newlabel{morphisms:alternating}{{5.1.2}{43}{\textcolor {Chapter }{Alternating forms}}{subsection.5…
201 \newlabel{morphisms:bilinear}{{5.1.3}{43}{\textcolor {Chapter }{Bilinear forms}}{subsection.5.1.3}{…
208 \newlabel{morphisms:degenerate}{{5.1.4}{45}{\textcolor {Chapter }{Degenerate forms}}{subsection.5.1…
210 \newlabel{morphisms:quadratic}{{5.2}{45}{\textcolor {Chapter }{Morphisms of quadratic forms}}{secti…
214 \newlabel{morphisms:singular}{{5.2.1}{46}{\textcolor {Chapter }{Singular forms}}{subsection.5.2.1}{…
216 \newlabel{morphisms_functions}{{5.3}{47}{\textcolor {Chapter }{Operations based on morphisms of for…
218 \newlabel{BaseChangeToCanonical}{{5.3.1}{47}{\textcolor {Chapter }{BaseChangeToCanonical}}{subsecti…
220 \newlabel{BaseChangeHomomorphism}{{5.3.2}{47}{\textcolor {Chapter }{BaseChangeHomomorphism}}{subsec…
222 \newlabel{IsometricCanonicalForm}{{5.3.3}{48}{\textcolor {Chapter }{IsometricCanonicalForm}}{subsec…
224 \newlabel{ScalarOfSimilarity}{{5.3.4}{49}{\textcolor {Chapter }{ScalarOfSimilarity}}{subsection.5.3…
226 \newlabel{WittIndex}{{5.3.5}{49}{\textcolor {Chapter }{WittIndex}}{subsection.5.3.5}{}}
228 \newlabel{IsEllipticForm}{{5.3.6}{50}{\textcolor {Chapter }{IsEllipticForm}}{subsection.5.3.6}{}}
230 \newlabel{IsParabolicForm}{{5.3.7}{50}{\textcolor {Chapter }{IsParabolicForm}}{subsection.5.3.7}{}}
232 \newlabel{IsHyperbolicForm}{{5.3.8}{50}{\textcolor {Chapter }{IsHyperbolicForm}}{subsection.5.3.8}{…
234 \newlabel{TypeOfForm}{{5.3.9}{51}{\textcolor {Chapter }{TypeOfForm}}{subsection.5.3.9}{}}