* Bug 15337 fixed: mistake in l_p definition in norm() page 82/19582/5
Samuel GOUGEON [Tue, 5 Dec 2017 21:14:44 +0000 (22:14 +0100)]
  http://bugzilla.scilab.org/15337

Change-Id: I5ea6856fe971477833df1b293fc285b2e6ea68c2

scilab/CHANGES.md
scilab/modules/elementary_functions/help/en_US/matrixoperations/norm.xml
scilab/modules/elementary_functions/help/fr_FR/matrixoperations/norm.xml
scilab/modules/elementary_functions/help/ja_JP/matrixoperations/norm.xml
scilab/modules/elementary_functions/help/pt_BR/matrixoperations/norm.xml
scilab/modules/elementary_functions/help/ru_RU/matrixoperations/norm.xml

index 5de245c..480bff9 100644 (file)
@@ -235,7 +235,7 @@ Help pages:
 * fixed / improved:  `members`, `part`, `ode`, `ode_optional_output`, `ode_roots`, `plot2d`, `roots`,
   `printf`, `sprintf`, `iconvert`, `stdev`, `xlabel`, `and_op`, `or_op`, `permute`, `tree2code`, `%helps`,
   `scilab|scilex`, `flipdim`, `Matplot_properties`, `meshgrid`, `ismatrix`, `xget`, `xset`, `ieee`, `evstr`,
-  `uigetfont`, `uigetdir`, `uigetfile`, `uiputfile`, `cat`, `makecell`, `xstring`
+  `uigetfont`, `uigetdir`, `uigetfile`, `uiputfile`, `cat`, `makecell`, `xstring`, `norm`
 * rewritten: `consolebox`, `double`, `isoview`, `pixel_drawing_mode`, `householder`, `or`, `|,||`,
 `and`, `&,&&`, `format`, `typeof`, `brackets`, `setlanguage`, `sleep`, `isinf`,
 `bitor`, `bitxor`, `bitand`, `macr2tree`, `geomean`, `clf`, `getPreferencesValue`, `gcd`, `isglobal`, `whereis`, `mode`
@@ -485,6 +485,7 @@ the [development mailing list](dev@lists.scilab.org) for a particular toolbox.
 * [#15302](http://bugzilla.scilab.org/show_bug.cgi?id=15302): `load` crashed when inputs arguments are not strings.
 * [#15306](http://bugzilla.scilab.org/show_bug.cgi?id=15306): After the behavior of `||` was changed, its help page was not up to date.
 * [#15308](http://bugzilla.scilab.org/show_bug.cgi?id=15308): Unlike `evstr(["1 2";"3 4"])`, `evstr(["1;2" "3;4"])` was not accepted.
+* [#15337](http://bugzilla.scilab.org/show_bug.cgi?id=15337): There was a mistake in the definition of the l_p norm of a vector in the `norm` page.
 
 ### Bugs fixed in 6.0.0:
 * [#592](http://bugzilla.scilab.org/show_bug.cgi?id=592): `linspace(a, b, n<=0)` returned `b` instead of `[]`
index 088d049..5109384 100644 (file)
  * along with this program.
  *
  -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="norm" xml:lang="en">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+    xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+    xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+    xmlns:scilab="http://www.scilab.org" xml:id="norm" xml:lang="en">
     <refnamediv>
         <refname>norm</refname>
-        <refpurpose>matrix norm</refpurpose>
+        <refpurpose>norms of a vector or a matrix</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Syntax</title>
-        <synopsis>[y]=norm(x [,flag])</synopsis>
+        <synopsis>
+        y = norm(x)
+        y = norm(x, normType)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Arguments</title>
             <varlistentry>
                 <term>x</term>
                 <listitem>
-                    <para>real or complex vector or matrix (full or sparse
-                        storage)
+                    <para>vector or matrix of real or complex numbers (full or sparse storage)
                     </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
-                <term>flag</term>
+                <term>normType</term>
                 <listitem>
-                    <para>string (type of norm) (default value =2)</para>
+                    <para>
+                        <itemizedlist>
+                            <listitem>
+                                For a matrix <literal>x</literal>: a number among
+                                <literal>1, 2, %inf, -%inf</literal>, or a word among
+                                <literal>"inf"</literal> (or <literal>"i"</literal>) or
+                                <literal>"fro"</literal> (or <literal>"f"</literal>).
+                            </listitem>
+                            <listitem>
+                                For a vector <literal>x</literal>: any number or <literal>%inf</literal>,
+                                <literal>-%inf</literal>; or a word <literal>"inf"</literal>
+                                (<literal>"i"</literal>), <literal>"fro"</literal> (<literal>"f"</literal>).
+                            </listitem>
+                        </itemizedlist>
+                    </para>
+                    Default value = 2.
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>y</term>
                 <listitem>
                     <para>
-                        norm
+                        norm: single positive real number.
                     </para>
                 </listitem>
             </varlistentry>
                 <term>norm(x,'inf'),norm(x,%inf)</term>
                 <listitem>
                     <para>
-                        The infinity norm of <literal>x</literal> (the largest row sum
-                        : <literal>max(sum(abs(x),'c'))</literal> ).
+                        The infinity norm of <literal>x</literal> (the largest row sum :
+                        <literal>max(sum(abs(x),'c'))</literal> ).
                     </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
                 <term>norm(x,'fro')</term>
                 <listitem>
-                    <para>Frobenius norm i.e.
-                        <literal>sqrt(sum(diag(x'*x)))</literal>.
+                    <para>Frobenius norm i.e. <literal>sqrt(sum(diag(x'*x)))</literal>.
                     </para>
                 </listitem>
             </varlistentry>
                 <term>norm(v,p)</term>
                 <listitem>
                     <para>
-                        The l_p norm (<literal>sum(v(i)^p))^(1/p)</literal> .
+                        The l_p norm <literal>sum(abs(v(i))^p)^(1/p)</literal> .
                     </para>
                 </listitem>
             </varlistentry>
     <refsection>
         <title>Examples</title>
         <programlisting role="example"><![CDATA[
-A=[1,2,3];
+A = [1,2,3];
 norm(A,1)
 norm(A,'inf')
-A=[1,2;3,4]
-max(svd(A))-norm(A)
+A = [1,2;3,4]
+max(svd(A)) - norm(A)
 
-A=sparse([1 0 0 33 -1])
+A = sparse([1 0 0 33 -1])
 norm(A)
  ]]></programlisting>
     </refsection>
index db9061b..3003a05 100644 (file)
@@ -1,12 +1,32 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="norm" xml:lang="fr">
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA
+ *
+ * Copyright (C) 2012 - 2016 - Scilab Enterprises
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+          xmlns:scilab="http://www.scilab.org" xml:id="norm" xml:lang="fr">
     <refnamediv>
         <refname>norm</refname>
-        <refpurpose>normes matricielles</refpurpose>
+        <refpurpose>normes d'un vecteur ou d'une matrice</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Séquence d'appel</title>
-        <synopsis>[y]=norm(x [,flag])</synopsis>
+        <synopsis>
+        y = norm(x)
+        y = norm(x, normType)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Paramètres</title>
             <varlistentry>
                 <term>x</term>
                 <listitem>
-                    <para>vecteur ou matrice (réelle ou complexe, pleine ou
-                        creuse)
+                    <para>vecteur ou matrice (réelle ou complexe, pleine ou creuse)
                     </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
-                <term>flag</term>
+                <term>normType</term>
                 <listitem>
-                    <para>chaîne de caractères (type de la norme, 2 par défaut)</para>
+                    <para>
+                        <itemizedlist>
+                            <listitem>
+                                Matrice <literal>x</literal>: un nombre parmi
+                                <literal>1, 2, %inf, -%inf</literal>, ou un mot parmi
+                                <literal>"inf"</literal> (ou <literal>"i"</literal>) ou
+                                <literal>"fro"</literal> (ou <literal>"f"</literal>).
+                            </listitem>
+                            <listitem>
+                                Vecteur <literal>x</literal>: un nombre réel quelconque ou
+                                <literal>%inf</literal>,
+                                <literal>-%inf</literal>; ou mot <literal>"inf"</literal>
+                                (<literal>"i"</literal>), <literal>"fro"</literal>
+                                (<literal>"f"</literal>).
+                            </listitem>
+                        </itemizedlist>
+                    </para>
+                    Valeur par défaut : 2.
+                </listitem>
+            </varlistentry>
+            <varlistentry>
+                <term>y</term>
+                <listitem>
+                    <para>
+                        norme : nombre réel positif unique.
+                    </para>
                 </listitem>
             </varlistentry>
         </variablelist>
                 <term>norm(v,p)</term>
                 <listitem>
                     <para>
-                        norme l_p (<literal>sum(v(i)^p))^(1/p)</literal> .
+                        norme l_p <literal>sum(abs(v(i))^p)^(1/p)</literal> .
                     </para>
                 </listitem>
             </varlistentry>
     <refsection>
         <title>Exemples</title>
         <programlisting role="example"><![CDATA[
-A=[1,2,3];
+A = [1,2,3];
 norm(A,1)
 norm(A,'inf')
-A=[1,2;3,4]
-max(svd(A))-norm(A)
+A = [1,2;3,4]
+max(svd(A)) - norm(A)
 
-A=sparse([1 0 0 33 -1])
+A = sparse([1 0 0 33 -1])
 norm(A)
  ]]></programlisting>
     </refsection>
index 6908aac..b120a15 100644 (file)
@@ -1,5 +1,4 @@
 <?xml version="1.0" encoding="UTF-8"?>
-
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * along with this program.
  *
  -->
-
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="norm" xml:lang="ja">
-
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+          xmlns:scilab="http://www.scilab.org" xml:id="norm" xml:lang="ja">
     <refnamediv>
-
         <refname>norm</refname>
-
         <refpurpose>行列のノルム</refpurpose>
-
     </refnamediv>
-
     <refsynopsisdiv>
-
         <title>呼び出し手順</title>
-
-        <synopsis>[y]=norm(x [,flag])</synopsis>
-
+        <synopsis>
+        y = norm(x)
+        y = norm(x, normType)
+        </synopsis>
     </refsynopsisdiv>
-
     <refsection>
-
         <title>引数</title>
-
         <variablelist>
-
             <varlistentry>
-
                 <term>x</term>
-
                 <listitem>
-
                     <para>実数または複素数のベクトルまたは(通常または疎の)行列 </para>
-
                 </listitem>
-
             </varlistentry>
-
             <varlistentry>
-
-                <term>flag</term>
-
-                <listitem>
-
-                    <para>文字列 (ノルムの型) (デフォルト値 =2)</para>
-
-                </listitem>
-
+                <term>normType</term>
+                    <para>
+                        <itemizedlist>
+                            <listitem>
+                                For a matrix <literal>x</literal>: a number among
+                                <literal>1, 2, %inf, -%inf</literal>, or a word among
+                                <literal>"inf"</literal> (or <literal>"i"</literal>) or
+                                <literal>"fro"</literal> (or <literal>"f"</literal>).
+                            </listitem>
+                            <listitem>
+                                For a vector <literal>x</literal>: any number or <literal>%inf</literal>,
+                                <literal>-%inf</literal>; or a word <literal>"inf"</literal>
+                                (<literal>"i"</literal>), <literal>"fro"</literal> (<literal>"f"</literal>).
+                            </listitem>
+                        </itemizedlist>
+                    </para>
+                    Default value = 2.
             </varlistentry>
-
             <varlistentry>
-
                 <term>y</term>
-
                 <listitem>
-
                     <para>
-
                         ノルム
-
                     </para>
-
                 </listitem>
-
             </varlistentry>
-
         </variablelist>
-
     </refsection>
-
     <refsection>
-
         <title>説明</title>
-
         <para>行列の場合</para>
-
         <variablelist>
-
             <varlistentry>
-
                 <term>norm(x)</term>
-
                 <listitem>
-
                     <para>
-
                         または<literal>norm(x,2)</literal> は
-
                         <literal>x</literal>の最大特異値 (<literal>max(svd(x))</literal>)
-
                         となります.
-
                     </para>
-
                 </listitem>
-
             </varlistentry>
-
             <varlistentry>
-
                 <term>norm(x,1)</term>
-
                 <listitem>
-
                     <para>
-
                         <literal>x</literal>のl_1 ノルム  (列の和の最大値:
-
                         <literal>max(sum(abs(x),'r'))</literal> ).
-
                     </para>
-
                 </listitem>
-
             </varlistentry>
-
             <varlistentry>
-
                 <term>norm(x,'inf'),norm(x,%inf)</term>
-
                 <listitem>
-
                     <para>
-
                         <literal>x</literal>の無限大ノルム (列の和の最大値
-
                         : <literal>max(sum(abs(x),'c'))</literal> ).
-
                     </para>
-
                 </listitem>
-
             </varlistentry>
-
             <varlistentry>
-
                 <term>norm(x,'fro')</term>
-
                 <listitem>
-
                     <para>フロベニウスノルム,すなわち,
-
                         <literal>sqrt(sum(diag(x'*x)))</literal>.
-
                     </para>
-
                 </listitem>
-
             </varlistentry>
-
         </variablelist>
-
         <para>ベクトルの場合</para>
-
         <variablelist>
-
             <varlistentry>
-
                 <term>norm(v,p)</term>
-
                 <listitem>
-
                     <para>
-
-                        l_p ノルム (<literal>sum(v(i)^p))^(1/p)</literal> .
-
+                        l_p ノルム <literal>sum(abs(v(i))^p)^(1/p)</literal> .
                     </para>
-
                 </listitem>
-
             </varlistentry>
-
             <varlistentry>
-
                 <term>norm(v), norm(v,2)</term>
-
                 <listitem>
-
                     <para>
-
                         l_2 ノルム
-
                     </para>
-
                 </listitem>
-
             </varlistentry>
-
             <varlistentry>
-
                 <term>norm(v,'inf')</term>
-
                 <listitem>
-
                     <para>
-
                         <literal>max(abs(v(i)))</literal>.
-
                     </para>
-
                 </listitem>
-
             </varlistentry>
-
         </variablelist>
-
     </refsection>
-
     <refsection>
-
         <title>例</title>
-
         <programlisting role="example"><![CDATA[
-A=[1,2,3];
+A = [1,2,3];
 norm(A,1)
 norm(A,'inf')
-A=[1,2;3,4]
-max(svd(A))-norm(A)
-A=sparse([1 0 0 33 -1])
+A = [1,2;3,4]
+max(svd(A)) - norm(A)
+
+A = sparse([1 0 0 33 -1])
 norm(A)
  ]]></programlisting>
-
     </refsection>
-
     <refsection role="see also">
-
         <title>参照</title>
-
         <simplelist type="inline">
-
             <member>
-
                 <link linkend="h_norm">h_norm</link>
-
             </member>
-
             <member>
-
                 <link linkend="dhnorm">dhnorm</link>
-
             </member>
-
             <member>
-
                 <link linkend="h2norm">h2norm</link>
-
             </member>
-
             <member>
-
                 <link linkend="abs">abs</link>
-
             </member>
-
             <member>
-
                 <link linkend="svd">svd</link>
-
             </member>
-
         </simplelist>
-
     </refsection>
-
-</refentry>
-
+</refentry>
\ No newline at end of file
index 4aca6ad..6d0568e 100644 (file)
@@ -1,4 +1,4 @@
-<?xml version="1.0" encoding="ISO-8859-1"?>
+<?xml version="1.0" encoding="UTF-8"?>
 <!--
  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
  * Copyright (C) 2008 - INRIA
  * along with this program.
  *
  -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="norm" xml:lang="pt">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns4="http://www.w3.org/1999/xhtml"
+          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+          xmlns:scilab="http://www.scilab.org" xml:id="norm" xml:lang="pt">
     <refnamediv>
         <refname>norm</refname>
-        <refpurpose>norma de matrizes</refpurpose>
+        <refpurpose>normas de um vetor ou uma matriz</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
-        <title>Seqüência de Chamamento</title>
-        <synopsis>[y]=norm(x [,flag])</synopsis>
+        <title>Seqüência de Chamamento</title>
+        <synopsis>
+        y = norm(x)
+        y = norm(x, normType)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
-        <title>Parâmetros</title>
+        <title>Parâmetros</title>
         <variablelist>
             <varlistentry>
                 <term>x</term>
                 </listitem>
             </varlistentry>
             <varlistentry>
-                <term>flag</term>
+                <term>normType</term>
+                    <para>
+                        <itemizedlist>
+                            <listitem>
+                                For a matrix <literal>x</literal>: a number among
+                                <literal>1, 2, %inf, -%inf</literal>, or a word among
+                                <literal>"inf"</literal> (or <literal>"i"</literal>) or
+                                <literal>"fro"</literal> (or <literal>"f"</literal>).
+                            </listitem>
+                            <listitem>
+                                For a vector <literal>x</literal>: any number or <literal>%inf</literal>,
+                                <literal>-%inf</literal>; or a word <literal>"inf"</literal>
+                                (<literal>"i"</literal>), <literal>"fro"</literal> (<literal>"f"</literal>).
+                            </listitem>
+                        </itemizedlist>
+                    </para>
+                    Default value = 2.
+            </varlistentry>
+            <varlistentry>
+                <term>y</term>
                 <listitem>
-                    <para>string (tipo da norma) (valor padrão = 2)</para>
+                    <para>
+                        norm: single positive real number.
+                    </para>
                 </listitem>
             </varlistentry>
         </variablelist>
     </refsection>
     <refsection>
-        <title>Descrição</title>
+        <title>Descrição</title>
         <para>For matrices</para>
         <variablelist>
             <varlistentry>
                 <term>norm(x)</term>
                 <listitem>
                     <para>
-                        ou <literal>norm(x,2)</literal> é o maior valor singular de
+                        ou <literal>norm(x,2)</literal> é o maior valor singular de
                         <literal>x</literal> (<literal>max(svd(x))</literal>).
                     </para>
                 </listitem>
                 <term>norm(v,p)</term>
                 <listitem>
                     <para>
-                        norma l_p (<literal>sum(v(i)^p))^(1/p)</literal> .
+                        norma l_p <literal>sum(abs(v(i))^p)^(1/p)</literal> .
                     </para>
                 </listitem>
             </varlistentry>
@@ -116,14 +143,14 @@ A=[1,2,3];
 norm(A,1)
 norm(A,'inf')
 A=[1,2;3,4]
-max(svd(A))-norm(A)
+max(svd(A)) - norm(A)
 
 A=sparse([1 0 0 33 -1])
 norm(A)
  ]]></programlisting>
     </refsection>
     <refsection role="see also">
-        <title>Ver Também</title>
+        <title>Ver Também</title>
         <simplelist type="inline">
             <member>
                 <link linkend="h_norm">h_norm</link>
index 3aba2b7..2791b82 100644 (file)
  * along with this program.
  *
  -->
-<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="norm" xml:lang="ru">
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+          xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
+          xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
+          xmlns:scilab="http://www.scilab.org" xml:id="norm" xml:lang="ru">
     <refnamediv>
         <refname>norm</refname>
-        <refpurpose>норма матрицы</refpurpose>
+        <refpurpose>нормы вектора или матрицы</refpurpose>
     </refnamediv>
     <refsynopsisdiv>
         <title>Синтаксис</title>
-        <synopsis>[y]=norm(x [,flag])</synopsis>
+        <synopsis>
+        y = norm(x)
+        y = norm(x, normType)
+        </synopsis>
     </refsynopsisdiv>
     <refsection>
         <title>Аргументы</title>
                 <term>x</term>
                 <listitem>
                     <para>
-                        вещественный или комплексный вектор/матрица (полной или разрежённой
-                        формы)
+                        вещественный или комплексный вектор/матрица (полной или разрежённой формы)
                     </para>
                 </listitem>
             </varlistentry>
             <varlistentry>
-                <term>flag</term>
+                <term>normType</term>
+                    <para>
+                        <itemizedlist>
+                            <listitem>
+                                For a matrix <literal>x</literal>: a number among
+                                <literal>1, 2, %inf, -%inf</literal>, or a word among
+                                <literal>"inf"</literal> (or <literal>"i"</literal>) or
+                                <literal>"fro"</literal> (or <literal>"f"</literal>).
+                            </listitem>
+                            <listitem>
+                                For a vector <literal>x</literal>: any number or <literal>%inf</literal>,
+                                <literal>-%inf</literal>; or a word <literal>"inf"</literal>
+                                (<literal>"i"</literal>), <literal>"fro"</literal> (<literal>"f"</literal>).
+                            </listitem>
+                        </itemizedlist>
+                    </para>
+                    Default value = 2.
+            </varlistentry>
+            <varlistentry>
+                <term>y</term>
                 <listitem>
-                    <para>строка (тип нормы) (значение по умолчанию 2)</para>
+                    <para>
+                        norm: single positive real number.
+                    </para>
                 </listitem>
             </varlistentry>
         </variablelist>
                 <term>norm(v,p)</term>
                 <listitem>
                     <para>
-                        l_p-норма  (<literal>sum(v(i)^p))^(1/p)</literal> .
+                        l_p-норма  <literal>sum(abs(v(i))^p)^(1/p)</literal> .
                     </para>
                 </listitem>
             </varlistentry>
     <refsection>
         <title>Примеры</title>
         <programlisting role="example"><![CDATA[
-A=[1,2,3];
+A = [1,2,3];
 norm(A,1)
 norm(A,'inf')
-A=[1,2;3,4]
-max(svd(A))-norm(A)
+A = [1,2;3,4]
+max(svd(A)) - norm(A)
 
 A=sparse([1 0 0 33 -1])
 norm(A)