GNOME.org
 

[genius] Mon Aug 30 15:31:37 2010 Jiri (George) Lebl <jirka 5z com>

commit 023275fc0406452631f5d3a518d7321aff101c16
Author: Jiri (George) Lebl <jirka 5z com>
Date:   Mon Aug 30 15:34:59 2010 -0700

    Mon Aug 30 15:31:37 2010  Jiri (George) Lebl <jirka 5z com>
    
    	* help/C/genius.xml, help/C/gel-function-list.xml:
    	  Hand apply some changes from Christian Kirbach
    	  (christian.kirbach at googlemail dot com) to fix typos
    
    	* lib/*/*.gel, src/funclib.c:  Fix some typos.  Fix spelling of the
    	  function name AuxiliaryUnitMatrix!

 ChangeLog                               |    9 +++
 NEWS                                    |    2 +
 help/C/gel-function-list.xml            |   82 +++++++++++++++---------------
 help/C/genius.xml                       |   28 +++++-----
 lib/linear_algebra/bilinear_forms.gel   |    4 +-
 lib/linear_algebra/linear_algebra.gel   |   15 +++---
 lib/linear_algebra/misc.gel             |    2 +-
 lib/linear_algebra/special_matrices.gel |    2 +-
 lib/number_theory/misc.gel              |    2 +-
 src/funclib.c                           |    2 +-
 10 files changed, 79 insertions(+), 69 deletions(-)
---
diff --git a/ChangeLog b/ChangeLog
index c4e6268..f15cd88 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,12 @@
+Mon Aug 30 15:31:37 2010  Jiri (George) Lebl <jirka 5z com>
+
+	* help/C/genius.xml, help/C/gel-function-list.xml:
+	  Hand apply some changes from Christian Kirbach
+	  (christian.kirbach at googlemail dot com) to fix typos
+
+	* lib/*/*.gel, src/funclib.c:  Fix some typos.  Fix spelling of the
+	  function name AuxiliaryUnitMatrix!
+
 Mon Aug 30 14:43:41 2010  Jiri (George) Lebl <jirka 5z com>
 
 	* src/gnome-genius.c, configure.in: Apply patch from
diff --git a/NEWS b/NEWS
index 6952e62..6ee97b7 100644
--- a/NEWS
+++ b/NEWS
@@ -4,6 +4,7 @@ Changes to 1.0.10
 * Add SlopefieldTicks, VectorfieldTicks, LinePlotVariableNames, and
   SurfacePlotVariableNames, parameters
 * Add AskButtons interactive function
+* CHANGE: spelling fix: AuxiliaryUnitMatrix doesn't have two l's
 * Support for setting legend on LinePlotDrawLine with a "legend" parameter
 * Allow comparisons (== and !=) with null, treating it as an empty matrix
 * Uses GIO instead of GnomeVFS (Jan de Groot)
@@ -12,6 +13,7 @@ Changes to 1.0.10
 * Fix some crashes in plotting code
 * Allow slopefield solutions to leave plot window by a small fudge factor.
 * Fix compilation with newer sealed vte (Vincent Untz)
+* Fix up some typos in the documentation (Christian Kirbach, me)
 
 * For some of the changes the author (Jiri) was partially supported by
   NSF grant DMS 0900885 and the University of Illinois at Urbana-Champaign
diff --git a/help/C/gel-function-list.xml b/help/C/gel-function-list.xml
index 16e27e0..9e43665 100644
--- a/help/C/gel-function-list.xml
+++ b/help/C/gel-function-list.xml
@@ -102,7 +102,7 @@ is blocked until the user responds.  If <varname>default</varname> is given, the
          <term>ComposePower</term>
          <listitem>
           <synopsis>ComposePower (f,n,x)</synopsis>
-          <para>Compose and execute a function with itself <varname>n</varname> times, passing <varname>x</varname> as argument.   Returning <varname>x</varname> if
+          <para>Compose and execute a function with itself <varname>n</varname> times, passing <varname>x</varname> as argument.  Returning <varname>x</varname> if
 <varname>n</varname> equals 0.
 		Example:
           <screen><prompt>genius></prompt> <userinput>function f(x) = x^2 ;</userinput>
@@ -152,7 +152,7 @@ and this builtin function makes it possible to make GEL functions aware of modul
 	    <constant>true</constant>) from a boolean value.
 	    <varname>bval</varname> can also be a number in which case a
 	    non-zero value will be interpreted as <constant>true</constant> and
-	    zero will be interpretted as <constant>false</constant>.
+	    zero will be interpreted as <constant>false</constant>.
 	  </para>
          </listitem>
         </varlistentry>
@@ -240,7 +240,7 @@ not consider <constant>null</constant> a matrix.</para>
          <listitem>
           <synopsis>Parse (str)</synopsis>
           <para>Parses but does not evaluate a string.  Note that certain
-	    precomputation is done during the parsing stage.</para>
+	    pre-computation is done during the parsing stage.</para>
          </listitem>
         </varlistentry>
 
@@ -440,7 +440,7 @@ unprotected variables as user defined.</para>
          <listitem>
           <synopsis>wait (secs)</synopsis>
           <para>Waits a specified number of seconds.  <varname>secs</varname>
-must be nonnegative.  Zero is accepted and nothing happens in this case,
+must be non-negative.  Zero is accepted and nothing happens in this case,
 except possibly user interface events are processed.</para>
          </listitem>
         </varlistentry>
@@ -450,7 +450,7 @@ except possibly user interface events are processed.</para>
          <listitem>
           <synopsis>version</synopsis>
           <para>Returns the version of Genius as a horizontal 3-vector with
-	  major version first, then minor version and finally patchlevel.</para>
+	  major version first, then minor version and finally the patch level.</para>
          </listitem>
         </varlistentry>
 
@@ -656,7 +656,7 @@ display <computeroutput>0.0</computeroutput> instead of the number.
 </para>
 <para>
 Output is never chopped if <function>OutputChopExponent</function> is zero.
-It must be a nonnegative integer.
+It must be a non-negative integer.
 </para>
 <para>
 If you want output always chopped according to
@@ -1635,7 +1635,7 @@ number is specified) of the given size returned.  For example
           <synopsis>DiscreteLog (n,b,q)</synopsis>
           <para>Find discrete log of <varname>n</varname> base <varname>b</varname> in
 	    F<subscript>q</subscript>, the finite field of order <varname>q</varname>, where <varname>q</varname>
-	    is a prime, using the Silver-Pohlig-Hellman algoritm.</para>
+	    is a prime, using the Silver-Pohlig-Hellman algorithm.</para>
           <para>
 	    See
 	    <ulink url="http://en.wikipedia.org/wiki/Discrete_logarithm";>Wikipedia</ulink> or
@@ -1715,7 +1715,7 @@ number is specified) of the given size returned.  For example
 	    includes all the non-prime factors as well.  It includes 1 and the
 	    number itself.  So for example to print all the perfect numbers
 	    (those that are sums of their factors) up to the number 1000 you
-	    could do (this is of course very inefficent)
+	    could do (this is of course very inefficient)
 	    <programlisting>for n=1 to 1000 do (
     if MatrixSum (Factors(n)) == 2*n then
         print(n)
@@ -2139,7 +2139,7 @@ that is if <userinput>b^(n-1) == 1 mod n</userinput>.  This calles the <function
          <term>PadicValuation</term>
          <listitem>
           <synopsis>PadicValuation (n,p)</synopsis>
-          <para>Returns the padic valuation (number of trailing zeros in base <varname>p</varname>).</para>
+          <para>Returns the p-adic valuation (number of trailing zeros in base <varname>p</varname>).</para>
           <para>
 	    See
 	    <ulink url="http://planetmath.org/encyclopedia/PAdicValuation.html";>Planetmath</ulink> for more information.
@@ -2218,7 +2218,7 @@ that is if <userinput>b^(n-1) == 1 mod n</userinput>.  This calles the <function
          <term>SilverPohligHellmanWithFactorization</term>
          <listitem>
           <synopsis>SilverPohligHellmanWithFactorization (n,b,q,f)</synopsis>
-          <para>Find discrete log of <varname>n</varname> base <varname>b</varname> in F<subscript>q</subscript>, the finite group of order <varname>q</varname>, where <varname>q</varname> is a prime using the Silver-Pohlig-Hellman algoritm, given <varname>f</varname> being the factorization of <varname>q</varname>-1.</para>
+          <para>Find discrete log of <varname>n</varname> base <varname>b</varname> in F<subscript>q</subscript>, the finite group of order <varname>q</varname>, where <varname>q</varname> is a prime using the Silver-Pohlig-Hellman algorithm, given <varname>f</varname> being the factorization of <varname>q</varname>-1.</para>
          </listitem>
         </varlistentry>
 
@@ -2328,7 +2328,7 @@ that is if <userinput>b^(n-1) == 1 mod n</userinput>.  This calles the <function
          <term>CompoundMatrix</term>
          <listitem>
           <synopsis>CompoundMatrix (k,A)</synopsis>
-          <para>Calculate the kth compund matrix of A.</para>
+          <para>Calculate the kth compound matrix of A.</para>
          </listitem>
         </varlistentry>
 
@@ -2404,7 +2404,7 @@ same size.  No conjugates are taken so this is a bilinear form even if working o
          <listitem>
           <synopsis>HermitianProduct (u,v)</synopsis>
           <para>Aliases: <function>InnerProduct</function></para>
-          <para>Get the hermitian product of two vectors.  The vectors must be of the same size.  This is a sesquilinear form using the identity matrix.</para>
+          <para>Get the Hermitian product of two vectors.  The vectors must be of the same size.  This is a sesquilinear form using the identity matrix.</para>
           <para>
 	    See
 	    <ulink url="http://mathworld.wolfram.com/HermitianInnerProduct.html";>Mathworld</ulink> for more information.
@@ -2480,7 +2480,7 @@ same size.  No conjugates are taken so this is a bilinear form even if working o
          <term>IsMatrixNonnegative</term>
          <listitem>
           <synopsis>IsMatrixNonnegative (M)</synopsis>
-          <para>Check if a matrix is nonnegative, that is if each element is nonnegative.
+          <para>Check if a matrix is non-negative, that is if each element is non-negative.
 	  Do not confuse positive matrices with positive semi-definite matrices.</para>
           <para>
 	    See
@@ -2621,7 +2621,7 @@ functions make this check.  Values can be any number including complex numbers.<
          <listitem>
           <synopsis>MatrixSum (A)</synopsis>
           <para>
-	    Calculate the sum of all elements in a matrix or vecgtor.  That is
+	    Calculate the sum of all elements in a matrix or vector.  That is
 	    we add all the elements and return a number that is the
 	    sum of all the elements.
 	  </para>
@@ -2794,11 +2794,11 @@ number of columns times the number of rows.</para>
     <sect1 id="genius-gel-function-list-linear-algebra">
       <title>Linear Algebra</title>
       <variablelist>
-        <varlistentry id="gel-function-AuxilliaryUnitMatrix">
-         <term>AuxilliaryUnitMatrix</term>
+        <varlistentry id="gel-function-AuxiliaryUnitMatrix">
+         <term>AuxiliaryUnitMatrix</term>
          <listitem>
-          <synopsis>AuxilliaryUnitMatrix (n)</synopsis>
-          <para>Get the auxilliary unit matrix of size <varname>n</varname>.  This is a square matrix matrix with that is all zero except the
+          <synopsis>AuxiliaryUnitMatrix (n)</synopsis>
+          <para>Get the auxiliary unit matrix of size <varname>n</varname>.  This is a square matrix matrix with that is all zero except the
 superdiagonal being all ones.  It is the Jordan block matrix of one zero eigenvalue.</para>
           <para>
 	    See
@@ -2846,7 +2846,7 @@ See also <link linkend="gel-function-CharacteristicPolynomialFunction">Character
          <term>CharacteristicPolynomialFunction</term>
          <listitem>
           <synopsis>CharacteristicPolynomialFunction (M)</synopsis>
-	  <para>Get the characteristic polynomial as a function.   This is
+	  <para>Get the characteristic polynomial as a function.  This is
 the polynomial defined by <userinput>det(M-xI)</userinput>.  The roots of this
 polynomial are the eigenvalues of <varname>M</varname>.
 See also <link linkend="gel-function-CharacteristicPolynomial">CharacteristicPolynomial</link>.
@@ -2994,7 +2994,7 @@ the eigenvalues and their algebraic multiplicities.
           <synopsis>GramSchmidt (v,B...)</synopsis>
 	  <para>Apply the Gram-Schmidt process (to the columns) with respect to
 inner product given by <varname>B</varname>.  If <varname>B</varname> is not
-given then the standard hermitian product is used.  <varname>B</varname> can
+given then the standard Hermitian product is used.  <varname>B</varname> can
 either be a sesquilinear function of two arguments or it can be a matrix giving
 a sesquilinear form.  The vectors will be made orthonormal with respect to
 <varname>B</varname>.</para>
@@ -3065,7 +3065,7 @@ a sesquilinear form.  The vectors will be made orthonormal with respect to
          <term>IsHermitian</term>
          <listitem>
           <synopsis>IsHermitian (M)</synopsis>
-          <para>Is a matrix hermitian.  That is, is it equal to its conjugate transpose.</para>
+          <para>Is a matrix Hermitian.  That is, is it equal to its conjugate transpose.</para>
           <para>
 	    See
 	    <ulink url="http://planetmath.org/encyclopedia/HermitianMatrix.html";>Planetmath</ulink> for more information.
@@ -3115,19 +3115,19 @@ a sesquilinear form.  The vectors will be made orthonormal with respect to
          <term>IsPositiveDefinite</term>
          <listitem>
           <synopsis>IsPositiveDefinite (M)</synopsis>
-          <para>Is <varname>M</varname> a hermitian positive definite matrix.  That is if
+          <para>Is <varname>M</varname> a Hermitian positive definite matrix.  That is if
 <userinput>HermitianProduct(M*v,v)</userinput> is always strictly positive for
 any vector <varname>v</varname>.
-<varname>M</varname> must be square and hermitian to be positive definite.
-The check that is performed is that every principal submatrix has a nonnegative
+<varname>M</varname> must be square and Hermitian to be positive definite.
+The check that is performed is that every principal submatrix has a non-negative
 determinant.
 (See <link linkend="gel-function-HermitianProduct">HermitianProduct</link>)</para>
 	  <para>
 	    Note that some authors (for example Mathworld) do not require that
-	    <varname>M</varname> be hermitian, and then the condition is
+	    <varname>M</varname> be Hermitian, and then the condition is
 	    on the real part of the inner product, but we do not take this
 	    view.  If you wish to perform this check, just check the
-	    hermitian part of the matrix <varname>M</varname> as follows:
+	    Hermitian part of the matrix <varname>M</varname> as follows:
 	    <userinput>IsPositiveDefinite(M+M')</userinput>.
 	  </para>
           <para>
@@ -3142,19 +3142,19 @@ determinant.
          <term>IsPositiveSemidefinite</term>
          <listitem>
           <synopsis>IsPositiveSemidefinite (M)</synopsis>
-          <para>Is <varname>M</varname> a hermitian positive semidefinite matrix.  That is if
-<userinput>HermitianProduct(M*v,v)</userinput> is always nonnegative for
+          <para>Is <varname>M</varname> a Hermitian positive semidefinite matrix.  That is if
+<userinput>HermitianProduct(M*v,v)</userinput> is always non-negative for
 any vector <varname>v</varname>.
-<varname>M</varname> must be square and hermitian to be positive semidefinite.
-The check that is performed is that every principal submatrix has a nonnegative
+<varname>M</varname> must be square and Hermitian to be positive semidefinite.
+The check that is performed is that every principal submatrix has a non-negative
 determinant.
 (See <link linkend="gel-function-HermitianProduct">HermitianProduct</link>)</para>
 	  <para>
 	    Note that some authors do not require that
-	    <varname>M</varname> be hermitian, and then the condition is
+	    <varname>M</varname> be Hermitian, and then the condition is
 	    on the real part of the inner product, but we do not take this
 	    view.  If you wish to perform this check, just check the
-	    hermitian part of the matrix <varname>M</varname> as follows:
+	    Hermitian part of the matrix <varname>M</varname> as follows:
 	    <userinput>IsPositiveSemidefinite(M+M')</userinput>.
 	  </para>
           <para>
@@ -3169,7 +3169,7 @@ determinant.
          <term>IsSkewHermitian</term>
          <listitem>
           <synopsis>IsSkewHermitian (M)</synopsis>
-          <para>Is a matrix skew-hermitian.  That is, is the conjugate transpose equal to negative of the matrix.</para>
+          <para>Is a matrix skew-Hermitian.  That is, is the conjugate transpose equal to negative of the matrix.</para>
           <para>
 	    See
 	    <ulink url="http://planetmath.org/encyclopedia/SkewHermitianMatrix.html";>Planetmath</ulink> for more information.
@@ -3338,7 +3338,7 @@ the nullspace; the dimension of the kernel of <varname>M</varname>.</para>
 	  <para>Projection of vector <varname>v</varname> onto subspace
 <varname>W</varname> with respect to inner product given by
 <varname>B</varname>.  If <varname>B</varname> is not given then the standard
-hermitian product is used.  <varname>B</varname> can either be a sesquilinear
+Hermitian product is used.  <varname>B</varname> can either be a sesquilinear
 function of two arguments or it can be a matrix giving a sesquilinear form.
 	  </para>
          </listitem>
@@ -3561,7 +3561,7 @@ Hermitian matrix (if the first element is real of course).</para>
           <synopsis>VectorAngle (v,w,B...)</synopsis>
           <para>The angle of two vectors with respect to inner product given by
 <varname>B</varname>.  If <varname>B</varname> is not given then the standard
-hermitian product is used.  <varname>B</varname> can either be a sesquilinear
+Hermitian product is used.  <varname>B</varname> can either be a sesquilinear
 function of two arguments or it can be a matrix giving a sesquilinear form.
 </para>
          </listitem>
@@ -3723,7 +3723,7 @@ divided to make all pivots 1.</para>
           <synopsis>Fibonacci (x)</synopsis>
           <para>Aliases: <function>fib</function></para>
           <para>
-	    Calculate <varname>n</varname>th fibonacci number.  That
+	    Calculate <varname>n</varname>th Fibonacci number.  That
 	    is the number defined recursively by
 	    <userinput>Fibonacci(n) = Fibonacci(n-1) + Fibonacci(n-2)</userinput>
 	    and 
@@ -3744,8 +3744,8 @@ divided to make all pivots 1.</para>
           <synopsis>FrobeniusNumber (v,arg...)</synopsis>
           <para>
 	    Calculate the Frobenius number.  That is calculate smallest
-	    number that cannot be given as a nonnegative integer linear
-	    combination of a given vector of nonnegative integers.
+	    number that cannot be given as a non-negative integer linear
+	    combination of a given vector of non-negative integers.
 	    The vector can be given as separate numbers or a single vector.
 	    All the numbers given should have GCD of 1.
 	  </para>
@@ -3769,11 +3769,11 @@ divided to make all pivots 1.</para>
          <listitem>
           <synopsis>FrobeniusNumber (n,v)</synopsis>
           <para>
-	    Find the vector <varname>c</varname> of nonnegative integers
+	    Find the vector <varname>c</varname> of non-negative integers
 	    such that taking the dot product with <varname>v</varname> is
 	    equal to n.  If not possible returns null.  <varname>v</varname>
 	    should be given sorted in increasing order and should consist
-	    of nonnegative integers.
+	    of non-negative integers.
 	  </para>
           <para>
 	    See
@@ -3813,7 +3813,7 @@ divided to make all pivots 1.</para>
           <synopsis>Multinomial (v,arg...)</synopsis>
           <para>Calculate multinomial coefficients.  Takes a vector of
 	    <varname>k</varname>
-	    nonnegative integers and computes the multinomial coefficient.
+	    non-negative integers and computes the multinomial coefficient.
 	    This corresponds to the coefficient in the homogeneous polynomial
 	    in <varname>k</varname> variables with the corresponding powers.
 	  </para>
diff --git a/help/C/genius.xml b/help/C/genius.xml
index 639095a..f1045d5 100644
--- a/help/C/genius.xml
+++ b/help/C/genius.xml
@@ -326,7 +326,7 @@ variables.  Finally it allows plotting functions using a user friendly dialog bo
 	work area.  If you are running the text only version then the console
 	will be the only thing that is available to you.  If you want to use
 	&app; as a calculator only, just type in your expression here and it
-	willg et evaluated.
+	will be evaluated.
       </para>
 
       <para>
@@ -693,7 +693,7 @@ Values in GEL can be <link linkend="genius-gel-values-numbers">numbers</link>, <
 Integers are the first type of number in GEL. Integers are written in the normal way.
 <programlisting>1234
 </programlisting>
-Hexidecimal and octal numbers can be written using C notation. For example:
+Hexadecimal and octal numbers can be written using C notation. For example:
 <programlisting>0x123ABC
 01234
 </programlisting>
@@ -1076,7 +1076,7 @@ this should be second nature. However genius can let you pretend it is a
 terminator somewhat, if a <literal>;</literal> is found at the end of a parenthesis or a block,
 genius will itself append a null node to it as if you would have written
 <userinput>;null</userinput>.
-This is usefull in case you do not want to return a value from say a loop,
+This is useful in case you do not want to return a value from say a loop,
 or if you handle the return differently. Note that it will slightly slow down
 the code if it is executed too often as there is one more operator involved.
       </para>
@@ -1310,7 +1310,7 @@ different from <literal>=</literal> because it never gets translated to a
          <term><synopsis>a.%b</synopsis></term>
          <listitem>
            <para>
-             Element by element the mod operator.  Returns the remaineder
+             Element by element the mod operator.  Returns the remainder
 	     after element by element <userinput>a./b</userinput>.
            </para>
          </listitem>
@@ -1588,7 +1588,7 @@ different from <literal>=</literal> because it never gets translated to a
          <term><synopsis>a:b</synopsis></term>
          <listitem>
            <para>
-             Build a vector from <varname>a</varname> to <varname>b</varname> (or specify a row, column region for the <literal>@</literal> operator).  For example to get rows 2 to 4 of mamtrix <varname>A</varname> we could do
+             Build a vector from <varname>a</varname> to <varname>b</varname> (or specify a row, column region for the <literal>@</literal> operator).  For example to get rows 2 to 4 of matrix <varname>A</varname> we could do
 	     <programlisting>A@(2:4,)
 	     </programlisting>
 	     as <userinput>2:4</userinput> will return a vector
@@ -1706,7 +1706,7 @@ until <expression1> do <expression2>
 do <expression2> while <expression1>
 do <expression2> until <expression1>]]></programlisting>
 
-These are similiar to other languages, however they return the result of the last iteration or <literal>NULL</literal> if no iteration was done.  In the boolean expression, <literal>=</literal> is translated into <literal>==</literal> just as for the <literal>if</literal> statement.
+These are similar to other languages, however they return the result of the last iteration or <literal>NULL</literal> if no iteration was done.  In the boolean expression, <literal>=</literal> is translated into <literal>==</literal> just as for the <literal>if</literal> statement.
         </para>
       </sect2>
 
@@ -1793,7 +1793,7 @@ If no body is executed (for example <userinput>sum i=1 to 0 do ...</userinput>)
 
       <para>
 	Normally <literal>=</literal> is translated to <literal>==</literal> if
-	it happens to be somewhere where GEL is expecing a condition such as
+	it happens to be somewhere where GEL is expecting a condition such as
 	in the if condition.  For example
 	<programlisting>if a=b then c
 if a==b then c
@@ -1817,7 +1817,7 @@ if a==b then c
 	To build up logical expressions use the words <literal>not</literal>,
 	<literal>and</literal>, <literal>or</literal>, <literal>xor</literal>.
 	The operators <literal>or</literal> and <literal>and</literal> are
-special beasts as they evaluate their arguemnts one by one, so the usual trick
+special beasts as they evaluate their arguments one by one, so the usual trick
 for conditional evaluation works here as well. For example, <literal>1 or a=1</literal> will not set
 <literal>a=1</literal> since the first argument was true.
       </para>
@@ -1902,7 +1902,7 @@ f();
 function f() = (a:=5);
 f();
 </programlisting>
-	  Sometimes, however, it is neccessary to set
+	  Sometimes, however, it is necessary to set
 a global variable from inside a function.  When this behaviour is needed,
 use the
 <function>set</function> function. Passing a string or a quoted identifier to
@@ -1923,7 +1923,7 @@ or:
         </para>
 	<para>
 	  So to recap in a more technical language:  Genius operates with
-	  different numberred contexts.  The top level is the context 0
+	  different numbered contexts.  The top level is the context 0
 	  (zero).  Whenever a function is entered, the context is raised,
 	  and when the function returns the context is lowered.  A function
 	  or a variable is always visible from all higher numbered contexts.
@@ -1994,7 +1994,7 @@ Example:
     <sect1 id="genius-gel-references">
       <title>References</title>
       <para>
-	It may be neccessary for some functions to return more than one value.
+	It may be necessary for some functions to return more than one value.
 	This may be accomplished by returning a vector of values, but many
 	times it is convenient to use passing a reference to a variable.
 	You pass a reference to a variable to a function, and the function
@@ -2043,7 +2043,7 @@ gives us 4.
     <term><userinput>a</userinput></term>
     <listitem>
       <para>
-	Identifier.  Here we would be setting the varable of name
+	Identifier.  Here we would be setting the variable of name
 	<varname>a</varname>.
       </para>
     </listitem>
@@ -2122,7 +2122,7 @@ could use the following code.
 	as just sequence of lines as if were entered on the command line.
 	In particular, you do not need to enter the separator at the end of the
 	line (unless it is of course part of several statements inside
-	parenteses).
+	parentheses).
       </para>
       <para>
 	The following code will produce an error when entered on the top
@@ -2140,7 +2140,7 @@ else
 	go on to the next
 	line, it will see <literal>else</literal>, and it will produce
 	a parsing error.  To fix this, use parentheses.  &app; will not
-	be satisfied until it has found that all parenteses are closed.
+	be satisfied until it has found that all parentheses are closed.
 <programlisting>if Something() then (
   DoSomething()
 ) else (
diff --git a/lib/linear_algebra/bilinear_forms.gel b/lib/linear_algebra/bilinear_forms.gel
index 2e5b8f1..4d12378 100644
--- a/lib/linear_algebra/bilinear_forms.gel
+++ b/lib/linear_algebra/bilinear_forms.gel
@@ -37,7 +37,7 @@ function SesquilinearFormFunction(A)=(`(v,w)[A]=(v'*A*w)@(1))
 
 # Projection onto a vector space
 # Projection of vector v onto subspace W given a sesquilinear form B
-SetHelp ("Projection", "linear_algebra", "Projection of vector v onto subspace W given a sesquilinear form B (if not given use hermitian product)")
+SetHelp ("Projection", "linear_algebra", "Projection of vector v onto subspace W given a sesquilinear form B (if not given use Hermitian product)")
 function Projection(v,W,B...) =
   (
         # if you don't give anything, assume standard inner product
@@ -55,7 +55,7 @@ function Projection(v,W,B...) =
 
 # Gram-Schmidt Orthogonalization
 # Described, for instance, in Hoffman & Kunze, ``Linear Algebra'' p.~280
-SetHelp ("GramSchmidt", "linear_algebra", "Apply the Gram-Schmidt process (to the columns) with respect to inner product given by B (if not given use hermitian product)")
+SetHelp ("GramSchmidt", "linear_algebra", "Apply the Gram-Schmidt process (to the columns) with respect to inner product given by B (if not given use Hermitian product)")
 function GramSchmidt(v,B...) =
 # Takes k column vectors v_1,...,v_k
 # and returns a collection, orthonormal with respect to the inner product given by B(-,-): V x V -> R
diff --git a/lib/linear_algebra/linear_algebra.gel b/lib/linear_algebra/linear_algebra.gel
index b76bb5e..14a9e66 100644
--- a/lib/linear_algebra/linear_algebra.gel
+++ b/lib/linear_algebra/linear_algebra.gel
@@ -186,17 +186,16 @@ function SmithNormalFormInteger(M) =
 	S
 )
 
-# AuxilliaryUnitMatrix
-SetHelp("AuxilliaryUnitMatrix", "linear_algebra", "Get the auxilliary unit matrix of size n")
-function AuxilliaryUnitMatrix(n) =
+# AuxiliaryUnitMatrix
+SetHelp("AuxiliaryUnitMatrix", "linear_algebra", "Get the auxiliary unit matrix of size n")
+function AuxiliaryUnitMatrix(n) =
 (
   if not IsInteger (n) or n < 2 then
-    (error ("AuxilliaryUnitMatrix: n must be an integer greater than 1");bailout)
+    (error ("AuxiliaryUnitMatrix: n must be an integer greater than 1");bailout)
   else
     [0,I(n-1);0,0]
 )
 
-# AuxilliaryUnitMatrix
 SetHelp("JordanBlock", "linear_algebra", "Get the jordan block corresponding to lambda and n")
 function JordanBlock(n,lambda) =
 (
@@ -207,7 +206,7 @@ function JordanBlock(n,lambda) =
   else if n == 1 then
     [lambda]
   else
-    lambda * I(n) + AuxilliaryUnitMatrix(n)
+    lambda * I(n) + AuxiliaryUnitMatrix(n)
 )
 SetHelpAlias("JordanBlock", "J")
 J = JordanBlock
@@ -328,14 +327,14 @@ function IsUnitary(M) = (
 	M' * M == I(columns(M))
 )
 
-SetHelp("IsHermitian", "linear_algebra", "Is a matrix hermitian")
+SetHelp("IsHermitian", "linear_algebra", "Is a matrix Hermitian")
 function IsHermitian(M) = (
 	if not IsMatrix(M) or not IsMatrixSquare(M) then
 		(error("IsHermitian: argument not a square matrix");bailout);
 	M' == M
 )
 
-SetHelp("IsSkewHermitian", "linear_algebra", "Is a matrix skew-hermitian")
+SetHelp("IsSkewHermitian", "linear_algebra", "Is a matrix skew-Hermitian")
 function IsSkewHermitian(M) = (
 	if not IsMatrix(M) or not IsMatrixSquare(M) then
 		(error("IsSkewHermitian: argument not a square matrix");bailout);
diff --git a/lib/linear_algebra/misc.gel b/lib/linear_algebra/misc.gel
index 7697cfc..2b310aa 100644
--- a/lib/linear_algebra/misc.gel
+++ b/lib/linear_algebra/misc.gel
@@ -271,7 +271,7 @@ function LowerTriangular(M) = (
 	UpperTriangular (M.').'
 )
 
-SetHelp("CompoundMatrix", "matrix", "Calculate the kth compund matrix of A")
+SetHelp("CompoundMatrix", "matrix", "Calculate the kth compound matrix of A")
 function CompoundMatrix(k,A) = (
 	if not IsInteger(k) or k < 1 or k > min(columns(A),rows(A)) or not IsMatrix(A) then
 		(error("CompoundMatrix: arguments of right type/size");bailout);
diff --git a/lib/linear_algebra/special_matrices.gel b/lib/linear_algebra/special_matrices.gel
index a9fb83b..2afc50f 100644
--- a/lib/linear_algebra/special_matrices.gel
+++ b/lib/linear_algebra/special_matrices.gel
@@ -40,7 +40,7 @@ function InverseHilbertMatrix(n) = HilbertMatrix(n)^(-1)
 #	pascal matrix
 #	toeplitz matrix 
 #		constant along diagonals
-#		take first column, first row (or just first row, and then make hermitian, i.e., set first column = conjugate of first row)
+#		take first column, first row (or just first row, and then make Hermitian, i.e., set first column = conjugate of first row)
 #	wilkinson (tridiagonal -- once off diagonals are all 1s, and the diagonal goes:
 # 3 2 1 0 1 2 3 (say, for n=7)
 # or
diff --git a/lib/number_theory/misc.gel b/lib/number_theory/misc.gel
index facee8d..57fd2fc 100644
--- a/lib/number_theory/misc.gel
+++ b/lib/number_theory/misc.gel
@@ -45,7 +45,7 @@ function PadicValuation(n,p) =
    );
   valuation
  )
-SetHelp("PadicValuation","number_theory","Returns the padic valuation (number of trailing zeros in base p).");
+SetHelp("PadicValuation","number_theory","Returns the p-adic valuation (number of trailing zeros in base p).");
 
 function RemoveFactor(n,m) =
  (
diff --git a/src/funclib.c b/src/funclib.c
index ba31756..c68e3fe 100644
--- a/src/funclib.c
+++ b/src/funclib.c
@@ -6448,7 +6448,7 @@ gel_funclib_addall(void)
 
 	FUNC (SetMatrixSize, 3, "M,rows,columns", "matrix", N_("Make new matrix of given size from old one"));
 	FUNC (IndexComplement, 2, "vec,msize", "matrix", N_("Return the index complement of a vector of indexes"));
-	FUNC (HermitianProduct, 2, "u,v", "matrix", N_("Get the hermitian product of two vectors"));
+	FUNC (HermitianProduct, 2, "u,v", "matrix", N_("Get the Hermitian product of two vectors"));
 	ALIAS (InnerProduct, 2, HermitianProduct);
 
 	FUNC (IsValueOnly, 1, "M", "matrix", N_("Check if a matrix is a matrix of numbers"));
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