genius r660 - in trunk: . help/C
- From: jirka svn gnome org
- To: svn-commits-list gnome org
- Subject: genius r660 - in trunk: . help/C
- Date: Wed, 4 Jun 2008 16:57:54 +0000 (UTC)
Author: jirka
Date: Wed Jun 4 16:57:54 2008
New Revision: 660
URL: http://svn.gnome.org/viewvc/genius?rev=660&view=rev
Log:
Wed Jun 04 11:56:25 2008 Jiri (George) Lebl <jirka 5z com>
* help/C/genius.xml, help/C/gel-function-list.gel: update the docs
a little, fix a few typos, add links.
Modified:
trunk/ChangeLog
trunk/help/C/gel-function-list.xml
trunk/help/C/genius.txt
trunk/help/C/genius.xml
Modified: trunk/help/C/gel-function-list.xml
==============================================================================
--- trunk/help/C/gel-function-list.xml (original)
+++ trunk/help/C/gel-function-list.xml Wed Jun 4 16:57:54 2008
@@ -1910,8 +1910,8 @@
previous prime you can use <userinput>-NextPrime(-n)</userinput>.
</para>
<para>
- This function uses the GMP's <function>mpz_nextprime</function> which in
- turn uses the probabilistic Miller-Rabin test
+ This function uses the GMP's <function>mpz_nextprime</function>
+ which in turn uses the probabilistic Miller-Rabin test
(See also <link linkend="gel-function-MillerRabinTest">MillerRabinTest</link>).
The probability
of false positive is not tunable, but is low enough
@@ -1944,7 +1944,9 @@
<para>
Compute <userinput>a^b mod m</userinput>. The
<varname>b</varname>'s power of <varname>a</varname> modulo
- <varname>m</varname>.
+ <varname>m</varname>. It is not neccessary to use this function
+ as it is automatically used in modulo mode. Hence
+ <userinput>a^b mod m</userinput> is just as fast.
</para>
</listitem>
</varlistentry>
@@ -2274,8 +2276,9 @@
<term>IsMatrixPositive</term>
<listitem>
<synopsis>IsMatrixPositive (M)</synopsis>
- <para>Check if a matrix is positive, that is if each element is positive. In particular,
- no element is 0. Do not confuse positive matrices with positive definite matrices.</para>
+ <para>Check if a matrix is positive, that is if each element is
+positive (and hence real). In particular, no element is 0. Do not confuse
+positive matrices with positive definite matrices.</para>
<para>
See
<ulink url="http://en.wikipedia.org/wiki/Positive_matrix";>Wikipedia</ulink> for more information.
@@ -2287,7 +2290,8 @@
<term>IsMatrixRational</term>
<listitem>
<synopsis>IsMatrixRational (M)</synopsis>
- <para>Check if a matrix is a matrix of rational (non-complex) numbers.</para>
+ <para>Check if a matrix is a matrix of rational (non-complex)
+numbers.</para>
</listitem>
</varlistentry>
@@ -2314,7 +2318,7 @@
<term>IsUpperTriangular</term>
<listitem>
<synopsis>IsUpperTriangular (M)</synopsis>
- <para>Is a matrix upper triangular. That is, are all the entries above the diagonal zero.</para>
+ <para>Is a matrix upper triangular? That is, a matrix is upper triangular if all all the entries below the diagonal are zero.</para>
</listitem>
</varlistentry>
@@ -2322,7 +2326,8 @@
<term>IsValueOnly</term>
<listitem>
<synopsis>IsValueOnly (M)</synopsis>
- <para>Check if a matrix is a matrix of numbers only.</para>
+ <para>Check if a matrix is a matrix of numbers only. Many internal
+functions make this check. Values can be any number including complex numbers.</para>
</listitem>
</varlistentry>
@@ -2375,7 +2380,7 @@
<varlistentry id="gel-function-MakeVector">
<term>MakeVector</term>
<listitem>
- <synopsis>MakeDiagonal (A)</synopsis>
+ <synopsis>MakeVector (A)</synopsis>
<para>Make column vector out of matrix by putting columns above
each other. Returns null when given null.</para>
</listitem>
@@ -2384,11 +2389,11 @@
<varlistentry id="gel-function-MatrixProduct">
<term>MatrixProduct</term>
<listitem>
- <synopsis>MatrixProduct (a)</synopsis>
+ <synopsis>MatrixProduct (A)</synopsis>
<para>
- Calculate the product of all elements in a matrix. That is
- we multiply all the elements and return a number that is the
- product of all the elements.
+ Calculate the product of all elements in a matrix or vector.
+ That is we multiply all the elements and return a number that
+ is the product of all the elements.
</para>
</listitem>
</varlistentry>
@@ -2396,9 +2401,9 @@
<varlistentry id="gel-function-MatrixSum">
<term>MatrixSum</term>
<listitem>
- <synopsis>MatrixSum (a)</synopsis>
+ <synopsis>MatrixSum (A)</synopsis>
<para>
- Calculate the sum of all elements in a matrix. That is
+ Calculate the sum of all elements in a matrix or vecgtor. That is
we add all the elements and return a number that is the
sum of all the elements.
</para>
@@ -2408,8 +2413,9 @@
<varlistentry id="gel-function-MatrixSumSquares">
<term>MatrixSumSquares</term>
<listitem>
- <synopsis>MatrixSumSquares (a)</synopsis>
- <para>Calculate the sum of squares of all elements in a matrix.</para>
+ <synopsis>MatrixSumSquares (A)</synopsis>
+ <para>Calculate the sum of squares of all elements in a matrix
+ or vector.</para>
</listitem>
</varlistentry>
@@ -2417,7 +2423,9 @@
<term>OuterProduct</term>
<listitem>
<synopsis>OuterProduct (u,v)</synopsis>
- <para>Get the outer product of two vectors.</para>
+ <para>Get the outer product of two vectors. That is, suppose that
+<varname>u</varname> and <varname>v</varname> are vertical vectors, then
+the outer product is <userinput>v * u.'</userinput>.</para>
</listitem>
</varlistentry>
@@ -2433,7 +2441,8 @@
<term>RowSum</term>
<listitem>
<synopsis>RowSum (m)</synopsis>
- <para>Calculate sum of each row in a matrix.</para>
+ <para>Calculate sum of each row in a matrix and return a vertical
+vector with the result.</para>
</listitem>
</varlistentry>
@@ -2449,7 +2458,11 @@
<term>RowsOf</term>
<listitem>
<synopsis>RowsOf (M)</synopsis>
- <para>Gets the rows of a matrix as a vertical vector.</para>
+ <para>Gets the rows of a matrix as a vertical vector. Each element
+of the vector is a horizontal vector which is the corresponding row of
+<varname>M</varname>. This function is useful if you wish to loop over the
+rows of a matrix. For example, as <userinput>for r in RowsOf(M) do
+something(r)</userinput>.</para>
</listitem>
</varlistentry>
@@ -2492,7 +2505,9 @@
<term>Submatrix</term>
<listitem>
<synopsis>Submatrix (m,r,c)</synopsis>
- <para>Return column(s) and row(s) from a matrix.</para>
+ <para>Return column(s) and row(s) from a matrix. This is
+just equivalent to <userinput>m@(r,c)</userinput>. <varname>r</varname>
+and <varname>c</varname> should be vectors of rows and columns (or single numbers if only one row or column is needed).</para>
</listitem>
</varlistentry>
@@ -2524,7 +2539,8 @@
<term>elements</term>
<listitem>
<synopsis>elements (M)</synopsis>
- <para>Get the number of elements of a matrix.</para>
+ <para>Get the total number of elements of a matrix. This is the
+number of columns times the number of rows.</para>
</listitem>
</varlistentry>
@@ -2548,7 +2564,7 @@
<term>zeros</term>
<listitem>
<synopsis>zeros (rows,columns...)</synopsis>
- <para>Make an matrix of all zeros (or a row vector if only one argument is given).</para>
+ <para>Make a matrix of all zeros (or a row vector if only one argument is given).</para>
</listitem>
</varlistentry>
@@ -2564,6 +2580,11 @@
<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
superdiagonal being all ones. It is the Jordan block matrix of one zero eigenvalue.</para>
+ <para>
+ See
+ <ulink url="http://planetmath.org/encyclopedia/JordanCanonicalFormTheorem.html";>Planetmath</ulink> or
+ <ulink url="http://mathworld.wolfram.com/JordanBlock.html";>Mathworld</ulink> for more information on Jordan Cannonical Form.
+ </para>
</listitem>
</varlistentry>
@@ -2588,7 +2609,16 @@
<listitem>
<synopsis>CharacteristicPolynomial (M)</synopsis>
<para>Aliases: <function>CharPoly</function></para>
- <para>Get the characteristic polynomial as a vector.</para>
+ <para>Get the characteristic polynomial as a vector. That is, return
+the coefficients of the polynomial starting with the constant term. 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-CharacteristicPolynomialFunction">CharacteristicPolynomialFunction</link>.
+</para>
+ <para>
+ See
+ <ulink url="http://planetmath.org/encyclopedia/CharacteristicEquation.html";>Planetmath</ulink> for more information.
+ </para>
</listitem>
</varlistentry>
@@ -2596,7 +2626,15 @@
<term>CharacteristicPolynomialFunction</term>
<listitem>
<synopsis>CharacteristicPolynomialFunction (M)</synopsis>
- <para>Get the characteristic polynomial as a function.</para>
+ <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>.
+</para>
+ <para>
+ See
+ <ulink url="http://planetmath.org/encyclopedia/CharacteristicEquation.html";>Planetmath</ulink> for more information.
+ </para>
</listitem>
</varlistentry>
@@ -2604,7 +2642,10 @@
<term>ColumnSpace</term>
<listitem>
<synopsis>ColumnSpace (M)</synopsis>
- <para>Get a basis matrix for the columnspace of a matrix.</para>
+ <para>Get a basis matrix for the columnspace of a matrix. That is,
+return a matrix whose columns are the basis for the column space of
+<varname>M</varname>. That is the space spanned by the columns of
+<varname>M</varname>.</para>
</listitem>
</varlistentry>
@@ -2612,7 +2653,9 @@
<term>CommutationMatrix</term>
<listitem>
<synopsis>CommutationMatrix (m, n)</synopsis>
- <para>Return the commutation matrix K(m,n) which is the unique m*n by m*n matrix such that K(m,n) * MakeVector(A) = MakeVector(A.') for all m by n matrices A.</para>
+ <para>Return the commutation matrix K(m,n) which is the unique m*n by
+m*n matrix such that K(m,n) * MakeVector(A) = MakeVector(A.') for all m by n
+matrices A.</para>
</listitem>
</varlistentry>
@@ -2650,7 +2693,8 @@
<term>ConvolutionVector</term>
<listitem>
<synopsis>ConvolutionVector (a,b)</synopsis>
- <para>Calculate convolution of two horizontal vectors.</para>
+ <para>Calculate convolution of two horizontal vectors. Return
+result as a vector and not added together.</para>
</listitem>
</varlistentry>
@@ -3022,7 +3066,8 @@
<listitem>
<synopsis>Nullity (M)</synopsis>
<para>Aliases: <function>nullity</function></para>
- <para>Get the nullity of a matrix.</para>
+ <para>Get the nullity of a matrix. That is, return the dimension of
+the nullspace; the dimension of the kernel of <varname>M</varname>.</para>
<para>
See
<ulink url="http://planetmath.org/encyclopedia/Nullity.html";>Planetmath</ulink> for more information.
@@ -3144,7 +3189,7 @@
<listitem>
<synopsis>Rotation2D (angle)</synopsis>
<para>Aliases: <function>RotationMatrix</function></para>
- <para>Rotation around origin in R<superscript>2</superscript>.</para>
+ <para>Return the matrix corresponding to rotation around origin in R<superscript>2</superscript>.</para>
</listitem>
</varlistentry>
@@ -3152,7 +3197,7 @@
<term>Rotation3DX</term>
<listitem>
<synopsis>Rotation3DX (angle)</synopsis>
- <para>Rotation around origin in R<superscript>3</superscript> about the x-axis.</para>
+ <para>Return the matrix corresponding to rotation around origin in R<superscript>3</superscript> about the x-axis.</para>
</listitem>
</varlistentry>
@@ -3160,7 +3205,7 @@
<term>Rotation3DY</term>
<listitem>
<synopsis>Rotation3DY (angle)</synopsis>
- <para>Rotation around origin in R<superscript>3</superscript> about the y-axis.</para>
+ <para>Return the matrix corresponding to rotation around origin in R<superscript>3</superscript> about the y-axis.</para>
</listitem>
</varlistentry>
@@ -3168,7 +3213,7 @@
<term>Rotation3DZ</term>
<listitem>
<synopsis>Rotation3DZ (angle)</synopsis>
- <para>Rotation around origin in R<superscript>3</superscript> about the z-axis.</para>
+ <para>Return the matrix corresponding to rotation around origin in R<superscript>3</superscript> about the z-axis.</para>
</listitem>
</varlistentry>
@@ -3238,9 +3283,13 @@
<varlistentry id="gel-function-Trace">
<term>Trace</term>
<listitem>
- <synopsis>Trace (m)</synopsis>
+ <synopsis>Trace (M)</synopsis>
<para>Aliases: <function>trace</function></para>
- <para>Calculate the trace of a matrix.</para>
+ <para>Calculate the trace of a matrix. That is the sum of the diagonal elements.</para>
+ <para>
+ See
+ <ulink url="http://planetmath.org/encyclopedia/Trace.html";>Planetmath</ulink> for more information.
+ </para>
</listitem>
</varlistentry>
@@ -3338,7 +3387,9 @@
<listitem>
<synopsis>ref (M)</synopsis>
<para>Aliases: <function>REF</function> <function>RowEchelonForm</function></para>
- <para>Get the row echelon form of a matrix.</para>
+ <para>Get the row echelon form of a matrix. That is, apply gaussian
+elimination but not backaddition to <varname>M</varname>. The pivot rows are
+divided to make all pivots 1.</para>
<para>
See
<ulink url="http://planetmath.org/encyclopedia/RowEchelonForm.html";>Planetmath</ulink> for more information.
@@ -3351,7 +3402,7 @@
<listitem>
<synopsis>rref (M)</synopsis>
<para>Aliases: <function>RREF</function> <function>ReducedRowEchelonForm</function></para>
- <para>Get the reduced row echelon form of a matrix.</para>
+ <para>Get the reduced row echelon form of a matrix. That is, apply gaussian elimination together with backaddition to <varname>M</varname>.</para>
<para>
See
<ulink url="http://planetmath.org/encyclopedia/ReducedRowEchelonForm.html";>Planetmath</ulink> for more information.
Modified: trunk/help/C/genius.txt
==============================================================================
--- trunk/help/C/genius.txt (original)
+++ trunk/help/C/genius.txt Wed Jun 4 16:57:54 2008
@@ -3282,7 +3282,9 @@
PowerMod (a,b,m)
- Compute a^b mod m. The b's power of a modulo m.
+ Compute a^b mod m. The b's power of a modulo m. It is not
+ neccessary to use this function as it is automatically used in
+ modulo mode. Hence a^b mod m is just as fast.
Prime
@@ -3524,9 +3526,9 @@
IsMatrixPositive (M)
- Check if a matrix is positive, that is if each element is
- positive. In particular, no element is 0. Do not confuse positive
- matrices with positive definite matrices.
+ Check if a matrix is positive, that is if each element is positive
+ (and hence real). In particular, no element is 0. Do not confuse
+ positive matrices with positive definite matrices.
See Wikipedia for more information.
@@ -3553,14 +3555,16 @@
IsUpperTriangular (M)
- Is a matrix upper triangular. That is, are all the entries above
- the diagonal zero.
+ Is a matrix upper triangular? That is, a matrix is upper
+ triangular if all all the entries below the diagonal are zero.
IsValueOnly
IsValueOnly (M)
- Check if a matrix is a matrix of numbers only.
+ Check if a matrix is a matrix of numbers only. Many internal
+ functions make this check. Values can be any number including
+ complex numbers.
IsVector
@@ -3598,38 +3602,40 @@
MakeVector
- MakeDiagonal (A)
+ MakeVector (A)
Make column vector out of matrix by putting columns above each
other. Returns null when given null.
MatrixProduct
- MatrixProduct (a)
+ MatrixProduct (A)
- Calculate the product of all elements in a matrix. That is we
- multiply all the elements and return a number that is the product
- of all the elements.
+ Calculate the product of all elements in a matrix or vector. That
+ is we multiply all the elements and return a number that is the
+ product of all the elements.
MatrixSum
- MatrixSum (a)
+ MatrixSum (A)
- Calculate the sum of all elements in a matrix. That is we add all
- the elements and return a number that is the sum of all the
- elements.
+ Calculate the sum of all elements in a matrix or vecgtor. That is
+ we add all the elements and return a number that is the sum of all
+ the elements.
MatrixSumSquares
- MatrixSumSquares (a)
+ MatrixSumSquares (A)
- Calculate the sum of squares of all elements in a matrix.
+ Calculate the sum of squares of all elements in a matrix or
+ vector.
OuterProduct
OuterProduct (u,v)
- Get the outer product of two vectors.
+ Get the outer product of two vectors. That is, suppose that u and
+ v are vertical vectors, then the outer product is v * u.'.
ReverseVector
@@ -3641,7 +3647,8 @@
RowSum (m)
- Calculate sum of each row in a matrix.
+ Calculate sum of each row in a matrix and return a vertical vector
+ with the result.
RowSumSquares
@@ -3653,7 +3660,10 @@
RowsOf (M)
- Gets the rows of a matrix as a vertical vector.
+ Gets the rows of a matrix as a vertical vector. Each element of
+ the vector is a horizontal vector which is the corresponding row
+ of M. This function is useful if you wish to loop over the rows of
+ a matrix. For example, as for r in RowsOf(M) do something(r).
SetMatrixSize
@@ -3685,7 +3695,9 @@
Submatrix (m,r,c)
- Return column(s) and row(s) from a matrix.
+ Return column(s) and row(s) from a matrix. This is just equivalent
+ to m@(r,c). r and c should be vectors of rows and columns (or
+ single numbers if only one row or column is needed).
SwapRows
@@ -3710,7 +3722,8 @@
elements (M)
- Get the number of elements of a matrix.
+ Get the total number of elements of a matrix. This is the number
+ of columns times the number of rows.
ones
@@ -3729,7 +3742,7 @@
zeros (rows,columns...)
- Make an matrix of all zeros (or a row vector if only one argument
+ Make a matrix of all zeros (or a row vector if only one argument
is given).
----------------------------------------------------------------------
@@ -3744,6 +3757,9 @@
matrix with that is all zero except the superdiagonal being all
ones. It is the Jordan block matrix of one zero eigenvalue.
+ See Planetmath or Mathworld for more information on Jordan
+ Cannonical Form.
+
BilinearForm
BilinearForm (v,A,w)
@@ -3764,19 +3780,31 @@
Aliases: CharPoly
- Get the characteristic polynomial as a vector.
+ Get the characteristic polynomial as a vector. That is, return the
+ coefficients of the polynomial starting with the constant term.
+ This is the polynomial defined by det(M-xI). The roots of this
+ polynomial are the eigenvalues of M. See also
+ CharacteristicPolynomialFunction.
+
+ See Planetmath for more information.
CharacteristicPolynomialFunction
CharacteristicPolynomialFunction (M)
- Get the characteristic polynomial as a function.
+ Get the characteristic polynomial as a function. This is the
+ polynomial defined by det(M-xI). The roots of this polynomial are
+ the eigenvalues of M. See also CharacteristicPolynomial.
+
+ See Planetmath for more information.
ColumnSpace
ColumnSpace (M)
- Get a basis matrix for the columnspace of a matrix.
+ Get a basis matrix for the columnspace of a matrix. That is,
+ return a matrix whose columns are the basis for the column space
+ of M. That is the space spanned by the columns of M.
CommutationMatrix
@@ -3813,7 +3841,8 @@
ConvolutionVector (a,b)
- Calculate convolution of two horizontal vectors.
+ Calculate convolution of two horizontal vectors. Return result as
+ a vector and not added together.
CrossProduct
@@ -4078,7 +4107,8 @@
Aliases: nullity
- Get the nullity of a matrix.
+ Get the nullity of a matrix. That is, return the dimension of the
+ nullspace; the dimension of the kernel of M.
See Planetmath for more information.
@@ -4166,25 +4196,28 @@
Aliases: RotationMatrix
- Rotation around origin in R2.
+ Return the matrix corresponding to rotation around origin in R2.
Rotation3DX
Rotation3DX (angle)
- Rotation around origin in R3 about the x-axis.
+ Return the matrix corresponding to rotation around origin in R3
+ about the x-axis.
Rotation3DY
Rotation3DY (angle)
- Rotation around origin in R3 about the y-axis.
+ Return the matrix corresponding to rotation around origin in R3
+ about the y-axis.
Rotation3DZ
Rotation3DZ (angle)
- Rotation around origin in R3 about the z-axis.
+ Return the matrix corresponding to rotation around origin in R3
+ about the z-axis.
RowSpace
@@ -4242,11 +4275,14 @@
Trace
- Trace (m)
+ Trace (M)
Aliases: trace
- Calculate the trace of a matrix.
+ Calculate the trace of a matrix. That is the sum of the diagonal
+ elements.
+
+ See Planetmath for more information.
Transpose
@@ -4324,7 +4360,9 @@
Aliases: REF RowEchelonForm
- Get the row echelon form of a matrix.
+ Get the row echelon form of a matrix. That is, apply gaussian
+ elimination but not backaddition to M. The pivot rows are divided
+ to make all pivots 1.
See Planetmath for more information.
@@ -4334,7 +4372,8 @@
Aliases: RREF ReducedRowEchelonForm
- Get the reduced row echelon form of a matrix.
+ Get the reduced row echelon form of a matrix. That is, apply
+ gaussian elimination together with backaddition to M.
See Planetmath for more information.
Modified: trunk/help/C/genius.xml
==============================================================================
--- trunk/help/C/genius.xml (original)
+++ trunk/help/C/genius.xml Wed Jun 4 16:57:54 2008
@@ -5,7 +5,7 @@
<!ENTITY appname "Genius">
<!ENTITY appversion "1.0.3">
<!ENTITY manrevision "0.2.2">
- <!ENTITY date "February 2008">
+ <!ENTITY date "June 2008">
<!ENTITY legal SYSTEM "legal.xml">
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