Commit d49551a6 authored by Jiri (George) Lebl's avatar Jiri (George) Lebl Committed by George Lebl

update the docs a little, fix a few typos, add links.


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.


svn path=/trunk/; revision=660
parent d22245ca
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.
Wed Jun 04 03:51:25 2008 Jiri (George) Lebl <jirka@5z.com>
* src/gnome-genius.c: figure out a way to work around VTE nonsense,
......
......@@ -1910,8 +1910,8 @@ that is if <userinput>b^(n-1) == 1 mod n</userinput>. This calles the <function
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 @@ that is if <userinput>b^(n-1) == 1 mod n</userinput>. This calles the <function
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ same size. No conjugates are taken so this is a bilinear form even if working o
<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 @@ superdiagonal being all ones. It is the Jordan block matrix of one zero eigenva
<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 @@ superdiagonal being all ones. It is the Jordan block matrix of one zero eigenva
<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 @@ superdiagonal being all ones. It is the Jordan block matrix of one zero eigenva
<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 @@ superdiagonal being all ones. It is the Jordan block matrix of one zero eigenva
<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 @@ superdiagonal being all ones. It is the Jordan block matrix of one zero eigenva
<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 @@ determinant.
<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 @@ function of two arguments or it can be a matrix giving a sesquilinear form.
<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 @@ function of two arguments or it can be a matrix giving a sesquilinear form.
<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 @@ function of two arguments or it can be a matrix giving a sesquilinear form.
<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 @@ function of two arguments or it can be a matrix giving a sesquilinear form.
<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 @@ Hermitian matrix (if the first element is real of course).</para>
<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 @@ function of two arguments or it can be a matrix giving a sesquilinear form.
<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 @@ function of two arguments or it can be a matrix giving a sesquilinear form.
<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.
......
......@@ -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.
......
......@@ -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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