[genius] Commit the updated genius.txt
- From: George Lebl <jirka src gnome org>
- To: commits-list gnome org
- Cc:
- Subject: [genius] Commit the updated genius.txt
- Date: Tue, 31 Aug 2010 05:45:11 +0000 (UTC)
commit 8b70f3660032c5afc465ef3fd0228eb6bd2e649d
Author: Jiri (George) Lebl <jirka 5z com>
Date: Mon Aug 30 22:44:41 2010 -0700
Commit the updated genius.txt
help/C/genius.txt | 169 ++++++++++++++++++++++++++++++++---------------------
1 files changed, 102 insertions(+), 67 deletions(-)
---
diff --git a/help/C/genius.txt b/help/C/genius.txt
index a3afc0a..d59434d 100644
--- a/help/C/genius.txt
+++ b/help/C/genius.txt
@@ -371,7 +371,7 @@ Using the Work Area
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 Genius
Mathematics Tool as a calculator only, just type in your expression here
- and it willg et evaluated.
+ and it will be evaluated.
Type your expression into the Console work area and press enter and the
expression will be evaluated. Expressions are written in a language called
@@ -603,7 +603,7 @@ Values
1234
- Hexidecimal and octal numbers can be written using C notation. For
+ Hexadecimal and octal numbers can be written using C notation. For
example:
0x123ABC
@@ -980,7 +980,7 @@ Separator
familiar with pascal this should be second nature. However genius can let
you pretend it is a terminator somewhat, if a ; 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 ;null. This is usefull in case you do not want to
+ you would have written ;null. 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.
@@ -1104,7 +1104,7 @@ List of GEL Operators
a.%b
- Element by element the mod operator. Returns the remaineder after
+ Element by element the mod operator. Returns the remainder after
element by element a./b.
a mod b
@@ -1220,7 +1220,7 @@ List of GEL Operators
a:b
Build a vector from a to b (or specify a row, column region for
- the @ operator). For example to get rows 2 to 4 of mamtrix A we
+ the @ operator). For example to get rows 2 to 4 of matrix A we
could do
A@(2:4,)
@@ -1311,7 +1311,7 @@ Loops
do <expression2> while <expression1>
do <expression2> until <expression1>
- These are similiar to other languages, however they return the result of
+ These are similar to other languages, however they return the result of
the last iteration or NULL if no iteration was done. In the boolean
expression, = is translated into == just as for the if statement.
@@ -1402,7 +1402,7 @@ Comparison Operators
0 if both sides are equal, 1 if left side is larger.
Normally = is translated to == if it happens to be somewhere where GEL is
- expecing a condition such as in the if condition. For example
+ expecting a condition such as in the if condition. For example
if a=b then c
if a==b then c
@@ -1417,7 +1417,7 @@ Comparison Operators
expression and means just what it should, that is (1<x and x=<y and y<5)
To build up logical expressions use the words not, and, or, xor. The
- operators or and and are special beasts as they evaluate their arguemnts
+ operators or and and are special beasts as they evaluate their arguments
one by one, so the usual trick for conditional evaluation works here as
well. For example, 1 or a=1 will not set a=1 since the first argument was
true.
@@ -1484,8 +1484,8 @@ Global Variables and Scope of Variables
function f() = (a:=5);
f();
- Sometimes, however, it is neccessary to set a global variable from inside
- a function. When this behaviour is needed, use the set function. Passing a
+ Sometimes, however, it is necessary to set a global variable from inside a
+ function. When this behaviour is needed, use the set function. Passing a
string or a quoted identifier to this function sets the variable globally
(on the top level). For example, to set a to the value 3 you could call:
@@ -1500,7 +1500,7 @@ Global Variables and Scope of Variables
must use passing by reference.
So to recap in a more technical language: Genius operates with different
- numberred contexts. The top level is the context 0 (zero). Whenever a
+ 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. When a variable was defined in a lower
@@ -1558,12 +1558,12 @@ Returning
References
- It may be neccessary 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 will set the
- variable for you using a dereference. You do not have to use references
- only for this purpose, but this is their main use.
+ 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 will set the variable for
+ you using a dereference. You do not have to use references only for this
+ purpose, but this is their main use.
When using functions that return values through references in the argument
list, just pass the variable name with an ampersand. For example the
@@ -1601,7 +1601,7 @@ Lvalues
a
- Identifier. Here we would be setting the varable of name a.
+ Identifier. Here we would be setting the variable of name a.
*a
@@ -1658,7 +1658,7 @@ Toplevel Syntax
Therefore think of programs 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).
+ inside parentheses).
The following code will produce an error when entered on the top level of
a program, while it will work just fine in a function.
@@ -1673,7 +1673,7 @@ Toplevel Syntax
will execute it. After the execution is done, Genius Mathematics Tool will
go on to the next line, it will see else, and it will produce a parsing
error. To fix this, use parentheses. Genius Mathematics Tool will not be
- satisfied until it has found that all parenteses are closed.
+ satisfied until it has found that all parentheses are closed.
if Something() then (
DoSomething()
@@ -2211,7 +2211,7 @@ Basic
Make integer (0 for false or 1 for true) from a boolean value.
bval can also be a number in which case a non-zero value will be
- interpreted as true and zero will be interpretted as false.
+ interpreted as true and zero will be interpreted as false.
IsBoolean
@@ -2277,7 +2277,7 @@ Basic
Parse (str)
Parses but does not evaluate a string. Note that certain
- precomputation is done during the parsing stage.
+ pre-computation is done during the parsing stage.
SetFunctionFlags
@@ -2440,7 +2440,7 @@ Basic
wait (secs)
- Waits a specified number of seconds. secs must be nonnegative.
+ Waits a specified number of seconds. secs must be non-negative.
Zero is accepted and nothing happens in this case, except possibly
user interface events are processed.
@@ -2449,7 +2449,7 @@ Basic
version
Returns the version of Genius as a horizontal 3-vector with major
- version first, then minor version and finally patchlevel.
+ version first, then minor version and finally the patch level.
warranty
@@ -2604,7 +2604,7 @@ Parameters
instead of the number.
Output is never chopped if OutputChopExponent is zero. It must be
- a nonnegative integer.
+ a non-negative integer.
If you want output always chopped according to OutputChopExponent,
then set OutputChopWhenExponent, to something greater than or
@@ -3319,7 +3319,7 @@ Number Theory
DiscreteLog (n,b,q)
Find discrete log of n base b in Fq, the finite field of order q,
- where q is a prime, using the Silver-Pohlig-Hellman algoritm.
+ where q is a prime, using the Silver-Pohlig-Hellman algorithm.
See Wikipedia or Planetmath or Mathworld for more information.
@@ -3370,7 +3370,7 @@ Number Theory
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)
+ course very inefficient)
for n=1 to 1000 do (
if MatrixSum (Factors(n)) == 2*n then
@@ -3638,7 +3638,7 @@ Number Theory
PadicValuation (n,p)
- Returns the padic valuation (number of trailing zeros in base p).
+ Returns the p-adic valuation (number of trailing zeros in base p).
See Planetmath for more information.
@@ -3690,8 +3690,8 @@ Number Theory
SilverPohligHellmanWithFactorization (n,b,q,f)
Find discrete log of n base b in Fq, the finite group of order q,
- where q is a prime using the Silver-Pohlig-Hellman algoritm, given
- f being the factorization of q-1.
+ where q is a prime using the Silver-Pohlig-Hellman algorithm,
+ given f being the factorization of q-1.
SqrtModPrime
@@ -3770,7 +3770,7 @@ Matrix Manipulation
CompoundMatrix (k,A)
- Calculate the kth compund matrix of A.
+ Calculate the kth compound matrix of A.
CountZeroColumns
@@ -3825,7 +3825,7 @@ Matrix Manipulation
Aliases: InnerProduct
- Get the hermitian product of two vectors. The vectors must be of
+ Get the Hermitian product of two vectors. The vectors must be of
the same size. This is a sesquilinear form using the identity
matrix.
@@ -3885,8 +3885,8 @@ Matrix Manipulation
IsMatrixNonnegative (M)
- Check if a matrix is nonnegative, that is if each element is
- nonnegative. Do not confuse positive matrices with positive
+ 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.
See Wikipedia for more information.
@@ -3988,7 +3988,7 @@ Matrix Manipulation
MatrixSum (A)
- 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.
@@ -4119,11 +4119,11 @@ Matrix Manipulation
Linear Algebra
- AuxilliaryUnitMatrix
+ AuxiliaryUnitMatrix
- AuxilliaryUnitMatrix (n)
+ AuxiliaryUnitMatrix (n)
- Get the auxilliary unit matrix of size n. This is a square matrix
+ Get the auxiliary unit matrix of size n. 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.
@@ -4271,7 +4271,7 @@ Linear Algebra
Apply the Gram-Schmidt process (to the columns) with respect to
inner product given by B. If B is not given then the standard
- hermitian product is used. B can either be a sesquilinear function
+ Hermitian product is used. B 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 B.
@@ -4323,7 +4323,7 @@ Linear Algebra
IsHermitian (M)
- Is a matrix hermitian. That is, is it equal to its conjugate
+ Is a matrix Hermitian. That is, is it equal to its conjugate
transpose.
See Planetmath for more information.
@@ -4359,16 +4359,16 @@ Linear Algebra
IsPositiveDefinite (M)
- Is M a hermitian positive definite matrix. That is if
+ Is M a Hermitian positive definite matrix. That is if
HermitianProduct(M*v,v) is always strictly positive for any vector
- v. M must be square and hermitian to be positive definite. The
+ v. M must be square and Hermitian to be positive definite. The
check that is performed is that every principal submatrix has a
- nonnegative determinant. (See HermitianProduct)
+ non-negative determinant. (See HermitianProduct)
Note that some authors (for example Mathworld) do not require that
- M be hermitian, and then the condition is on the real part of the
+ M 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 M
+ perform this check, just check the Hermitian part of the matrix M
as follows: IsPositiveDefinite(M+M').
See Planetmath or Mathworld for more information.
@@ -4377,16 +4377,16 @@ Linear Algebra
IsPositiveSemidefinite (M)
- Is M a hermitian positive semidefinite matrix. That is if
- HermitianProduct(M*v,v) is always nonnegative for any vector v. M
- must be square and hermitian to be positive semidefinite. The
+ Is M a Hermitian positive semidefinite matrix. That is if
+ HermitianProduct(M*v,v) is always non-negative for any vector v. M
+ must be square and Hermitian to be positive semidefinite. The
check that is performed is that every principal submatrix has a
- nonnegative determinant. (See HermitianProduct)
+ non-negative determinant. (See HermitianProduct)
- Note that some authors do not require that M be hermitian, and
+ Note that some authors do not require that M 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 M as follows:
+ check the Hermitian part of the matrix M as follows:
IsPositiveSemidefinite(M+M').
See Planetmath or Mathworld for more information.
@@ -4395,7 +4395,7 @@ Linear Algebra
IsSkewHermitian (M)
- Is a matrix skew-hermitian. That is, is the conjugate transpose
+ Is a matrix skew-Hermitian. That is, is the conjugate transpose
equal to negative of the matrix.
See Planetmath for more information.
@@ -4515,7 +4515,7 @@ Linear Algebra
Projection (v,W,B...)
Projection of vector v onto subspace W with respect to inner
- product given by B. If B is not given then the standard hermitian
+ product given by B. If B is not given then the standard Hermitian
product is used. B can either be a sesquilinear function of two
arguments or it can be a matrix giving a sesquilinear form.
@@ -4689,7 +4689,7 @@ Linear Algebra
VectorAngle (v,w,B...)
The angle of two vectors with respect to inner product given by B.
- If B is not given then the standard hermitian product is used. B
+ If B is not given then the standard Hermitian product is used. B
can either be a sesquilinear function of two arguments or it can
be a matrix giving a sesquilinear form.
@@ -4810,7 +4810,7 @@ Combinatorics
Aliases: fib
- Calculate nth fibonacci number. That is the number defined
+ Calculate nth Fibonacci number. That is the number defined
recursively by Fibonacci(n) = Fibonacci(n-1) + Fibonacci(n-2) and
Fibonacci(1) = Fibonacci(2) = 1.
@@ -4821,10 +4821,10 @@ Combinatorics
FrobeniusNumber (v,arg...)
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. The vector can be given
- as separate numbers or a single vector. All the numbers given
- should have GCD of 1.
+ 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.
See Mathworld for more information.
@@ -4839,10 +4839,10 @@ Combinatorics
FrobeniusNumber (n,v)
- Find the vector c of nonnegative integers such that taking the dot
- product with v is equal to n. If not possible returns null. v
+ Find the vector c of non-negative integers such that taking the
+ dot product with v is equal to n. If not possible returns null. v
should be given sorted in increasing order and should consist of
- nonnegative integers.
+ non-negative integers.
See Mathworld for more information.
@@ -4872,7 +4872,7 @@ Combinatorics
Multinomial (v,arg...)
Calculate multinomial coefficients. Takes a vector of k
- 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 k variables with the corresponding powers.
@@ -5461,6 +5461,22 @@ Equation Solving
See Mathworld, or Wikipedia for more information.
+ EulersMethodFull
+
+ EulersMethodFull (f,x0,y0,x1,n)
+
+ Use classical Euler's method to numerically solve y'=f(x,y) for
+ initial x0, y0 going to x1 with n increments, returns a 2 by n+1
+ matrix with the x and y values. Suitable for plugging into
+ LinePlotDrawLine.
+
+ Systems can be solved by just having y be a (column) vector
+ everywhere. That is, y0 can be a vector in which case f should
+ take a number x and a vector of the same size for the second
+ argument and should return a vector of the same size.
+
+ See Mathworld, or Wikipedia for more information.
+
FindRootBisection
FindRootBisection (f,a,b,TOL,N)
@@ -5554,6 +5570,22 @@ Equation Solving
See Mathworld, or Wikipedia for more information.
+ RungeKuttaFull
+
+ RungeKuttaFull (f,x0,y0,x1,n)
+
+ Use classical non-adaptive fourth order Runge-Kutta method to
+ numerically solve y'=f(x,y) for initial x0, y0 going to x1 with n
+ increments, returns a 2 by n+1 matrix with the x and y values.
+ Suitable for plugging into LinePlotDrawLine.
+
+ Systems can be solved by just having y be a (column) vector
+ everywhere. That is, y0 can be a vector in which case f should
+ take a number x and a vector of the same size for the second
+ argument and should return a vector of the same size.
+
+ See Mathworld, or Wikipedia for more information.
+
----------------------------------------------------------------------
Statistics
@@ -5894,13 +5926,16 @@ Plotting
4-vector, and for arrow either "origin", "end", "both", or "none".
For "window" we can specify "fit" rather than a vector in which
case, the x range will be set precisely and the y range will be
- set with five percent borders around the line.
+ set with five percent borders around the line. Finally, the legend
+ can be specified by adding "legend" and the string with the
+ legend.
Examples:
- genius> LinePlotDrawLine(0,0,1,1,"color","blue","thickness",3)
- genius> LinePlotDrawLine([0,0;1,-1;-1,-1])
- genius> LinePlotDrawLine([0,0;1,1],"arrow","end")
+genius> LinePlotDrawLine(0,0,1,1,"color","blue","thickness",3)
+genius> LinePlotDrawLine([0,0;1,-1;-1,-1])
+genius> LinePlotDrawLine([0,0;1,1],"arrow","end")
+genius> LinePlotDrawLine(EulersMethodFull(`(x,y)=y,0,3,100),"color","blue","legend","The Solution")
LinePlotParametric
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