batch.el meta and latex syntax fixes

batch.el

@@ -1,3 +1,24 @@
+;;; batch.el --- Description -*- lexical-binding: t; -*-
+;;
+;; Copyright (C) 2024 Paul Alesius
+;;
+;; Author: Paul Alesius <[email protected]>
+;; Maintainer: Paul Alesius <[email protected]>
+;; Created: January 05, 2024
+;; Modified: January 05, 2024
+;; Version: 0.0.1
+;; Keywords: Symbol’s value as variable is void: finder-known-keywords
+;; Homepage: https://github.com/noname/something
+;; Package-Requires: ((emacs "24.3"))
+;;
+;; This file is not part of GNU Emacs.
+;;
+;;; Commentary:
+;;
+;;  Description
+;;
+;;; Code:
+
 (require 'org)
 (require 'ox-md)
 
@@ -72,3 +93,7 @@
       (export-src))))
 
 (main)
+
+
+(provide 'something)
+;;; batch.el ends here

src/llmath/algebra/concepts/division.org

@@ -7,12 +7,12 @@ In mathematical terms, if we have a dividend \( a \) and a divisor \( b \), the
 
 * Basic Division Operation
 In its simplest form, division can be represented as:
-\[ \frac{a}{b} = c \]
+\\[ \frac{a}{b} = c \\]
 where \( a \) is the dividend, \( b \) is the divisor, and \( c \) is the quotient.
 
 * Division by Zero
 It's important to note that division by zero is undefined. For any number \( a \),
-\[ \frac{a}{0} \]
+\\[ \frac{a}{0} \\]
 is not defined.
 
 * Examples of Division
@@ -40,14 +40,14 @@ print(quotient3)
 
 * Division in Algebraic Expressions
 Division is often seen in algebraic expressions. For example, in the expression
-\[ \frac{x + 2}{y - 3} \]
+\\[ \frac{x + 2}{y - 3} \\]
 \( x \) and \( y \) are variables, and the expression represents the division of the quantity \( x + 2 \) by \( y - 3 \).
 
 * Division Properties
 - Commutative Property: Division is not commutative. That is, \( a \div b \neq b \div a \).
 - Associative Property: Division is not associative. Changing the grouping of the numbers in a division operation changes the result.
 - [[file:../properties/distributive.org][Distributive Property]]: Division distributes over addition and subtraction in the following way:
-  \[ \frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c} \]
+  \\[ \frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c} \\]
 
 * Practice
 - Divide 42 by 7.
@@ -56,24 +56,24 @@ Division is often seen in algebraic expressions. For example, in the expression
 
 This is not a simple division operation but rather an algebraic equation involving division. As the division is the operation of finding the quotient of the dividend by a divisor, you can reverse the division by multiplying by the quotient \( (y - 1) \):
 
-\[ (2y + 4) = 3(y - 1) \]
+\\[ (2y + 4) = 3(y - 1) \\]
 
 Next, we can expand and simplify both sides of the equation with the distributive property of multiplication over division and sibtraction. The distributive property state that for any numbers \( a \), \( b \), and \( c \), the equation \( a(b+c) = ab + ac \) holds true. The distributive property also holds true for subtraction where \( (a(b-c) = ab - ac) \) so that we can distribute \( 3(y - 1) \) over \( 3y - 3 \) to simplify the equation as
 
-\[ 2y + 4 = 3y - 3 \]
+\\[ 2y + 4 = 3y - 3 \\]
 
 Now we can isolate \( y \) by moving all terms involving \( y \) to one side of the equation and the constant terms to the other side
 
-\[ 2y - 3y = -3 - 4 \]
+\\[ 2y - 3y = -3 - 4 \\]
 
 The process of moving terms from one side of the equation to the other without breaking the equation is based on the fundamental principle of equality in algebra. The principle states that if you perform the same operation on both sides of the an equation, the equation remain valid or "balanced".
 
 Simplifying furthe
 
-\[ -y = -7 \]
+\\[ -y = -7 \\]
 
 or finally
 
-\[ y = 7 \]
+\\[ y = 7 \\]
 
 Remember, practice is key to mastering division in algebra.

src/llmath/algebra/concepts/pemdas.org

@@ -6,22 +6,22 @@ The acronym PEMDAS helps to remember the order of operations in algebra. It stan
 * Parentheses
 First, perform all operations inside parentheses.
 
-\[ (a + b) \times c \]
+\\[ (a + b) \times c \\]
 
 * Exponents
 Then, solve the exponents (or powers).
 
-\[ a^b \]
+\\[ a^b \\]
 
 * Multiplication and Division
 Next, perform multiplication and division from left to right.
 
-\[ \frac{a \times b}{c} \]
+\\[ \frac{a \times b}{c} \\]
 
 * Addition and Subtraction
 Finally, perform addition and subtraction from left to right.
 
-\[ a + b - c \]
+\\[ a + b - c \\]
 
 * Examples in R
 Let's see some examples of these operations using R programming language.

src/llmath/algebra/factoring/difference-of-squares.org

@@ -3,9 +3,9 @@
 
 The concept of the "Difference of Squares" is a fundamental algebraic technique used in factoring expressions. It is based on the simple identity:
 
-\[
+\\[
 a^2 - b^2 = (a + b)(a - b)
-\]
+\\]
 
 This identity states that the difference between the squares of two numbers, \(a\) and \(b\), can be factored into the product of the sum and the difference of those two numbers.
 

src/llmath/algebra/factoring/perfect-square-trinomials.org

@@ -1,18 +1,18 @@
 #+title: Perfect Square Trinomials
 #+PROPERTY: header-args:R :cache yes :results output graphics file :exports code :tangle yes
 
-Perfect square trinomials are a form of quadratic expression that can be factored into the square of a binomial. They have a specific pattern: \[a^2 + 2ab + b^2 = (a + b)^2\] or \[a^2 - 2ab + b^2 = (a - b)^2\]. Recognizing these patterns is key to factoring them efficiently.
+Perfect square trinomials are a form of quadratic expression that can be factored into the square of a binomial. They have a specific pattern: \\( a^2 + 2ab + b^2 = (a + b)^2 \\) or \\( a^2 - 2ab + b^2 = (a - b)^2 \\). Recognizing these patterns is key to factoring them efficiently.
 
 * Factoring Perfect Square Trinomials
 A perfect square trinomial is formed by squaring a binomial. It looks like this:
-\[ (x + a)^2 = x^2 + 2ax + a^2 \] or \[ (x - a)^2 = x^2 - 2ax + a^2 \].
+\\( (x + a)^2 = x^2 + 2ax + a^2 \\) or \\( (x - a)^2 = x^2 - 2ax + a^2 \\).
 
 ** Examples
-1. Factor \[ x^2 + 6x + 9 \].
-   \[ x^2 + 6x + 9 = (x + 3)^2 \], because \( 3^2 = 9 \) and \( 2 \cdot x \cdot 3 = 6x \).
+1. Factor \\( x^2 + 6x + 9 \\).
+   \\( x^2 + 6x + 9 = (x + 3)^2 \\), because \\( 3^2 = 9 \\) and \\( 2 \cdot x \cdot 3 = 6x \\).
 
-2. Factor \[ x^2 - 10x + 25 \].
-   \[ x^2 - 10x + 25 = (x - 5)^2 \], because \( 5^2 = 25 \) and \( -2 \cdot x \cdot 5 = -10x \).
+2. Factor \\[ x^2 - 10x + 25 \\].
+   \\( x^2 - 10x + 25 = (x - 5)^2 \\), because \\( 5^2 = 25 \\) and \\( -2 \cdot x \cdot 5 = -10x \\).
 
 ** Checking Our Work with R
 We can use R to verify the factoring of perfect square trinomials.
@@ -31,7 +31,7 @@ f2(2) # Should return 9 (2 - 5)^2
 We can plot a perfect square trinomial to see its parabolic shape, which is characteristic of quadratic functions.
 
 ** Plot Example
-Let's plot \[ x^2 + 6x + 9 \].
+Let's plot \\[ x^2 + 6x + 9 \\].
 
 #+BEGIN_SRC R :exports both :file perfect_square_plot.png
 x <- seq(-10, 10, by = 0.1)

src/llmath/algebra/properties/commutative.org

@@ -5,7 +5,7 @@ The commutative property is a fundamental aspect of basic arithmetic and algebra
 
 * The Commutative Property of Addition
 The commutative property of addition can be written in mathematical terms as:
-\[ a + b = b + a \]
+\\[ a + b = b + a \\]
 For example, \( 3 + 5 = 5 + 3 \) which equals 8.
 
 * The Commutative Property of Multiplication