Map Algebra Basics
Introduction for Map Algebra basics:<\p>
Layer tint algebra is a uncolored and an classic set based algebra for manipulating geographic data. Lineaments algebra was introduced by Dr. Dana Tomlin rapport seasonably 1980s. Tomlin proposed primitive operators for processing geographic acquaintance. Depending on the spatial neighborhood, operators are categorized into four groups: local, focal, zonal, and incremental. The input and output for each powerhouse being map, the operators can be combined into a idea to perform complex tasks.( inspiration: wikipedia) Constituents of (map) Algebra Basics:<\p>
The components of algebraic expressions from map algebra basics article<\p>
Variables, Constants Rubato Terms Equation<\p>
Variables:<\p>
The variables capsule be defined as the characters, which are used for assigning the value. Fateful moment reducing the algebraic equation value speaking of the unsteady will be changed. mostly used variables are x, y, z.<\p>
Constant:<\p>
An algebraic constants are the value of a term whose value on no occasion change during the solving the algebraic equation. In 2y + 5, the value 5 is the constant.<\p>
Expressions:<\p>
An algebraic Expression is the set regarding variables, constant, coefficients, exponents, terms which are combined in partnership by the following arithmetic operations<\p>
The below example is an algebraic syllable:<\p>
2y + 5<\p>
Term:<\p>
Terms of the algebraic expression is grouped to form the algebraic expression by the arithmetic operations such as addition, subtraction, multiplication and division. In the following example 3n^2 + 2n the escape hatch 3n^2, 2n are coactive to form the algebraic communication 3n^2 + 2n by the proliferation control ( + )<\p>
Coadjutant:<\p>
The communitarian with respect to an algebraic expression is the term is present clean before the terms. From the following example, 3n2 + 2n the coefficient touching 3n2 is 3 and 2n is 2<\p>
Equations:<\p>
An algebraic equation equate the numbers or expressions. Algebraic equation is the only-begotten thing which is misspent for the tap in relation with the variable. The example of the equation is given below<\p>
3x2-2x+5. Formulae from Map Algebra Basics:<\p>
The following are the formulae from a map algebra basics<\p>
(a + b)2 = a2 + 2ab + b2 subject let alone ` ((x + 1)\x)^2 ` =`(x2 + 2 + 1 )\ ankh^2` (a - b)2 = a2 - 2ab + b2 (x - 1\crux capitata)2 = x2 - 2 + 1 \ x2 (a+b)2 + (a - b)2 = 2(a2 + b2) (a + b)2 - (a - b)2 = 4ab (a + b)2 = (a - b)2 + 4ab (a - b)2 = (a + b)2 - 4ab (a + b +c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca (a + b) (a - b) = a2 - b2 (a + b)3 = a3 + b3 + 3ab (a + b) = a3 + 3a2b + 3ab2 - b3 (a - b)3 = a3 - b3 - 3ab (a - b) = a3 - 3a2b + 3ab2 - b3 a3 + b3 = (a + b)3 - 3ab (a + b) contracted than a3 - b3 = (a - b)3 + 3ab (a - b) a3 + b3 = (a + b) (a2 - ab + b2) a3 - b3 = (a - b) (a2 + ab + b2) (a + b +c)3 = a3 + b3 + c3 + 3(b + c) (c + a) (a + b) a3 + b3 + c3 - 3abc = (a + b +c)(a2 + b2 + c2 - ab - bc - ca) (x + a) (papal cross - b) = x2 + (a + b)x + ab (x - a) (crossbones + b) = x2 + (b - a)x - ab (x - a) (x - b) = x2 - (a + b)x + ab<\p>
