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  "Math in ONE"

Reference Manual

      Contents

open   System Overview
open open Definitions
open open Algebra
open open (W) Statistics
open open (W)(AP) Matrices
open open Calculus
open open Unit Conveerter
open   Input data
open open Input Field, Memories & Expressions
open open Data Entry to Memory
open open (W)(AG) Import File
open open (W)(AP) Matrix Setup
open open (W)(AG) Export Data
open   Basic Operations
open open Function Expressions
open open (W)(AP) Matrix Expressions
open open Binary Expressions
open open Working with Memories
open open Variables use - Graphs
open open SigFigs
open   Response to Customer Comments

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Function Expressions

IMPORTANT: This program requires expressions to be written strictly following mathematical rules. Any shortcuts commonly used, are not permitted (e.g. skipping '*' multiplication operator (1+2)(3+4) or 1.2(2.3+3.4) will generate error). Complex numbers can only be entered in format a+ib.

This program performs all calculations in Complex Numbers (a + i b) where a & b are real expressions, and ' i ' is an imaginary number ( i * i = -1 ). An ' i ' before a number (real expression) indicates imaginary part of complex number

(e.g. sin(0.5) + i(cos(0.6)) + (1+i2) * ln(2+i3) will produce the output -0.203687229..+i4.37307869).

The result from the expression evaluation is automatically stored in "arg" variable and is ready to use in the next calculations. In addition, the value can be redirected to a given memory using Colon command:
Syntax :mN=expression - colon ' : ', letter ' m ', number N ' 1 ', ' 2 '..., equal sign ' = ', then expression
(e.g. :m0=sin0.53). That command will send calculation result to memory window item #0. If item exist, it value will be overwritten. If there is no number after 'm', the calculation result will be appended after last memory item.

Relative subject: Comma Command

The following rules have to be adhered when an expression is written:

  1. Use valid symbol names:
    1. Numbers depend on a Numerical systems mode:
      • hexadecimal mode: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F - ( base 16: A is 10, B is 11 ... F is 15)
      • decimal mode: 0,1,2,3,4,5,6,7,8,9 - (base 10)
      • octal mode: 0,1,2,3,4,5,6,7 - (base 8)
      • binary mode: 0,1 - (base 2)
    2. Operators:
      • arithmetic operators: ' + ',    ' - ',    ' * ',     ' / ',    ' % ',    ' ! ',    ' ^ ',    ' i '
      • binary operators: ' ~ ',    ' & ',    ' | ',     ' ` ',    ' >> ',    ' << '
      • matrix operators: ' => ',    ' < '     (' + ',    ' - ',    ' * ',    ' / ' are used in matrix mode as well)
    3. Separators: ' . ',    ' , ',    ' : ',    ' = ',     ' ( ',    ' ) ',    ' [ ',    ' ] '
    4. Variables: m, x, y, z, t, θ
    5. Use valid names of:
  2. All functions designations follow a general rule: An open bracket follows any function name, except when a function requires only one parameter and parameter is a real number and not an expression.
    • Scalar functions - use round brackets
    • Matrix and Vector functions - use square brackets
    • Statistic functions - don't use parameters therefore the brackets are not use.
  3. In order for expression to be valid, the number of open brackets must be equal to the number of close brackets.
  4. The relative precedence levels (order of execution) of operators need to be taken into consideration:
    1 ' ( ',    ' [ ' Grouping, scope, block
    2 (W) ' < ' or (AP) '//' Right division - matrix
    3 function Any build in function
    4 ' ~ ',    ' ! ' Bitwise NOT, factorial, (AP) Logical expressions NOT
    5 ' ^ ' Power
    6 ' * ',    ' / ',    ' % ' Multiplication, division, reminder in integer division
    7 ' + ',    ' - ' Addition, subtraction
    8 ' >> ',    ' << ' Bitwise shift left and right
    9 ' & ' Bitwise AND, (AP) Logical expressions AND
    10 ' | ',    ' ` ' Bitwise inclusive (normal) OR and exclusive OR, , (AP) Logical expressions OR
    11 ' = ',    ' => ' Assignment operator
    If the precedence levels of operators is the same, the program will execute from left to right.
(AG)

Functions appXXX and drawXXX under Applications and Graphing spinners, require two groups of information: parameters and expressions.

  1. Parameters describe initial conditions and/or give instructions to an application in what way to evaluate expression. The descriptions of appXXX and drawXXX parameters are identified by various abbreviations of names describing the meaning of a particular parameter. (e.g. acc, Xstart, Xmin, XY, ...)
  2. Expressions are used by applications to perform designed tasks. In the description of appXXX and drawXXX, expressions are identified by the letter 'F' (e.g. Fn0, Fn1, DFn0, ...).
  3. (e.g. appCFZ(acc, XY, Fn0) - acc and XY are parameters, Fn0 is an expression). XY represents four different parameters Xmin, Xmax, Ymin, Ymax.

Valid Parameters & Expresions entry:

  1. Functions, numbers or expression (e.g. 1E-14, -pi/3, pi/3, -5, 5, sin(1.2)+2 )
  2. .
  3. Memories.
    1. Memory that contain valid mathematical expression, numbers or other memories (e.g. m0 = 1+ln(5), m1 = m2+m0, m2 = 1E-14) nesting is unlimited.
    2. Memory contained expressions separated by comma ',' can be used only in appXXX and drawXXX and no nesting is permitted. In this situation one memory item can contain multiple parameters (e.g. m0 = 1e-14 and m1 = -pi/3, pi/3, -5, 5 then function will look like this appCFZ(m0, m1, sin(x)) )
    3. The following example will generate error: (e.g. appCFZ(m0,sin(x)) where m0 = m1, m2 & m1=1e-14 and m2 = -pi/3, pi/3, -5, 5 memory m2 is nested so it can only contain a valid expression, as a result commas are not permitted).
  4. Variables x, y and z are not allowed to be used in parameters expressions.
  5. Expressions can be called other expressions and memories without any nesting limitations. (e.g. m1 = -pi/m3 or m1 = -pi/m3, pi/m3, -m4, m4 and m3 = 3 and m4 = 5 )
  6. Expressions can be called only from appXXX or drawXXX function in an expression group. (e.g. appCFZ(m0,F1) where m0 = m1, -pi/m2, pi/m2, -5, 5 & m1=1e-14 & m2=3 and F1=sin(x) )

IMPORTANT: All appxxx and drawxxx functions operate only in the decimal system numbers and trigonometric functions in the radian angular system.

Under Applications (spinner) the following functions can be find

  1. appRFZ( acc, Xmin, Xmax, Fn0) Real Function Zeros.
    • acc - calculation accuracy (e.g. 0.00000001 or 1e-15) or stored in memories (e.g. m2)
    • Xmin - calculation range from (e.g. 0.1 or m0)
    • Xmax - calculation range to (e.g. 7.2 or m1)
    • Fno - function that is evaluated, it can be explicit (e.g. ln(x)) or stored in "expressions" (e.g. F3)

    • appREZ(0.000001,0.1,7.2,ln(x))
  2. appRFZN( acc, Xstart, Fn0, DFn0) Real Function Zeros - Newton method.
    • acc - calculation accuracy(e.g. 0.00000001 or 1e-15 or m0)
    • Xstart - calculation starting point (e.g. 0.1 or m1)
    • Fn0 - function that is evaluated, it can be explicit (e.g. ln(x)) or stored in "expressions" (e.g. F0)
    • DFn0 - derivative of Fn0 (e.g. 1/x) or stored in "expressions" (e.g. F1)

    • appRFZN(m0,m1,F0,F1)
  3. appTRFI( acc, Xmin, Xmax, Fn0, Fn1) intersection of two Real Functions.
    • acc - calculation accuracy(e.g. 0.00000001 or 1e-15 or m0)
    • Xmin - calculation range from (e.g. 0.1 or m1)
    • Xmax - calculation range to (e.g. 7.2 or m2)
    • Fn0 - first function that is evaluated (e.g. ln(x)) or F0)
    • DFn0 - secound function that is evaluated (e.g. cos(x) or F1)

    • appTRFI(1e-15,m1,m2,F0,F1)
  4. appCFZ( acc, XY, Fno) roots of a complex function.
      XY = Xmin, Xmax, Ymin, Ymax
    • acc - calculation accuracy(e.g. 0.00000001 or 1e-10 or m0)
    • Xmin - calculation range from (e.g. -pi or m1)
    • Xmax - calculation range to (e.g. pi or m2)
    • Ymin - calculation range from (e.g. 0 or m3)
    • Ymax - calculation range to (e.g. 2*pi or m4)
    • Fn0 - function that is evaluated (e.g. exp(z)-z^2) or F0)

    • appCFZ(1e-10,-pi,pi,0,2*pi,exp(z)-z^2)