How to use GEOMECA and Function of GEOMECA

functions					5	4e
Formula input	Rectangular coordinate system	Cur ve	2D	Positive function y=f(x), x=f(y)	O	O
				Parametric function x=f(u): y=g(u)
				Implicit function f(x,y)=0
			3D	Parametric function x=f(u): y=g(u): z=h(u)
		Cur ved sur face	3D	Positive function z=f(x,y), x=f(y,z), y=f(z,x)
				Parametric function x=f(u,v): y=g(u,v): z=h(u,v)
				Implicit function f(x,y,z)=0
	Polar coordinate system	Cur ve	2D	Positive function r=f(u), u=angle
				Implicit function f(r,u)=0
	Spherical coordinate system	Cur ve	3D	Parametric function r=f(u): c=g(u): p=h(u)
		Cur ved sur face	3D	Positive function r=f(u,v)
				Parametric function r=f(u,v): c=g(u,v): p=h(u,v)
	Cylindrical coordinate system	Cur ve	3D	Parametric function r=f(u): p=g(u): z=h(u)
		Cur ved sur face	3D	Parametric function r=f(u,v): p=g(u,v): z=h(u,v)
Other shapes		Cur ve	2,3D	Using commands - in a dialog box or input window
		sur face, soliId	2,3D	Using commands - in a dialog box or input window
				Range, Scl, Wchr commands		X
Figure tool -		Drawing of basic shapes, functions, quadratic curves, etc. using only the mouse in 2D and 3D coordinate systems				O
		(1, 7) Draw arbitrary lines (curves) - Add and delete lines (curves) 14. Using 'graph, figure information window', 15. Coordinates, section paper; grid, 16. Coordinates, coordinate axes only1, 7) 17.Polar coordinates Half (circle, ellipse), half ellipse, oval (fan, arc)				X
Rotating body - rotation of lines drawn with functions and drawing tools, lines drawn with commands, etc. Creates a rotating body at a specified angle and subdivision around the x, y, z axis and a randomly defined straight line or a straight line passing through two specified points.						O
Transformation - Designate a graph or figure to be drawn by designating it (parallel movement, rotational movement, symmetrical movement, transformation by matrix, orthogonal projection, composite transformation, etc.)
Tracking-Tracking the position value of the graph
Zoom in/out of graph - Zoom in or out of the graph centered on the specified point or flashing point or center of the screen

functions					5	4e
Drawing Screen	Adjustable to size				O	O
	Resize the coordinate system area		2D coordinates system
			2D coordinates system
	Relating to the two-dimensional coordinate system display method		Grid coordinates display
			Show Coordinates Axis Only
			Do not display
			polar coordinates system display
			Arrowhead display: Automatic and options
			Display origin, axis and coordinate values	Direct input
				Automatic and Options
	Relating to the three-dimensional coordinate system display method		Draw Space frame and coordinate axis	2D
				3D
			Space frame (not) visible
			Temporary display of dotted and solid lines in the space frame
			Whether the line is displayed in the middle of the space frame surface
			Draw a line to grasp the spatial location of a point		O	X
			Space frame display method - parallel and perspective projection		O	O
			When the space frame is rotated, view the selected items consecutively (animation)
			Arrowhead, axis display: Automatic
			Display coordinate values	Direct input
				Automatic (and Options)
	Variable range section equalization and shape subdivision adjustment - Adjust for speed, accuracy, and good picture
	Coordinate Axis Actual Distance Ratio Auto Options ; to 1:1
	Specify the area to draw only the area to be drawn in the coordinate range (Square area mouse control)
	Character input - make the background transparent or opaque Modify Character, move, delete, copy, paste, etc.
	2D: Coordinate range including function values - Automatic adjustment					X
	Create SET_Range (current coordinate range)
	Character separation -When drawing and input (to the picture collection screen), when saving (gcm)					O
	Save		As bmp file: drawing screen picture only
			As gcm file: Pictures, contents and pictures are saved as bmp separately As gcd file :drawn graph only
			When saving (gcm, gcg) for a reproducible formula editor's picture (formula) Check whether or not exclusion		O	X
	Edit		Copy, cut (specify area), paste (string, picture)		O	O
			Paste (from formula editor)			X
			Symbols...
			Formula Editor...
			Modify ; move ; unchecked 'RC'	character modification		O
				Select, move
				picture operation		X
				Shape correction: unchecked 'RC'
				Drawing shapes:'RC' without check mark
				Delete: (Selected)
				Copy and paste (selected)
				Paste (related to the above two menus)
			character modification, location shift: [Delete all, restore (recently deleted), string-(copy, delete, paste)]		X	O
			To the very front, To the very back		O	X
			Change: character background
			Make the color you specify transparent
			Show overlapping bottom
			Tie, untie
			Regenerating pictures of the formula editor
			Select All
	View		a Graduated ruler		O	X
			Figure information of 'figure Tools'
			Information on characters and figures drawn when '...RC' is unchecked state
			Information of 'graph and figure' related to coordinates
			Info window of 'graph and figure': To the right
			Where to input the range of coordinates and variables
			Only the drawing screen
			Change function arangement
			Frame rotation button
			Screen zoom
			Function name
			(drawing screen) Paste Picture - as background
			Language used - Korean, English
Formula input(keyboard)
Selection, Move(keyboard)
Setting of start environment
On-screen picture enlargement, reduction, inversion, view picture description				O
Picture operation (OR, XOR, AND, NOT, making the specified color transparent)				X
Drawing method		Curve	Point unit			O	O
			line unit
			face (polygon) unit
	cylinder unit (hidden surface removal)
	rectangle, rectangular parallelepipe unit
	ray trace
	rotation-body(hidden surface removal)
	rotation-body(face unit)
	ray trace - A frame surrounding a point			X
	Curved surface		Point unit				O
			line unit	In two variable directions
				Only in one variable direction
				Implicit function : cross section perpendicular to the x axis
				Implicit function : cross section perpendicular to the y axis
				Implicit function : cross section perpendicular to the z axis
		face (polygon) unit
		hidden surface removal
		rectangular parallelepipe unit
		ray trace
Color of solid surfaces	black, white				O	O
	color in the color dialogue box (With the specified color)
	brightness-color in memory
	illumination-color in memory
	As the color (specified color) in the color dialog box (no face division)
	Transparent (with face division) - frame
Shape of solid surfaces	triangle - The subdivision of the polygon that make up the face into triangles.
	Polygon - Leave the point that forms the face
	Number of vertexes of line(Cylinder type)(3~20), Blocked cylinder type					X
Lighting-Adjust the direction and intensity of light when drawing a 3D solid Also specify the shadow effect and light transparency and refractive and reflectance.					O	O
3D coordinate system direction control (space frame direction control) - Can be drawn in various directions.		Direct input of rotation angle
		Option button for specific direction				X
Correct the restriced area, color, and thickness of the graph you drew						O
Color designation	Graph or shape
	Screen background, coordinate axis, and shape interior Grid coordinates, coordinate scale-specified and automatic options
	Specify character colors separately in 2D and 3D screen.
	the inside of the figure (tool) 2					X
	Line color (automatic adjustment of brightness) - Specified color, color according to brightness, and inverse of color depending on brightness
Line designation	thickness	Graphs or shapes, axes, Space frame		1 ~ 7	O	O
				8 ~ 14
		Grid coordinates, coordinate scale designation and automatic options
	Length	Coordinate scale designation and automatic option
	type	Solid line
		dotted line
To stop in the middle of drawing, tracking, or calculating
Picture Collection Screen	Collection screen paper size adjustment				O	O
	Resize picture box to contain			existing option
				B: 100% input automatic		X
	Create and input and move picture boxes to contain					O
	Modification Mode - Allows you to modify the contents and the picture of the selected picture box by moving it to the drawing screen.
	Group file (gcg) list view : When multiple group files are created or opened, gcg files of the selected list can be viewed View explanation contents of selected picture box
	Copy, delete, and paste picture boxes
	Add page, delete page, move page
	Save: Save together as a gcg file, or only the selected one as a gcm file or Only the expression for the selected one is as a gcd file
	Change picture box name (individual file name)
	Modify (move to formula editor), Modify (move to drawing screen)					X
	Edit	Copy, paste(picture)
		paste(from formula editor)
		Formula editor...
		Select all(current page)
		copy current page(picture)
		(copy)Selected pictures margin.
		To the very front, To the very back
		Change: character background
		Make the color you specify transparent
		Show overlapping bottom
		Tie, untie
		Regenerating pictures of the formula editor
	View	Picture box name
		Picture frame border
		Ruler, grid settings...
		Picture Collection Screen Tools Menu
		Selection, Move (Keyboard)
		Setting start environment
		Language used (Korean, English)
Reexecution	Using the executed expression collection window					O
	information window of Graph and figure related to coordinate system(temporary graph memory display window)
Import the gcm file into the drawing screen or preserve the contents in the graph and figure information window (temporary memory display window) of the drawing screen in the modification mode on the picture collection screen (that is, add on it)					O
View the graph, figure information window (temporary graph display window) related to the coordinate system, or the contents of the window above it in a large window
View information window of figure and character not checked in 'RC' and its contents						X
Print	Drawing screen, Picture collection screen(All, seleted pictures or group, designated page, Specifying the size and number of drawing screen picture				O	O
	Preview, Setting margin... Designation among Background color + content, bitmap, contents; Move Coordinate value to the very front Number of print copies, etc.					X
Coordinate Range and Scale Interval, Arbitrary Direct Entry of Variable Range, and Default Designation						O
Function	Trigonometric function, int, abs, exp, log, ln, sqr, x^y, Pi, atn
	Inverse trigonometric function, hyperbolic function, inverse hyperbolic function, sgn, conj
	Draw function graph in the built-in range by double-clicked function

functions					5	4e
Calculation	Scientific(approximated value)				O	O
	Quotient calculation(True value)
	Parmetric multi-variable function expression calculation
	Single integral			Numerical integral
				Indefinite integral
	Double integral
	Differentiation(Derivative), (High-order differential, Partial differential)
	Differential coefficient, (High-order, Partial)
	Calculation in complex numbers - Complex number operations and functions included
	Unlimited number of digits : prime factorization, nPr, nCr, nHr, n!, Arithmetic operation(+,-,*,/), sqr
Matrix calculation		- Sum, Difference, Product, Scalar product, Inverse matrix, Determinant, Cofactor matrix, Transposed matrix, Echelon, solution of a simultaneous equation, alternating product of row vectors
		Data transformation - Adjust arrangement of matrix A or B, Extract columns of matrix A or B; Change the column position of matrix A or B				X
		Input(keyboard)
		Decomposition- LU, QR, SVD
		Diagonalization of matrix, Schur Decomposition
		Cross product, inner product of two row vectors; (Inner product of A and B), Length of A Distance between A and B
		Characteristic Polinomial of square matrix A
		Eigenvalue, Eigenvector
		Transforming the matrix A - To Hessenberg form, To Bidiagonal form, To Frobenius form
		Root of a characteristic equation(complex numbers range): Root of an equation f(z) = 0
		Matrix A test - Symmetric, Skew-symmetric, Hermitian, skew-Hermitian, Unitary, Normal
		Matrix, vector Norm - Euclidian, Column Norm, Row Norm, Normalization of column vectors
		window arrangement
		Verification display- SVD, Schur decomposition, Diagonalization of A
		Eigenvector decimal place display
		Rational mumber - Decimal display method: Diaplay as decimal, Only for infinite decimal as (improper) fraction, Only for infinite decimal as (proper) fraction, Display as (improper) fraction, Display as (proper) fraction
		Programming - (Matrix calculation, graphic) Basic commands similar to 'software basic language' commands related with matrix and graphicasic
Statistical calculation		File- Open, Save, Print			O	O
		Data	Data (sample) input classification	sample values, name labels designation
				- Distiction picture explanation		X
			Change sample input form
			Input status, sample classification method			O
			()Function transformation Change the position of rows and columns Input row number ()Get inverse matrix (*)matrix Cholesky decomposition: Get P like A = P'P			X
		Check items, run checked items	Check items Group to calculate, Horizontal - Vertical calculation Calculation, Graph, Frequency table Class interval in class-classification Condition for region and color of a graph, characters			O
			Run ckecked items Run the calculation Create frequency table Draw a graph Run Horizontal-Vertical calculationi Stop execution
		AB-Type	1 Variable: Measure of Center - trendency, Measure of variation Estimation, Test 2 Variables: Sample regression line, regression parabola, correlation coefficient, Estimation, Test 3 Variables: Sample regression plane, Quadratic surface. correlation coefficient, Test
		C-Type	Model of regression equation			O
			Regression coefficient Estimation	OLS
				WLS,GLS		X
			Investigation for regression models	Investigate multicollinearity between independent variables. Investigate observations (outlier, influential). Investigate Autocorrelation. Residual data for independency, normality investigation		O
			Estimation, Test Variable Choice( To find best regression eqution etc.)
			Sample regression coefficient Analysis of variance, Error term variance, Coefficient of determination, Mallow's statistic Sample correlation coefficient Regression coefficient, (Co)variance Residual Variance-covariance
		Fre- quency table	Items to include in the frequency table, Table for 1, 2, 3 variables
		Graph	1 Variable	Line diagram, Histogram, Frequency polygon, Cumulative frequency function, Box diagram, Circle graph		O
				Normal probability paper		X
			Function, Curve - Function of povwer of test, OC Curve, probability or density function
			2 Variables - Scatter diagram, Regression line, Regression parabola, Bar graph			O
			3 Variables - Regression plane, Regression quadratic surface, Bar graph
			For C-Type	Scatter diagram, Regression curve, Regression surface, Scatter diagram of residual, Confidence band of mean response, Prediction interval
				Normal probability paper		X
		Others	Distribution table, Test table	Binomial distribution Normal distribution Student's t distribution Chi-square distribution Kolmogorov - Smirnov test F distribution (95%, 99%) Durbin-Watson test Table for nonparmetric methods (A: randomness test, B: Equality test, C: Wilcoxen's Singed-rank test D: Wilcoxen' Rank- sum test, E: Mann-Whitney U-test F: Kruskal-Wallis test, G: Friedman test, H: Spearman rank-order correlation coefficient)
			Calculation of distribution function
			Factor experiments			O
			Comparison of 'means, variance' of two normal distributions Chi-square test Comparison of two regression lines, Comparison of slop of two regression lines Autocorrelation test Nonparametric methods - median sign test, sample randomness test, equivalence test of distribution function, Wilcoxon 1 sample test, 2 sample rank-sum test, Mann-Whitney U test, Kruskal-Wallis test, Friedman Test, Rrank correlation coefficient			X
		Window	Input window, Result window			O
			Table box(result window 2), Backup window			X