ENG English 97765133542 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 Andrey Ivashov (75.8%), Anonymous (13.5%), tivasyk (10.5%), Other (0.3%) 2014.02.10.03 d54d74e83ab84e518dd54929051f09ed //583 Save changes in Author E-Mail Web-site Date Actions OK Default Menu File Open Save Save as Edit Undo Redo Cut Copy Paste Delete Recalculate page Tool panels Arithmetic Symbols Matrices Functions System Hide all Show all Pages New page Close page Options Calculation Invert Determinant Contents About SMath Studio Help Exit Complex Real Imaginary Auto Decimal places Auto calculation Answer (set) Calculation Results that are multiple values Show all values Show repeated values only once Fractions Decimal Fraction Auto Angle units Radians Degrees Interface Selection color Background color Text highlight color Text color Auto Black White Red Green Blue Yellow Gray Font size Create a page Page Insert Text region Export Interface language View Taskbar Fullscreen Picture Create From file Differentiate Simplify Select all Calculate Function Insert Cancel All Matrix and vector Complex numbers Trigonometric Hyperbolic Function's name Category Translation {0} Functions style Europe World Donate Separator Disable evaluation Enable evaluation Interrupt processing Decimal symbol Arguments separator period comma semicolon Minimize Close New Delete Area Disable Enable Dynamic assistance Please consider making a donation to support the SMath project; we appreciate any amount. Your donation will help us to improve the program in the future. You can choose a donation method: Also, please contact the author of this program with any additional help you can provide: andrey@smath.info.\nThank you for any help and thanks for using SMath Studio. Standard Boolean Rows Columns Insert matrix Insert Matrix Buttons Choose action: Hook of pressing buttons Clear all Release Association completed successfully Action is not chosen! Press the button Integrals: accuracy Solve Roots (range) Reference book Close Home Back Forward Programming Scrollbar thickness Antiflicker Skin Save layout Plot 2D 3D Polar Refresh Grid OK Cancel File name: File type: Save File dialog Save Open File dialog Open Open folder Open Folder dialog Check for updates Tools Updates Check for updates on start Checking for the latest program version. Please wait... New program version available! After download, SMath Studio will exit so you can install the new version. Title Version Size Details Goto web-page Install You are using the latest program version! Can't establish connection to the server. Please check your internet connection and your firewall or try again later. Developer Application components Calculation h. min. sec. build Operator Description Example Show/hide side panel No Files Clear Files list Recent Files Files quantity in History Don't check for updates Check for stable version updates only Check for any updates Print Preview Page Setup Print Zoom Page Language Metadata Keywords Company Title File info Type Size Location Name Summary File attributes Read-only File Properties Available examples Examples Properties Align horizontally Align vertically How to add your example here? Installed Plugins Plugins Plugin handles primitives listed below Start session Join session Domain name / IP adress Session password Login name Default value Session options Host address of server. Unique name to identify you in a chat window. Use an empty value for session without password protection. Session ID: Specify ID of the session you want to join. Create New session ID Join Session #{0} You have joined the room. Border on/off Strings Files Dimension Unit Insert Unit Acceleration Activity Angle Area Capacitance Catalytic activity Charge Conductance Dose Electric current Energy Flow rate Force Force density Force per length Frequency Illuminance Inductance Length Luminous intensity Magnetic field strength Magnetic flux Magnetic flux density Mass Money Permeability Permittivity Potential Power Pressure Resistance Resolution Substance Temperature Time Torque Velocity Viscosity, dynamic Viscosity, kinematic Volume Celsius RĂ©aumur Fahrenheit Degree Radian Acre Meter Mile Kilometer Decimeter Centimeter Millimeter Micrometer Nanometer Picometer Angstrom Bohr Foot Furlong Inch Yard Smoot Barns Hectare Second Year Day Hour Minute Kilosecond Millisecond Microsecond Nanosecond Picosecond Hertz Gigahertz Megahertz Kilohertz Kilogram Megagram Metric ton Ton Gram Milligram Microgram Ounce Pound Liter Milliliter Gallon Newton Teranewton Giganewton Meganewton Kilonewton Millinewton Micronewton Dyne Pascal Gigapascal Megapascal Kilopascal Atmosphere Bar Torr Joule Terajoule Gigajoule Megajoule Kilojoule Millijoule Calorie Kilocalorie Watt Gigawatt Megawatt Kilowatt Milliwatt Microwatt Nanowatt Picowatt Horsepower Water Horsepower Volt Kilovolt Millivolt Microvolt Nanovolt Picovolt Mole Kilomole Millimole Micromole Farad Millifarad Microfarad Nanofarad Picofarad Coulomb Millicoulomb Microcoulomb Nanocoulomb Picocoulomb Ampere Kiloampere Milliampere Microampere Nanoampere Picoampere Henry Millihenry Microhenry Ohm Megohm Kilohm Gray Sievert Lux Candela Lumen Tesla Gauss Speed of light Knot Kilometers per hour Miles per hour Poise Katal Dots per inch Stokes Gravitational acceleration Kelvin Rankine Information Bit Byte Petabyte Terabyte Gigabyte Megabyte Kilobyte Pebibyte Tebibyte Gibibyte Mebibyte Kibibyte Slug Pound-force Pounds-force per square inch Pounds-force per square foot British thermal unit Paper options Landscape Portrait Orientation Size Margins (millimeters) Bottom Top Right Left Header and Footer Header Footer Revolution Kilogram Force Metric Ton Force Ton Force Kip Optimization Quick search Symbolic Numeric None Kilo-pounds-force per square inch Revolutions per minute Radians per minute Kilo-pounds-force per square foot Unit of energy and mechanical work Newtonian constant of gravitation Planck constant Avogadro's number Magnetic constant Elementary charge Electron mass Proton mass Neutron mass Unified atomic mass unit - dalton Gas constant Boltzmann constant Any Complex number Number Imaginary number String Variable Unit Function Expression Symbolic expression Numeric expression Matrix Vector-row Vector File name Condition Increment Action Delimiter Argument Name Date Currency All supported All files Worksheet options Print Area regions Use "=" sign for all definitions and equalities on print out Accept Create password Fill in password to protect Area region Repeat password to verify it Password request Password required to continue Lock Unlock Region protection Grad - gon Snippet Manager Available snippets Snippet Shortcut Insert snippet inside Area Region Press {0} to insert Press {0} to insert inside Area Region Snippet Animate Frame rate Force evaluation before use No variables found to define range Ready Axes Play once Repeat indefinitely No animation Next frame Previous frame Display input data Units language Changes will take effect after program restart Exponential threshold Angular velocity Revolutions per hour Output window Trailing zeros Printing bounds Show description Not for sale or commercial usage Pound-mole Background Preview No background Background image Browse Select image Image size Fit Stretch Fill Original Inherit Page range Current page Print background images Go to definition Loading list of available items. Please wait... No items found. No updates found. Update Download New version of SMath Studio available. Please select item to install it. Run Applications Dependencies Snippets Translations Extensions Manager Local storage Online gallery How to improve translations? Handbooks Interactive books Use by default //124 Finds the derivative of expression {0} relative to variable {1}. X-Y plot. Simplify expression. Natural logarithm. Returns the hyperbolic sine. Returns the hyperbolic cosine. Returns the hyperbolic tangent. Returns the hyperbolic cotangent. Returns the hyperbolic secant. Returns the hyperbolic cosecant. Returns the inverse hyperbolic sine. Returns the inverse hyperbolic cosine. Returns the inverse hyperbolic tangent. Returns the inverse hyperbolic cotangent. Returns 0 if x=0, 1 if x>0, and -1 otherwise. Argument must be a real number. Returns the inverse sine. Returns the inverse cosine. Returns the inverse tangent. Returns the inverse cotangent. Returns the sine. Returns the cosine. Returns the tangent. Returns the cotangent. Returns the secant. Returns the cosecant. Returns the base 10 logarithm of a number. Returns the logarithm of {0} to the specified base {1}. Percent. For example, if {1} is 5 and {0} is 100, then this function returns 5% of 100. Square root. Root. Matrix trace - sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of a square matrix. Absolute value. Matrix determinant. Matrix rank. Inverted value. Matrix transpose. Returns the angle from the real axis to the given complex number. Returns submatrix with the specified row ({1}) and column ({2}) removed from the given matrix ({0}). Minor of matrix. Cofactor (algebraically signed minor) of matrix. Matrix. System of values or equations. Returns the inverse secant. Returns the inverse cosecant. Definite integral of an expression {0} with independent variable {1}. {2}-lower limit, {3}-upper limit. Returns the trigonometric view of algebraic number. Returns the specified row {1} of the matrix/vector {0}. Returns the specified column {1} of the matrix/vector {0}. Returns the specified element {1} of the vector {0}. Returns the number of rows of the matrix/vector. Returns the number of columns of the matrix/vector. Converts the rectangular coordinates of a point in 2D space to polar coordinates. Converts the polar coordinates of a point in 2D space to rectangular coordinates. Summation of an expression {0} in summation variable {1} with lower limit {2} and upper limit {3}. Iterated product. Product of an expression {0} in variable {1} with lower limit {2} and upper limit {3}. Returns the real part of a complex number. Returns the imaginary part of a complex number. Returns the roots of the polynomial whose coefficients are in {0}. Returns the exponential function, e raised to the power {0}. Returns the largest element of vector or matrix. If any value is complex, returns max(Re(...)) + i*max(Im(...)). Returns the smallest element of vector or matrix. If any value is complex, returns min(Re(...)) + i*min(Im(...)). Returns the submatrix consisting of elements in rows {1} through {2} and columns {3} through {4}. Returns a vector of eigenvalues for the given square matrix. Returns the integer part of a real number {0} by removing the fractional part. Rounds the real number {0} to {1} places. Returns the remainder on dividing the {0} by {1}. Arguments must be real. Returns an n x n identity matrix (a matrix of 0's with 1's along the diagonal). {0} must be a positive integer. Returns the number of elements in the matrix or vector. Returns a scalar. Returns {1}-statement if logical {0}-statement is true (non-zero), {2}-statement otherwise. Returns a random number within the range of 0 to {0}. Results are uniformly distributed within the range. Returns real roots of expression {0} with respect to variable {1}. For loop. The function of controlled iterations. The cycle repeats {3}, while {0} satisfies the condition {1} and after each passage necessarily satisfied {2}. Repeating expressions can be set to any number of expressions. Serves for a choice of one of variants of execution of a code from several mutually exclusive. A function for iterating. The loop body, {1} is repeatedly executed as long as the condition {0} is true. Multiple expressions can be included in {1} by means of the line(...) function. For grouping 2 or more lines of code into a block. Returns a zero matrix of the specified size {0}-rows, {1}-columns. Expression limit. Write math expression {0} to a file {1}. If a file with the given {1} exists, it will be overwritten. The function returns '1' if successful, otherwise '0'. Read math expression from file, if such file exists. Often returns symbolic result. Remove file from file system, if such file exists. The function returns '1' if successful, otherwise '0'. Returns a vector (column matrix) of values within the range of {0} to {1}, inclusive. Each value is obtained by adding a step equal to 1 to the previous value, starting with {0}. {1} does not necessarily appear in the output vector. Gamma function. Returns a 2-element vector (2x1 matrix) of the numerator and denominator of {0}. Returns an array formed by placing arguments top to bottom. Arguments are matrices/vectors having the same number of columns, or they are scalars and vectors. (A vector is a column matrix.) Returns a square matrix containing on its diagonal the elements of the given vector (a vector is a column matrix). Returns a matrix formed by placing the arguments left to right. Arguments are matrices/vectors having the same number of rows, or they are scalars and row matrices. Converts the given expression from symbolic to numeric notation. Returns a linearly interpolated y-value at x={2} for data vectors x-vector {0} and y-vector {1} of the same size. (A vector is a column matrix.) Returns a cubic-spline interpolated y-value at x={2} for data vectors x-vector {0} and y-vector {1} of the same size. (A vector is a column matrix.) Returns an Akima-spline interpolated y-value at x={2} for data vectors x-vector {0} and y-vector {1} of the same size. (A vector is a column matrix.) Returns the infinity norm of the matrix. Returns the L1 norm of the matrix. Returns the Euclidean norm of the matrix. Returns a vector with the values sorted in ascending order. (A vector is a column matrix.) Returns a matrix/vector {0} formed by rearranging columns until specified row {1} is in ascending order. Returns a matrix/vector {0} formed by rearranging rows until specified column {1} is in ascending order. Reverses the order of rows in a matrix, or of elements in a vector. (A vector is a column matrix.) Returns math expression formed by converting from specified string. Converts specified math expression to a string. Returns the string formed by concatenating the given strings. Returns a vector (a column matrix) of the start positions of string {1} within string {0}, or -1 if no matches found. Returns a substring of {0}. {1} is a starting character position of substring. Replaces all occurrences of the string {1} within string {0} with the string {2}. Returns the number of characters in specified string. Returns 1 if specified argument is a string. Returns 0 otherwise. Shows standard SMath Studio error tip with text from the function's argument. Returns a matrix of loaded data from specified file using default parsing parameters. Returns a matrix of loaded data from specified file {0}. Function can be used with 1-9 of the arguments specified. Digit 0 (zero) can be used for the arguments (except {0}) to get the built-in default values. Function is able to read data with manually specified Decimal Symbol ({1}), Arguments Separator ({2}) and columns delimiters ({3}). To read a specific region of the data file rows an columns ranges can be requested ({4} - start row, {5} - end row, {6} - start column, {7} - end column). To read a data represented symbolically {8} can be set to 1. Exports a matrix of data to the specified file using default export parameters. Exports a matrix of data to the specified file. Function can be used with 2-10 of the arguments specified. Digit 0 (zero) can be used for the arguments (except 'dataMatrix' and 'fileName') to get the built-in default values. Returns 1 if all variables and functions in the expression are defined, 0 - otherwise. Finds roots for system of nonlinear equations. Returns the values of {1} to make the set of functions {0} equal to zeros. Finds roots for system of nonlinear equations according to specified approaches {2}. Returns the value of {1} to make the set of functions {0} equal to zeros. Returns the Jacobian matrix of the vector function {0}. Returns the element of the matrix {0} in the row {1} and column {2}. Returns real roots of expression {0} with respect to variable {1} in the interval between {2} and {3}. Finds the order {2} derivative of expression {0} relative to variable {1}. For loop. The function of controlled iterations. The cycle repeats {2}, while {0} uses all the values from {1}. Repeating expressions can be set to any number of expressions. Returns a vector (column matrix) of values within the range of {0} to {1}, inclusive. Each value is obtained by adding a difference between {2} and {0}. {1} does not necessarily appear in the output vector. Returns a substring of {0}. Where {1} is a starting character position of substring; {2} is a length of result string. Returns a string containing the value of the arguments with output order and surrounding text specified by first argument. Outputs values in the Output Window. Specifying of the first text argument is optional. Summation of the vector/matrix elements. Retrieves all rows of the {0} where {1} exists in column {2}. Returns 0 if no matches found. Returns Description text of the definition {0} using current language. //96 Fill in all empty elements. Provide an operator. - not defined. Systems not supported. Argument must be scalar. Limits must be integer. Type conversion error. Please contact the developer. Argument of zero is not defined. There is no result. Critical error occurred. If restoration is unsuccessful, you will find emergency preservation of the data in the following folder: Uncertainty. Argument must be a positive integer. Coefficient of rounding should be in the range from 0 to 15 inclusive. The variable of integration is not specified, or specified incorrectly. Limits must be real. No real roots. Inequalities are not supported. Cannot find file: Variable and function names can't start with a number. One or more items on this page cannot be displayed. {0} error(s) occurred while parsing your .xmcd document. This file cannot be fully parsed with this version of the program. Please check for program updates, otherwise send the document to the developers so that it can be supported in the future. Real part of the argument must be greater than zero. {0} error(s) occurred while saving your .xmcd document. The installed version of the program can't fully save the document in the selected format. Please save the document in SMath Studio (*.sm) file format. Array dimensions do not match. Calculation interrupted by user. Argument must be a vector (a column matrix). File {0} was created using later version of {1}: {2}. File {0} requires newer version of plugin {1}: {2} or higher. File {0} requires the following plugin to be installed: {1} (version: {2}; GUID: {3}). A problem occurred while opening file {0}. The result content you will see on the page may be wrong. Do you want to open the file {0} anyway? Error occured while trying to load third-party assembly. Plugin disabled. Plugin {0} requires later version of {1}: {2} or higher. Plugin {0} requires newer version of additional plugin {1} to be installed: {2} or higher. Plugin {0} requires additional plugin to be installed: {1} (version: {2}; GUID: {3}). A problem occurred while loading plugin {0}. Note, unexpected visual and/or calculation errors can appear using this plugin. Do you want to enable plugin {0} anyway? Wrong domain name or IP address specified. Wrong login name specified. Wrong password specified. Wrong Session ID specified. - function is not defined. Result is above max. allowed positive number. Result is below min. allowed negative number. Argument must be a string. Cannot parse string: Function has some invalid arguments. Action could not be performed with text. Result is above max. allowed for byte. File has wrong format. Data import cannot be performed. File is empty. No data imported. Result is above max. allowed when increasing. Result is below min. allowed when decreasing. Increase max. number length ('Menu' >> 'Options' >> 'Calculation' >> 'Max. number length'). Variables should be defined for argument-functions. Number base must be within the range of 1 to 37. Division by zero. Logarithm of zero is not defined. Argument must be a real number. Number of rows and/or columns of matrices or vectors do not match. Number of rows and/or columns of matrices or vectors do not match. Divisor matrix must be square. Cross product can only be calculated for three-component vectors (3 rows x 1 column). Cannot calculate. Matrix must be square. Factorial is defined for real numbers and zero. Matrix is noninvertible (determinant equals zero) Syntax is incorrect. Argument cannot be scalar; must be matrix or vector. Cannot solve. Check program options. Logarithm cannot have 0 as its base. Logarithm cannot have 1 as its base. Can't parse matrix (Matrices within matrices not supported). Units don't match. Cannot insert. Cannot parse Please select an expression or part of an expression. Export error. Operation cannot be performed with units. Argument doesn't match to expected kind. Equation too long to be displayed. Result placed on the clipboard. Highlight variable. Assign variable. File does not exist. Fill in file name. File already exists. Do you want to continue? Requested matrix element doesn't exist. Password cannot be empty. Password entries do not match. Password does not match. Output value must be defined for the called procedure. {0} requires the following plug-in(s) to be installed and enabled. Please ensure dependencies are resolved before continuing. Not all dependencies resolved. Do you want to continue anyway? Press "No" to abort {0} loading. Plug-in(s) installation failed. //133 Contents Identities Exponent properties Properties of arithmetic roots Properties of fractions Proportions Polynomial multiplication and factorization Average values of final array of elements Absolute-value properties Theory of combinations Factorial Double factorial Newton's symbol Basic concepts Progressions Arithmetic progression Geometrical progression Trigonometry General concepts Table of values of trigonometric functions Reduction formulas Signs on trigonometric functions Definitions Functional relations of a single angle Argument addition formulas Argument multiplication formulas Addition of trigonometric functions Multiplication of trigonometric functions Formulas of power reduction Half angle formulas Universal trigonometric substitution Inverse trigonometric functions Relations of angles in a triangle Formulas of oblique-angled triangles Transformation of expressions Logarithms Definition of a logarithm Basic logarithmic identities Properties of logarithms Analytical geometry (R2) Straight line Distances Relations between objects Straight lines of the second order Circle Ellipse Hyperbola Parabola Systems of coordinates Appendices Analytical geometry (R3) Plane Straight line Distances Vector Relations between objects Appendices Matrices Matrix operations Properties of determinants Determinant operations Inverse matrix Derivatives Definition of a derivative Table of derivatives Rules of differentiation Logarithmic derivative Parametric functions Appendices Limits Properties of limits Classical limits Equivalency of infinitely-small values Comparison of infinitely-small values Uncertainty transformation methods Investigation of graphs of functions Differential calculus Basic concepts Integrals Table of integrals Main rules Euler's substitutions Universal trigonometric substitution Method of uncertain coefficients Appendices Complex numbers Definitions Basic properties Values of complex functions arguments Series Definitions Decomposition into power series Indications of series convergence Table of functions expanded into power series Appendices Probability theory Main rules Solution of equations Quadratic equations Cubic equations Power equations of higher orders Trigonometric equations Special cases of trigonometric equations Logarithmic equations Systems of linear algebraic equations Differential equations Solution of inequalities Double inequalities Power inequalities Logarithmic inequalities Trigonometric inequalities Inverse trigonometric inequalities Appendices Mathematical constants Mathematical designations Mathematical functions Greek alphabet Latin alphabet Conversion of degrees to radians Conversion of radians to degrees Sine theorem Cosine theorem Tangent theorem if n-set of Z Converting to another base Notation for base-10 logarithm Notation for natural logarithm Substitution of a variable Integration in parts Newton-Leibniz formula Theorem of average Improper integral //153 Number 'zero' Number 'one' Number 'two' Number 'three' Number 'four' Number 'five' Number 'six' Number 'seven' Number 'eight' Number 'nine' Raise to '0' Raise to '1' Raise to '2' Raise to '3' Raise to '4' Raise to '5' Raise to '6' Raise to '7' Raise to '8' Raise to '9' Raise to '-1' (inverse) Raise to '-2' Raise to '-3'' Raise to '-4' Raise to '-5' Raise to '-6' Raise to '-7' Raise to '-8' Raise to '-9' Operator 'plus/minus' Operator 'minus/plus' Addition Subtraction Multiplication (dot product) Cross product Division Definition Evaluate numerically Evaluate numerically in decimal fractions Evaluate numerically in common fractions Evaluate symbolically Positive infinity Number 'Pi' Imaginary unit Raise to power Backspace Parenthesis Absolute value Square root Nth root Arguments delimiter Decimal point Factorial Boolean 'equal to' Boolean 'less than' Boolean 'greater than' Boolean 'less than or equal to' Boolean 'greater than or equal to' Boolean 'not equal to' Boolean 'not' Boolean 'and' Boolean 'or' Boolean 'exclusive or (xor)' Logarithm Sine Inverse sine Hyperbolic sine Inverse hyperbolic sine Cosine Inverse cosine Hyperbolic cosine Inverse hyperbolic cosine Natural logarithm Tangent Inverse tangent Hyperbolic tangent Inverse hyperbolic tangent Cotangent Inverse cotangent Hyperbolic cotangent Inverse hyperbolic cotangent Base 10 logarithm Secant Hyperbolic secant Cosecant Hyperbolic cosecant Algebraic sign Principal argument System of values or equations Summation Derivative Plot Iterated product Definite integral Remainder on dividing Insert matrix or vector Matrix Square matrix 2x2 Vector 3x1 Vector 1x3 Determinant Matrix transpose Algebraic addition to matrix Minor {0} Matrix rank {0} Matrix trace 2D Plot Rotate Move Scale 3D Plot Graph by points Graph by lines Refresh If statement For loop While loop Add line Left Up Right Down Enter Number 'e' Requires one operand. Requires two operands. Supports both one and two operands. Returns 1 if x equal to y, 0 otherwise. Returns 1 if x not equal to y, 0 otherwise. Returns 1 if either x or y are non-zero (true). Returns 0 otherwise. Returns 1 if either x or y, but not both, are non-zero (true). Returns 0 otherwise. Returns 1 if both x and y are non-zero (true). Returns 0 otherwise. Returns 1 if x less than y, 0 otherwise. Returns 1 if x more than y, 0 otherwise. Returns 1 if x equal to or less than y, 0 otherwise. Returns 1 if x equal to or more than y, 0 otherwise. Returns 1 if x is zero (false). Returns 0 otherwise. Numeric calculation of the equation. Symbolic calculation of the equation. Equal sign for definition. Returns the sum of x and y. Subtracts y from x. Returns the product of x and y. Returns x divided by y. If y=0, returns an error message. Returns x raised to the y-th power. Returns a set of 2 values: the difference and sum of x and y. Returns a set of 2 values: the sum and difference of x and y. Returns the vector cross product of x and y. Product of all positive integers less than or equal to operand. Terminates the execution of the nearest enclosing loop in which it appears. Control passes to the statement that follows the terminated statement, if any. Ends the current iteration of a loop.