SpaceTime Manual

8/6/2019 SpaceTime Manual

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Getting Started

Entering Expressions Graphing Equations Time Graphing

Calculations

Functions Lists Matrices Strings

Plot Functions

Plot Plot3D ListPlot BodePlot ImagePlot

Programming

Scripts Script Functions Numerical Scripts Commands Compiler Include Include Folder

Interface

Button Pad Function Catalog Keyboard Shortcuts Main Menu Options Quick Menu Options Overview

Screenshots Capturing Screenshots Animation Lab


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Entering Expressions

From SpaceTimeWiki

An expression is a group numbers, operators, variables, and functions or a combination of these elements.

Expressions are evaluated by pressing Enter on your keyboard or by pressing the Solve Button on the

button pad.

Simple Expressions

Algebraic Expressions

Derivatives

Integrals


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You can also enter multiple lines in an entry by pressing Shift + Enter to create a new line.

See also

Button pad Keyboard Shortcuts


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Graphing Equations

From SpaceTimeWiki

You can plot equations using many different methods in SpaceTime.

The simplest method is by pressing Ctrl + Enter on your keyboard or by pressing the PlotButton on thebutton pad.

You can also plot expressions using Plot orPlot3D.


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See also

Plot, 2D Graphing, ListPlot, ImagePlot, BodePlot

Plot3D, 3D Graphing

Time Graphing


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Time Graphing

From SpaceTimeWiki

The variable T is used to create time graphs for2D and 3D graphing. The value ofT is incremented every

frame by T-step in the Time Window. This creates an animated graph.

This example graphs two 2D polar time plots.

This example graphs two 3D parametric time plots.

See also


Plot3D, 3D Graphing


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Lists

From SpaceTimeWiki

Lists are created using square or curly brackets and each element in the list is separated by a comma.

Set a variable equal to a list by using the equals sign.

Set a list of variables equal to a list of values. Both lists must be the same length

Access the values of a list using parenthesis. The starting index of a list is one.


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Access multiple values of a list by inputting of list for the indexes. This example returns the first, third,

and fifth element in the list.

Access multiple values of a list by using colon notation. This example returns a list starting at the second

element and ending at the fourth element in the list.

Set a value in a list equal to another value by using the equals sign.

See also

Max(List) , Min(List) , Mean(List) , Variance(List) , StandardDeviation(List)


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Matrices

From SpaceTimeWiki

Matrices are created using square or curly brackets and each element in the matrix is separated by a

comma. This example creates a 2x2 matrix.

Set a variable equal to a matrix by using the equals sign.

Access the values of a matrix using parenthesis. The starting index of matrix values is one. This example

returns the second value from the first row.

Set a value in a matrix equal to another value by using the equals sign.


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See also

Matrix functions


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Strings

From SpaceTimeWiki

SpaceTime can also output strings.

Strings can be concatenated with other strings, values, ... by using the Append(a,b) command Currently, you cannot do any other operation on strings

Examples


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Plot

From SpaceTimeWiki

The Plot function plots 2D functions, parametric, polar, implicit, and contour graphs. This function also

lets you specify your graphing variable, graphing window, and type of 2D graph.

You can also plot graphs by clicking the Plot Button or by pressing Ctrl + Enter. Learn moreabout 2D Graphing.

Plot(equation)

This is the simplest way to use plot. These examples plot a single equation and the type of graph is auto

detected by using the default 2D graphing variables.


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Plot(equation, window, [type])

These examples let you specify your graphing variable, graphing window, and type of 2D graph.

Equation

Description: The parameter is the equation to graph.

Example: sin(x)

Window

Description: This parameter is a list containing the graphing variable name and window values.

Example: [x, -5, 5]

Type

Description: This parameter specifies the type of plot to graph. This will graph 2D functions by default if

no parameter is specified.

Example: function, parametric, polar, implicit, or contour


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Plot(equation1, equation2, ...)

These examples plot a list of equations. The type of graph is auto detected by using the default 2D

graphing variables. You can also input a list of equations using one parameter like this, Plot([equation1,equation2, ...]).


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Plot(index1, index2, ...)

These examples plot a list of plots. This allows you to graph multiple types of 2D plots in the same graph.

The index parameters represent the index numberof each entry in the notebook. These numbers can be

found on the index button on each entry. You can also use a list of numbers, Plot([2,4,12]), instead of

multiple parameters to plot a list of plots.

See also

2D Graphing, ListPlot, ImagePlot, BodePlot

Plot3D, 3D Graphing

Time Graphing


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Plot3D

From SpaceTimeWiki

The Plot3D function plots 3D functions, parametric, spherical, and cylindrical graphs. This function also

lets you specify your graphing variable, graphing window, and type of 3D graph.

You can also plot graphs by clicking the Plot Button or by pressing Ctrl + Enter. Learn more about

3D Graphing.

Plot3D(equation)

This is the simplest way to use plot. These examples plot a single equation and the type of graph is auto

detected by using the default 3D graphing variables.

This example graphs a 3D parametric plot followed by a 3d function plot.


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This example uses multiple line input to graph a more complicated 3D parametric plot.


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Plot3D(equation, window1, window2, [type])

These examples let you specify your graphing variable, graphing window, and type of 3D graph.

Equation

Description: The parameter is the equation to graph.

Example: sin(x)

Window1

Description: This parameter is a list containing the graphing variable name and window values. The last

parameter points is optional.

Example: [x, min, max, (points)]

Window2

Description: This parameter is a list containing the graphing variable name and window values. The last

parameter points is optional.

Example: [y, min, max, (points)]

Type

Description: This parameter specifies the type of plot to graph. This will graph 3D functions by default if

no parameter is specified.Example: function, parametric, spherical, or cylidrical


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Plot3D(equation1, equation2, ...)

These examples plot a list of equations. The type of graph is auto detected by using the default 3D

graphing variables. You can also input a list of equations using one parameter like this, Plot([equation1,

equation2, ...]).

Image:Plot79.png

Plot3D(index1, index2, ...)These examples plot a list of plots. This allows you to graph multiple types of 3D plots in the same graph.

The index parameters represent the index numberof each entry in the notebook. These numbers can be

found on the index button on each entry. You can also use a list of numbers, Plot([2,4,12]), instead of

multiple parameters to plot a list of plots.

See also


3D Graphing

Time Graphing


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ListPlot

From SpaceTimeWiki

The ListPlot function plots 2D scatter plots, histograms, box plots, and normal probability plots.

ListPlot(list)

ListPlot(list, type)

type can be eitherscatter orhistogram


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ListPlot(list1, list2, ...)

list1 = x-values first group list2 = y-values first group list3 = x-values second group list4 = y-values second group ....

(the number oflists should always be a pair number)

See also

Plot, 2D Graphing, ImagePlot, BodePlot

Plot3D, 3D Graphing

Time Graphing


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BodePlot(function,var)

From SpaceTimeWiki

BodePlot(function,variable,minimum,maximum,mode) creates a Bode plot for the given function.

function : is the function to plot variable : is the independant variable minimum : start sweep frequency : min (rad/sec) maximum : end sweep frequency : max (rad/sec) mode = 0 : magnitude plot (= default mode) mode = 1 : phase plot in degrees mode = 2 : phase plot in radians

The x-axis is a logarithmic scale and represents the frequency in rad/sec

x = -2 : => = 0.01 rad/sec x = -1 : => = 0.1 rad/sec x = 0 : => = 1 rad/sec x = 1 : => = 10 rad/sec x = 2 : => = 100 rad/sec x = 3 : => = 1000 rad/sec ...

When the frequency is not given, then min = 0.01 rad/sec and max = 1000 rad/sec.

The y-axis is either the magnitude in dB (mode=0) or the phase in degrees (mode=1) or the phase in

radians (mode=2)

See also

Plot, 2D Graphing, ListPlot, ImagePlot

Plot3D, 3D Graphing

Time Graphing

Examples


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ImagePlot

From SpaceTimeWiki

The ImagePlot function plots an image from a matrix of real values.

ImagePlot(matrix)

This plots a grayscale image. The values in matrix are assumed to be from 0.0 to 1.0 wherezero is blackand one is white.

ImagePlot(r, g, b)

This plots a color image. The values in r, g, and b are assumed to be from 0.0 to 1.0 wherezero is black

and one is red, green, or blue.


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Scripts

From SpaceTimeWiki

Scripts are a series ofCommands, Expressions, Functions, and Script Functions which all together create

a new function.

Creating Scripts

Scripts are created by pressing the index button located next to each entry. The index button is the blue

square numbered button.

Scripts have a Name and a list ofParameters that are used to identify them. Once written, thescript is called as Name(parameter(s))

A parameter has the name and the function of a variable. Parameters are used to pass user input tothe script.

You can specify multiple parameters by separating each variable name by a comma in theParameters field.

Optional parameters should be given as parameter_name=value. When the caller does notsupply parameter, then value is taken per default.

All variables (including the parameters) used within a script are local variables. They are ONLYavailable within the script.

You can use conditional statements orspecial commands within a script. Scripts can return single values, lists, matrices, strings or they can createplots. Scripts are called just like built-in functions in SpaceTime by typing the script name followed by

each parameter separated by a comma between parenthesis.

You can call a script as a single statement or you can assign the result of a script to a globalvariable.


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Another simple script to calculate the area of a rectangular.

Name : Area Parameters : width, depth Script Definition : width * depth Script Return : area Script Calling : Area(value width, value depth)


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This script creates a matrix for use with ImagePlot. Scripts can also return images and graphs when the

output is a plot function.

Name : Static Parameter : size Script Definition : from line 1 to 7 Script Return : ImagePlot Script Calling : Static(value)

See also

Creating Scripts, Script Functions, Commands, Compiler, Include, Include Folder


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Script Functions

From SpaceTimeWiki

If(condition)

Ifcondition evaluates to zero then the block of code is skipped. Ifcondition evaluates to a non-zero value

then the block of code is evaluated.

Following comparison signs can be used :

equal to : == not equal to : != greather than : > greather than or equal to : >= less than :


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Loop(iterations)

This function will loop through and evaluate a block of code the specified number ofiterations.

Note : in above script x++ means x=x+1.

Following functions are available within scripts :

x++ (x=x+1), x-- (x=x-1), x+=n (x=x+n), x-=n (x=x-n), x*=n (x=x*n), x/=n (x=x/n)

Loop(variable, start, end, [step=1])

This function will loop through a block of code using a loop variable. The variable is initialized with the

start value. The loop variable is incremented bystep after each iteration and the loop ends once the loop

variable is greater then end.


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While(condition)

This function will loop through and evaluate a block of code untilcondition evaluates to zero.

Break

This statement will terminate a loop.

Error

This statement stops all further calculations and forces an error message to the user


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Trace(variable)

This function is used for debugging. This function will output every instance when the specified variable's

value was changed.

Include(file)

This function include SpaceTime files or SpaceTime code files into your notebook. This allows you to

call all the scripts that are in the included file.

See also : Include Folder

See also

Append(a,b), Part(expression, index), Strings, Function(function,Parameters), Call(function,Parameters)

for other usefull script commands.


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Numerical Scripts

From SpaceTimeWiki

SpaceTime uses a computer algebra system called MobileCAS for calculations. SpaceTime can store

results symbolically as well as in decimal format. This is different from other programs such as

MATLAB that store all numerical results as a decimal number.

You can reduce these answers to numbers in your scripts in two different ways.

This example uses the numerical command to force all results to reduce to a number. This is thebest method to use in your scripts if you want the entire script to run in a numerical mode.

This example uses the number function to reduce a single result to a number.


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Computer Algebra

numerical

Switches to numerical mode.

symbolic

Switches to symbolic mode.

CompilerFrom SpaceTimeWiki

The compiler can compile scripts into Code files that you can include into SpaceTime using the Include

function or by placing the file in yourInclude Folder.

Include

From SpaceTimeWiki

You can include SpaceTime files and code files into your notebook by using the Include function. Here is

an example.

This notebook is saved as Cube.st.

Include the file into the new notebook and call the script Cube.

See also : Include Folder


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Keyboard Shortcuts

From SpaceTimeWiki

Enter

Enter

Evaluates an entry

Shift + Enter

Creates a new line in the input of the entryCtrl + Enter

This graphs an entry in the notebookCtrl + Shift + Enter

Evaluates all the entries in the notebookSymbols

Special symbols are accessed by holding Crtl + Shift down and then pressing one of following

characters.


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Main Menu

From SpaceTimeWiki

File

New

Creates a new file.

Open

Opens a file.

Save

Saves a file.

Save As...

Saves a file as a new name.

Compile...

Saves all the scripts into a compiled file.

Edit

Undo

Redo

Insert Entry

Inserts a new entry into the notebook.

Delete Entry

Deletes the selected entry from the notebook.

Cut Entry

Cuts the entry from the notebook.

Copy Entry

Copies the selected entry from the notebook.

Paste Entry

Pastes the copied entry into the notebook.

Order Entries

Orders the indexes of the entries starting from 1.

Insert File Name...

Opens a dialog to insert a file name


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View

Options

Opens the Options dialog.

Animation Lab

Opens the Animation Lab.

Include Folder

Opens the Include Folder.

Screenshots Folder

Opens the Screenshots Folder.

Help

Tutorials

Shows the tutorials


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Options

From SpaceTimeWiki

Calculation Mode

Exact : press "enter" on an equation line Decimal : press "enter" again on the same equation line

Number mode

Fractions Decimals


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Numbers

Normal Scientific Engineering

Angles

Radians Degrees

Complex Numbers

Rectangular Polar

note : Polar mode ALWAYS returns the result with argument in radians !


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Precision

0 .. 16

Fraction Limit

1/1000 1E-6 1E-8 1E-10

Others

Always graph in radians Auto Crop Auto Evaluate


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Quick Menu Options

From SpaceTimeWiki

Auto Evaluate

When Auto Evaluate is set ON (green) then all equation lines are re-evaluated at startup. When Auto Evaluate is switched OFF (blank) then no recalculation is done at startup. At any time you can recalculate the whole file by pressing the keyboard shortcut Ctrl + Shift +

Enter.

Debug Mode

Pressing "ESC" during the execution of a script cancels all further operations of that script. This can be

very usefull if the script is running in an endless loop.

(In versions prior to V3.0.0.3 this could be set On/OFF. Since version V3.0.0.3 this is always set to ON

and does not slowdown SpaceTime anymore.)

Auto Crop

When Auto Crop is switched ON, then screenshots are limited to equation and plot lines. When Auto Crop is switched OFF, then a full screenshot (including right panel) is taken.

Options

This button is a fast access to the Options menu.


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Functions

From SpaceTimeWiki

Elementary Functions

Basic functions : Plus(+), Minus(-), Multiply (*),Divide(/) Mod(m,n) sqrt(z) Power (^) nRoot(z,n) Factorial(n) or n! nCr(n,r) nPr(n,r) Binomial(n,r) Multinomial(nList) Pochhammer(n,k) Floor(z) Ceil(z) Sign(z) fPart(x) Round(number, digits)

Complex Functions

Re(z) Im(z) Abs(z) Arg(z) Conj(z)

Logarithmic & Exponential Functions

ln(z) log(z) log(n,z) exp(z) or e^(z)

Trigonometric Functions

TrigExpand(function) TrigReduce(function) TrigCollect(function) TrigConvert(function) ExpConvert(function) TrigSolve(f(z),z)new in revision V3.0.3

Circular Functions

Sin(z), Cos(z), Tan(z)


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Asin(z),Acos(z), Atan(z) Csc(z), Sec(z), Cot(z) Acsc(z), Asec(z), Acot(z)

Hyperbolic Functions

Sinh(z), Cosh(z), Tanh(z) Asinh(z),Acosh(z), Atanh(z) Csch(z), Sech(z), Coth(z) Acsch(z), Asech(z), Acoth(z)

Number Functions

Random(min, max) Bernoulli(n) Euler(n) Catalan(n) Fibonacci(n) Lucas(n) nFactors(n) nPrimes(n) Prime(n,p) IsPrime(n)

Algebra Functions

Expand(function) Together(function) Apart(function) Factor(function) SimplifyPoly(function) Solve(f(z),z)changed in revision V3.0.3 pSolve(f(z),z) nSolve(f(z),z,guess) Eval(f(z),z,val) PolyDivide(f(z),g(z)) Quotient(f(z),g(z)) Remainder(f(z),g(z)) PolyFit(pList,var)

Special Polynomials

Bernoulli(n,z) Euler(n,z) Fibonacci(n,z) Lucas(n,z) ChebyshevT(n,z)


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ChebyshevU(n,z) LegendreP(n,z) LegendreQ(n,z) LaguerreL(n,z) HermiteH(n,z) GegenbauerC(n,a,z)

Calculus Functions

Sum(f(n),n,n1,n2) Product(f(n),n,n1,n2) Limit(f(x),x,x0,-1/0/+1) D(f(x),x) D(f(x),x,n) Diff(f(x),x) fDiff(f(x,y,z,..),(x,y,z,...)) iDiff(f(x,y,z,..),(d_vars),i_var) pDiff(f(x,y,z,..),(f_vars),(f_equ),i_var) Int(f(x),x) Int(f(x),x,a,b) NIntegrate(f(x),x,a,b) Series(f(z),z,n) FourierSin(f(x),x,w) FourierCos(f(x),x,w) FourierSeries(f(x),x,n)

Vector Calculus Functions

dot(A,B) cross(A,B) Norm(A) Gradient(function,varlist) Divergence(vector,varlist) Curl(vector,varlist) Laplacian(function,varlist) Jacobian(function,varlist,point)

Hessian(function,varlist) Duf(function,varlist,point,direction) SurfaceNormal(function,varlist,point)

Graphing Functions

Plot Plot3D ListPlot BodePlot(function,var) ImagePlot


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clip(x,min,max) SquareWave(x,T) TriangleWave(x,T) SawToothWave(x,T) StaircaseWave(x,T) FullRectSineWave(x,T) HalfRectSineWave(x,T)

Special Functions

Gamma(z) Gamma(a,z) = Incomplete Gamma DiGamma(z) or Psi(z) Beta(m,n) Zeta(z) = Riemann Zeta Zeta(z,a) = Hurwitz Zeta Harmonic(z) Si(z), Ci(z)

Ei(z), Li(z) Shi(z), Chi(z) FrenselSin(z) FresnelCos(z) Erf(z) Erfc(z) BesselJ(v,z) BesselY(v,z) BesselI(v,z) BesselK(v,z) KelvinBer(v,z) KelvinBei(v,z) KelvinKer(v,z) KelvinKei(v,z) HankelH1(v,z) HankelH2(v,z) AiryAi(z) AiryBi(z) Gudermannian(z) invGudermannian(z)

Matrices

Identity(n) Inverse(A) Transpose(A) Det(A) RowReduce(A) Eigenvalues(A) QR(A)


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SVD(A) Cholesky(A)

Statistical Functions

Min(List) Max(List) Mean(List) Variance(List) StandardDeviation(List) BinomialPDF, BonomialCDF ChiSquarePDF, ChiSquareCDF GeoPDF, GeoCDF NormalPDF, NormalCDF StudentPDF, StudentCDF PoissonPDF PoissonCDF InverseNormal

Data Functions

Constant Table

Other Functions

Clear(variable) Append(a,b) Part(expression, index) Size(list) Choose(test1, value1, test2, value2, ...) Variables(expression) Call(function,Parameters) Function(function,Parameters)

Documents

SpaceTime Manual