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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
Plot, 2D Graphing, ListPlot, ImagePlot, BodePlot
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
Plot, 2D Graphing, ListPlot, ImagePlot, BodePlot
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)