MathStudio MathStudio Express

Lists

Lists are an ordered collection of expressions separated by commas and surrounded by a pair of square brackets.

Elements of a list can be accessed by assigning the list to a variable. Lists are 1-indexed meaning the first element starts at index 1.

Lists elements in a variable can be accessed using an integer, range or a list of integers.

Examples


Creating Lists

[1, 2, 3, 4, 5]
1:10
@[10]

Accessing elements in a list

a=[10, 20, 30] a(1)
a=[10, 20, 30] a(1)+a(2)+a(3)

Accessing elements in a list using a range

a=[1, 2, 3, 4, 5, 6, 7, 8, 9] a(2..5)
a=[1, 2, 3, 4, 5, 6, 7, 8, 9] a(1..$ -> 2)

Accessing elements in a list using another list

primes=[2, 3, 5, 7, 11, 13, 17, 19, 23] primes([2, 5])

Accessing elements from the end using the index and size operators

a=[1, 2, 3, 4, 5, 6, 7, 8, 9] a(#$)
a=[1, 2, 3, 4, 5, 6, 7, 8, 9] a(#$ - 1)

Combining lists using the transformation operator

[1, 2, 3, 4] -> [5, 6]

Sublists using the transformation operator

[1, 2, 3, 4, 5, 6, 7, 8, 9] -> 2..5
[1, 2, 3, 4, 5, 6, 7, 8, 9] -> 6..$
[1, 2, 3, 4, 5, 6, 7, 8, 9] -> (1..$ -> 2)

Deleting elements in a list using the index operator

[1, 2, 3, 4, 5, 6, 7, 8, 9] -> #2..5
[1, 2, 3, 4, 5, 6, 7, 8, 9] -> #6..$
Using MathStudio
The Basics
1. Introduction
2. Trigonometric Functions
3. Special Values
4. Lists
5. Matrices
6. Algebra
7. Calculus
8. Fourier Analysis
9. Units
10. Base Conversions
11. Regression Analysis
12. Natural Language
13. Constants
14. Dynamic Variables
Operators
1. Basic Operators
2. Double Power Operator
3. Comparison Operators
4. Logical Operators
5. Compound Assignment Operators
6. Type Comparison Operators
7. Size Operator
8. Range Operator
9. Transformation Operator
10. Index Operator
11. Union Operator
12. Intersection Operator
13. Difference Operator
14. Double Modulo Operator
15. Matrix Operator
16. Matrix Size Operator
17. Angle Operator
18. Choose Operator
19. String Concatenation Operator
20. Conditional Operator
21. Append Operator
22. Element Operator
Graphing
1. 2D Graphing
2. Plot Styles
3. Min, Max and Zero Values
4. 3D Graphing
5. Multiple Plots
6. Color Names
7. Time Graphing
Scripting Language
Variables
1. Creating Variables
2. Unicode Characters
3. Variable Functions
4. Strings
5. Wildcards
Scripts
1. Creating Scripts
2. Semicolons
3. Comments
4. Variable Controls
5. Conditional Statements
6. For-In Loops
7. While Loops
8. Timing
9. Objects
10. Working with JSON
Functions
A
abs(z)
AiryAi(z)
AiryBi(z)
AlternatingSeries(n, [terms])
Angle(A, B)
Animate(variable, start, end, [step], [value], [fps])
Apart(f(x), x)
Append(expression1, expression2)
Arg(z)
B
BarPlot(list1, list2, ...)
Bernoulli(n, [z])
BesselI(v, z)
BesselJ(v, z)
BesselK(v, z)
BesselY(v, z)
Beta(m, n)
Binomial(n, r)
BinomialCDF(n, p, x)
BinomialPDF(n, p, x)
BodePlot(function, variable, minimum, maximum, mode)
BoxPlot(x, [y], [x2], [y2], ...)
Button(name, [list], [value])
C
Call(function, parameter1, parameter2, ...)
Caps(string, index, [mode])
Catalan(n)
Ceil(z)
cFrac(n, [terms])
Char(x)
ChebyshevT(n, z)
ChebyshevU(n, z)
CheckBox(variable, [value])
Chi(z)
ChiSquareCDF(lower, upper, df)
ChiSquarePDF(x, df)
Cholesky(A)
Choose(test1, value1, test2, value2, ...)
Ci(z)
Clear(variable, ...)
clip(x, [min], [max])
Coefficient(f(x), x, degree)
coFactor(matrix, i, j)
Command(setting)
Conj(z)
ContourPlot(expression, ...)
Convergents(n, [mode=0], [terms])
Cross(A, B)
CubicFit([x], y)
CubicFitModel([x], y)
CubicFitPlot([x], y)
Curl(vector, [varlist], [mode])
CylindricalPlot3D(expression, ...)
D
D(f(x), x, [n])
Date(letter)
Dawson(z)
Degree(expression)
DEGtoDMS(angle, [digits])
Delete(expression, position, [length])
Denominator(expression)
Det(A)
Diff(f(x), x)
DiGamma(z)
DiLog(z)
Dirichlet_Eta(z)
Dirichlet_Lambda(z)
Divergence([varlist], vector, [mode])
Divisors(n)
DivisorSigma(n)
Dot(A, B)
DSolve(equation, dependent(independent), values, mode=1)
Duf(function, [varlist], [point], [direction])
dynamic(name, value)
E
Ei(z)
Eigenvalues(A)
Eigenvectors(A)
Else If(condition)
Erf(z)
Erfc(z)
Error(string)
Euler(n, [z])
Eulerian(n, k)
Eval(function, variable, value)
Exp(z)
Expand(expression)
ExpConvert(expression)
ExpFit([x], y)
ExpFitModel([x], y)
ExpFitPlot([x], y)
ExponentialFit([x], y)
ExponentialFitModel([x], y)
ExponentialFitPlot([x], y)
Extract(expression, position, [length])
F
Factor(expression)
Factorial(n)
Fcdf(lower, upperbound, numerator, denominator)
fDiff(f(x,y,z,..), (x,y,z,...))
Fibonacci(n, [z])
Finance(PV, FV, Pmt, i, n, [mode=0])
FindFit(function, variable, [x], y)
FindFitModel(function, variable, [x], y)
FindFitPlot(function, variable, [x], y)
Flatten(matrix)
Floor(z)
FourierCos(f(x), x, w)
FourierExpSeries(f(x), x, n)
FourierSeries(f(x), x, [n], [mode])
FourierSin(f(x), x, w)
FourierTrigSeries(f(x), x, n)
fPart(z)
Fpdf(x, d1, d2)
FractalPlot(expression, ...)
FresnelCos(z)
FresnelSin(z)
FullRectSineWave(x, [T])
Function(function, parameter1, parameter2, ...)
G
Gamma(z)
GCD(n1, n2)
GegenbauerC(n, a, z)
GeoCDF(p, x)
GeoPDF(p, x)
Gradient(function, [varlist], [mode])
Gudermannian(z)
H
HalfRectSineWave(x, [T])
HankelH1(v, z)
HankelH2(v, z)
Harmonic(z)
Heaviside(x)
HermiteH(n, z)
Hessian(function, [varlist], [mode])
HRStoHMS(hours, [digits])
http(url, [filter])
Hypergeom_2F1(a, b, c, z, [mode])
I
Identity(n)
iDiff(f(x,y,z,..), dependant_variables, independant_variables)
If(condition)
iLaplace(F(s), s)
Im(z)
ImagePlot(data)
ImaginaryPart(expression)
ImplicitPlot(expression, ...)
Include(filename)
Insert(expression, item, position)
Integrate(f(x), x, [a], [b])
Inverse(A)
InverseNormal(p, [mu], [sigma])
invGudermannian(z)
iPart(z)
IsList(expression)
IsMatrix(expression)
IsNumber(expression)
IsPoly(expression, variable)
IsPrime(n)
J
Jacobian(function, [varlist], [point])
json(data, [filter])
JuliaPlot(expression, ...)
K
KelvinBei(v, z)
KelvinBer(v, z)
KelvinKei(v, z)
KelvinKer(v, z)
L
LaguerreL(n, z)
LambertW(z)
Laplace(f(t), t)
Laplacian(function, [varlist], [mode])
LCM(n1, n2)
Left(expression)
LegendreP(n, z)
LegendreQ(n, z)
Length(expression)
Li(x)
Limit(function, variable, point, [direction])
LinearFit([x], y)
LinearFitModel([x], y)
LinearFitPlot([x], y)
List(length)
ListMap(list, name, [value])
ListPlot(x, [y], [x2], [y2])
ListPlot3D(x, y, z, [x2], [y2], [z2], ...)
Ln(z)
LnFit([x], y)
LnFitModel([x], y)
LnFitPlot([x], y)
LnGamma(z)
local(name, value)
Log([n], z)
LogisticFit([x], y)
LogisticFitModel([x], y)
LogisticFitPlot([x], y)
Lucas(n, [z])
M
Matrix(rows, [columns])
MatrixLU(matrix, [mode])
MatrixMap(matrix, name, [value])
MatrixQR(A)
MatrixSVD(A)
Max(number, ...)
Mean(list)
MedianFit([x], y)
MedianFitModel([x], y)
MedianFitPlot([x], y)
Message(string)
Min(list)
Mod(m, n)
Multinomial(nList)
MultiPlot(plot1, plot2, ...)
MultiPlot3D(expression, ...)
N
nCr(n, r)
NIntegrate(f(x), x, a, b)
Norm(z)
NormalCDF(lower, upper, [mu], [sigma])
NormalPDF(x, mu, sigma)
nPr(n, r)
nPrimes(n)
nRoot(z, n, [mode])
P
ParametricPlot(expression, ...)
ParametricPlot3D(expression, ...)
Part(expression, n)
pDiff(f(x,y,z,..), dependent_variables, dependent_equations, independent_variables)
Pi_Digits(n)
Plot(expression, ...)
Plot3D(expression, ...)
Pochhammer(n, k)
PoissonCDF(mu, x)
PoissonPDF(mu, x)
PolarPlot(expression, ...)
PolyDivide(f(z), g(z))
PolyFit(pList, var)
PolyGamma(n, z)
PolyGCD(polynomial1, polynomial2)
PolyLCM(polynomial1, polynomial2, [mode=1])
PolyLog(n, z)
PowerExpand(expression)
PowerFit([x], y)
PowerFitModel([x], y)
PowerFitPlot([x], y)
Prime(n)
Primorial(n)
Product(f(n), n, start, end)
Psi(z)
Q
QuadraticFit([x], y)
QuadraticFitModel([x], y)
QuadraticFitPlot([x], y)
QuarticFit([x], y)
QuarticFitModel([x], y)
QuarticFitPlot([x], y)
Quotient(f(x), g(x))
R
Random(min, max, [size1], [size2])
Re(z)
RealPart(expression)
Remainder(f(x), g(x))
Replace(expression, old, new)
Reshape(matrix)
Return(expression)
Reverse(list)
Right(expression)
RK4(function, t, y, a, b, y0, N=10)
RK45(function, t, y, a, b, y0, Tol=10E-5, hmax=0.25, hmin=10E-6, N=20)
Round(number, digits)
RowReduce(A)
S
SawToothWave(x, [T])
Sequence(f(x), x, start, end, [step], [start term], [number of terms])
Series(f(z), z, n)
Shi(z)
Si(z)
Sign(z)
SimplifyFunction(expression)
SimplifyPoly(f(x)/g(x), [variable])
sin(z)
SinFit([x], y)
SinFitModel([x], y)
SinFitPlot([x], y)
Size(list)
Slider(variable, start, end, [step], [initial value])
Solve(f(x), x, [guess])
SolveSystem(equations, [variables], [guesses])
Sort(list)
SphericalPlot3D(expression, ...)
Sqrt(z)
SquareWave(x, [T])
StaircaseWave(x, [T])
StandardDeviation(list)
String(expression1, expression2, ...)
StudentTCDF(x, df)
StudentTPDF(x, df)
Sum(f(n), n, start, end)
SurfaceNormal(function, [varlist], [point])
T
Together(expression)
Trace(variable)
Transpose(A)
TriangleWave(x, [T])
TrigConvert(expression)
TrigExpand(expression)
TrigReduce(expression)
V
Variables(expression)
Variance(list)
VectorPlot(list, ...)
VectorPlot3D(list, ...)
W
While(condition)
Z
Zeta(z, [a])