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performances, instructions, examples
(Roberto Bigoni - May 2015)

SuperCalculator, unlike an ordinary calculator, can perform calculations on integer, rational, real and complex numbers with the desired precision.

Calculations on integer and rational numbers, represented by fractions or by repeating decimals, are always exact.

Integers can be input as binary or hexadecimal: in this case the sequence of digits must end with @b (or @B) or @h (or @H). Example: 1011000111011111101@b; 12ABCEF01@H.

Rational numbers can be input as fractions or repeating decimals. In this case the repeated digits must be written between square brackets ([...]). Example: 1.2[34].

The decimal separator in real and rational numbers is the period; commas are not allowed: commas act only as separators between the items of a list.

Real numbers can be input in exponential notation. Example: 1.234e-5.

The constants selector allows you to enter directly into the input field the values of the most common mathematical and physical constants.

Other constants can be stored in memory for further usage.

When calculations generate real numbers, results will be approximated to the number of digit written in the accuracy field (by default 6).

Obviously, if this number is too high, the computing time may become intolerable.

The imaginary unit is written as I or i: Examples 1+I; 2/3-3/2i; 1.2+3.4i; (2+3I)^2; Sqrt[1-I].

It is possible to make some calculations on matrices and on vectors. Vectors can be written as lists and the matrices as lists of lists. Example: Det[{{1,2,3},{0,1/2,-3},{a,b,0}}].

These objects can also be input using the button matrix in the U.I.

Square matrices (if not singular) and vectors can be used together to obtain solutions of a systems of linear equations.

It is possible to define functions of one or more variables, assigning their expression to arbitrary identifiers.

One can get tables and graphs of real functions.

One can describe and draw simple plane geometric figures.

The operators selector allows you to enter directly into the input field the names of the most common mathematical functions and operators.

You can get documentation on the use of an operator by typing the question mark ? followed by the name of the operator or by writing Help followed by a pair of square brackets with the operator's name in quotes.
Examples: ?integral; Help["Integral"].

Input and output

In the input field you can write expressions that must be immediately evaluated. These expressions must be typewritten using the standard operation signs (see below) and, eventually, parentheses. After, click the execute button or push the keys Alt+Enter.

You can also write two or more statements separated by a semicolon (;).
Examples: 100!; 100!!; 100!/100!!
f[x]:=x^2-1; Graph[x,f[x],-2,2]
c=Circ[(0,0),1]; Draw[c].

In the input field you can too declare a function or assign a constant value. In these cases execute does'nt generate an explicit result but only stores the function or the constant.

However, every activation of the execute button writes, in the output field, the expression in the input field and, below, the result of the evaluation. These two lines are numbered so you can get them using the commands In and Out.

To set a new calculation, you can click on the button new input or the pair of keys Alt+End.

You can download and save the sequence of inputs of the current session in a *.txt by clicking the button download input.

You can download and save the sequence of outputs of the current session in a Html page by clicking the button download output.

Since images and tables are generated in separate frames, if you want insert an image or a table in this page, you must explicitly save these outputs by clicking the button save of the frame.

Immediate expressions, declarations of function, assignments of constant can contain the following operation signs:

 

operation signs
sign operation
+ addition
- subtraction
* multiplication(or blank space)
/ real division
^ power
! factorial

 

The following operation signs work only on integer operands.

integer operations signs
sign operation
: integer division
% remainder of integer division
!! double factorial
& and
| or
# xor

 

The following operation signs work on logical operands.

logical operations signs
sign operation
- not
& and
| or
# xor

The priority in the evaluation of an expression is given by parentheses, eventually nested.

 

Expressions may contain the following constants.

(Physical constants have precision limited to their experimental values.)

predefined constants
constant name
PI greek pi
E Euler's number
PHI golden number
I imaginary unit
TRUE boolean true value
FALSE boolean false value
GAMMA Euler-Mascheroni constant
G gravitational constant
PLANCK Planck's constant
C speed of light in vacuum
AVOG Avogadro's constant
R ideal gas constant
BOLTZ Boltzmann constant
ELM electron rest mass
ELC charge of an electron
PRM proton rest mass
PRC charge of a proton
EPS0 vacuum permittivity
MU0 vacuum permeability
RYDB Rydberg constant,
BOHR Bohr Radius
COMPTON Compton wavelength
STEFAN Stefan-Boltzmann constant
SG Standard acceleration of gravity on the Earth's surface
ATM Standard Atmosphere

 

In the input field you can call the following functions that require only one real or complex argument (exceptionally two in powers, radices and logarithms). If the argument is represented by x, it must be real; if the argument is represented by z it can be real or complex. You can obtain tables or graphs only for real function of real variable.

real functions
function name example
Id[z] identity Id[PI]; Id[i]
Int[x] integer part Int[PI]
Frac[x] fractional part Frac[PI]
Abs[z] absolute value Abs[1+i]
Rec[z] reciprocal (multiplicative inverse) Rec[1+i]
Arg[z] argument of a complex Arg[3+4i]
Real[z] real part of a complex Real[3+4i]
Im[z] imaginary part of a complex Im[3+4i]
Sqr[z] square Sqr[PI]; Sqr[1+i]
Cube[z] cube Cube[PI]; Cube[1+i]
Sqrt[z] square root Sqrt[PI]; Sqrt[1+i]
Cubert[z] cube root Cubert[PI]; Cubert[1+i]
Nrt[x,n] n-th root (n natural ≥ 2) Nrt[8,3]
Fact[z] factorial Fact[100]; Fact[PI]; Fact[[1+i]
Sin[z] circular sine Sin[PI/2]; Sin[ArcSin[2]]
Cos[z] circular cosine Cos[PI/4]; Cos[ArcCos[2]]
Tan[z] circular tangent Tan[PI/4]; Tan[1+i]
Sec[z] circular secant Sec[PI/3]; Sec[1+i]
Cosec[z] circular cosecant Cosec[PI/2]; Sec[1+i]
Cotan[z] circular cotangent Cotan[PI/4]; Cotan[1+i]
ArcSin[z] circular arcsine ArcSin[1/2]; ArcSin[1+i]
ArcCos[z] circular arccosine ArcCos[1/2]; ArcCos[1+i]
ArcTan[z] circular arctangent ArcTan[Sqrt[3]]; ArcTan[1+i]
Exp[z] natural exponential Exp[-2]; Exp[i]
Ln[z] natural logarithm Ln[Sqr[E]]; Ln[1+i]
Log[β,z] base β logarithm Log[2,16]; Log[i,Cube[i]]
Sinh[z] hyperbolic sine Sinh[1]; Sinh[1+i]
Cosh[z] hyperbolic cosine Cosh[Ln[2]]; Cosh[1+i]
Tanh[z] hyperbolic tangent Tanh[Ln[2]]; Tanh[1+i]
Sech[z] hyperbolic secant Sech[1]; Sech[1+i]
Cosech[z] hyperbolic cosecant Cosech[1]; Cosech[1+i]
Cotanh[z] hyperbolic cotangent Cotanh[PI/4]; Cotanh[1+i]
ArcSinh[z] hyperbolic arcsine ArcSinh[1]; ArcSinh[1+i]
ArcCosh[z] hyperbolic arccosine ArcCosh[2]; ArcCosh[1+i]
ArcTanh[z] hyperbolic arctangent ArcTanh[1]; ArcTanh[1+i]
Gamma[z] Euler's gamma Gamma[11]==10!; Gamma[1+i]
Zeta[x] Riemann's Zeta Zeta[-2]
EllipticK[x] complete elliptic integral of the first kind EllipticK[1/2]
EllipticE[x] complete elliptic integral of the second kind EllipticE[1/2]
Gauss[x] normalized gaussian (mean 0) Gauss[1]
Erf[x] Error function Erf[1]

These functions can be directly integrated, graphed or tabulated.

Example:

Graph[x,Sin[x],0,2PI]
Graph[x,Erf[x],-2,2,0.1]
Table[x,Sqrt[x],0,4]
List[x,Cosh[x],-1,1,0.1]

You can also call the following functions with real arguments.

Other functions with real argument
function result example
DBinomiale[x,n,k] distribuzione binomiale con probabilità x (0 ≤ x ≤ 1) DBinomiale[0.3,10,4]
EllipticL[e,a] calculate the length of the ellipse with eccentricity 0<e<1 and major semiaxis a EllipticL[1/2,1]
LegendreP[n,x] Legendre function of the first kind LegendreP[2,1.5]; LegendreP[1/2,1.5]
LegendreQ[n,x] Legendre function of the second kind LegendreQ[2,1.5]; LegendreQ[1/2,1.5]
ChebyshevT[n,x] Chebyshev's polynomial of the first kind ChebyshevT[2,1.5]
ChebyshevU[n,x] Chebyshev's polynomial of the second kind ChebyshevU[2,1.5]
Gauss[x,σ] gaussian with standard deviation σ and mean 0 Gauss[1,1/2]
Gauss[x,σ,μ] gaussian with standard deviation σ e mean μ Gauss[2,1,0.5]
If[boolean,then,else] If boolean is true, gives then, else gives else f[x]:= If[x>0,1,-1]

The graphs of these functions cannot be directly produced. To get their graphs, you must declare a function giving it your identifier and writing one or more of the upper names in the second term of the declaration.

Example:

lp2[n]:=LegendreP[n,2]; Table[n,lp2[n],0,10,1]

 

There are also the following operators on real numbers.

real numbers operators
operator result example
F[x] if x is rational shows x as a fraction; otherwise produces the best rational approximation of x with the current precision. F[Sin[PI/6];Sin[PI/6]]
ToContinued[x] gives the sequence of the terms of the expansion of the absolute value of f in continued fraction. ToContinued[79/122]
DegRad[x] from decimal degrees to radians DegRad[60]
RadDeg[x] from radians to decimal degrees RadDeg[PI/3]
DecDms[x] from decimal degrees to degrees-minutes-seconds Dms[RadDeg[1]]
DmsDec[x] from sexagesimal to decimal DmsDec[DecDms[RadDeg[1]]]

 

The following operators act on list of real numbers.

real numbers list operators
operator result example
Mean[vector] arithmetic mean Mean[PI,E,Sqrt[2]]
SSDev[vector] sample standard deviation SSDev[PI,E,Sqrt[2]]
PSDev[vector] population standard deviation PSDev[PI,E,Sqrt[2]]

The list can be represented by a previously declared constant.

Example:

data = 12,14,13,15,11,12,12,14
Mean[data]

 

The following operator act on a rational numbers.

rational numbers operators
operator result example
Num[f] the numerator of the fraction f Num[Bernoulli[10]]
Den[f] the denominator of the fraction f Den[Bernoulli[10]]
N from fraction to decimal or from repeating to decimal N[2/3]; N[1.2[3]]
Egyptian[r] a fraction as sum of distinct unit fractions, said egyptian fractions Egyptian[3/7]
ToContinued[f] gives the sequence of the terms of the expansion of the absolute value of f in continued fraction. ToContinued[79/122]
FromContinued[a0,a1,a2,...an] generates the fraction corresponding to the sequence of the given coefficients. FromContinued[0,1,1,1,5,7]

 

The following operators act on one or more natural numbers.

natural number operators
operator result example
Gcd[list] greatest common divisor Gcd[123456,234567,345678]
Lcm[list] least common multiple Lcm[123,234,345]
PrimeQ[n] true or false if the argument is prime or not PrimeQ[1234567]
PrimeF[n] prime factor decomposition PrimeF[1234567]
Prime[n] n-th prime number Prime[12]
Binomial[n,k] binomial coefficient Binomial[100,37]; Binomial[-1/2,3]
BinomialD[p,n,k] binomial distribution BinomialD[0.3,10,4]
Partition[n] evaluations of the partition functiona of a natural number Partition[100]
Base[n,β] from base 10 to the base given by the second argument Base[1234,16]
Fibonacci[n] Fibonacci's sequence n-th number Fibonacci[1234]
Padovan[n] Padovan's sequence n-th number Padovan[1234]
Perrin[n] Perrin's sequence n-th number Perrin[1234]
Bernoulli[n] Bernoulli's n-th number Bernoulli[13]
Euler[n] Euler's n-th number Euler[14]
Bell[n] Bell's sequence n-th number Bell[12]; Table[n,Bell[n],0,50,1]
DFact[n] double factorial DFact[14]
Collatz[n] Collatz's sequence Collatz[27]
Triples[min,max] Pythagorean triples formed by numbers between min and max Triples[3,300]
Hn[n] harmonic: gives the sum of the reciprocal of the natural numbers from 1 to n Hn[10]-Hn[9]
Stirling2[n,k] Stirling's number of the second kind Stirling2[100,37]

Binomial can compute also pairs of real or complex numbers.

 

The following operators act on one o more previously declared functions. The function identifier or a list of such identifiers must be the first argument. The second and the third argument give the analyzed range.

functions operators
operator result example
Derive[x,f[x],x0] approximate calculation of the derivative of a real function at a point in its domain Derive[x,Sin[x],0]
DeriveL[x,f[x],x0] approximate calculation of the left derivative of a real function at a point in its domain DeriveL[x,Abs[Sin[x]],0]
DeriveR[x,f[x],x0] approximate calculation of the right derivative of a real function at a point in its domain DeriveR[x,Abs[Sin[x]],0]
Integrate[x,f[x],x1,x2] approximate calculation of the integral of a function in an interval of his domain Integrate[x,Sin[x],0,PI/2]
Table[x,f[x],x1,x2] gives the table of a function in the given range Table[x,f[x],0,2PI]
Table[x,f[x],x1,x2,dx] gives the table of a function in the given range with given increment Table[x,Sin[x],0,2PI,PI/6]
List[x,f[x],x1,x2] same as Table but in text mode List[x,Sin[x],0,2PI,PI/6]
Values[x,f[x],x1,x2] gives the set of the values y of a function in the given range Values[x,f[x],0,2PI]
Values[x,f[x],x1,x2,dx] gives the set of the values y of a function in the given range with given increment Values[x,Sin[x],0,2PI,PI/6]
Zeroes[x,f[x],x1,x2] gives the approximations of the zeroes in the given range Zeroes[x,Sin[2x],-5,5]
Analysis[x,f[x],x1,x2] finds the approximations to the most important points of a graph of a function in the given range Analysis[x,f[x],-5,5]

 

The following operators allow to get graphs of real functions of one real variable or some geometric plane figures.

operatori grafici
operator result example
PlotRangeX[x1,x2] sets the lower and the upper bounds of the abscissas of the points of a graph; by default [-10,10] PlotRangeX[-20,20]
PlotRangeY[y1,y2] sets the lower and the upper bounds of the ordinates of the points of a graph; by default [-10,10] PlotRangeY[-20,20]
Graph[x,f[x],x1,x2] draws the graph of a function in a given interval using a fixed number of values of the argument equally spaced Graph[x,Sqr[Sin[x]],0,2PI]
Graph[x,f[x],x1,x2,dx] draws the graph of a function in a given interval with fixed increment of the argument Graph[x,x^2-1,-2,2,0.1]
Graph[x,{f[x],g[x]},x1,x2] draws of the graph of two or more functions in a given interval using a fixed number of values of the argument equally spaced Graph[x,{Sin[x],Cos[x]},0,2PI]
Graph[x,{f[x],g[x]},x1,x2,dx] draws of the graph of two or more functions in a given interval with fixed increment of the argument Grafico[x,{Sin[x],Cos[x]},0,2PI,0.1]
Istogramma[titolo,lista] disegno dell'istogramma con titolo di una lista t={12,13,14,12,10,8};Istogramma["temperature",t]]
Segment defines a segment given the coordinates of its ends s=Segment[(-1,-1),(1,1)]
Circ defines a circle given its center and its radius c=Circ[(0,0),1]
Ellipse defines an ellipse given its eccentricity and its semi-major axis el=Ellipse[(0,0),3,1]
Polygon defines a regular polygon given its centre, its circumscribed radius and its number of sides hepta=Polygon[(0,0),1,7]
Polygonal defines a sequence of consecutive segments given the coordinates of their ends para=List[Sqr,-1,1]; poly= Polygonal[para]; Draw[poly]
Draw draws one or more figures generated by previous operators c=Circ[(0,0),1]; Draw[c]; para=List[Sqr,-1,1]; poly= Polygonal[para]; Draw[{c,poly}]
Translate translates the figures generated by previous operators q=Polygon[(0,0),1,4]; tq=Translate[q,(-1,2)]; Draw[tq]
Rotate rotates the figures generated by previous operators q=Polygon[(0,0),1,4]; rq=Rotate[q,30°]; Draw[rq]

 

The following operators act on one or more numerical vectors.

vectors operators
operator result example
Norm[v] the length of the vector Norm[v]
PolarAngle[v] gets the polar angle of a real two-dimensional vector PolarAngle[{1/2,Sqrt[3]/2}]
UnitVector[v] the unit vector with the same polar angle UnitVector[v]

 

The following operators act on square matrices.

square matrices operators
operator result example
Det[m] square matrix determinant Det[matr]
Transpose[m] evaluation of the transposed matrix Transpose[matr]
Inverse[m] evaluation of the inverse matrix Inverse[matr]
Conjugate[m] evaluation of the conjugate matrix Conjugate[matr]
Adjoint[m] evaluation of the adjoint matrix Adjoint[matr]
LinearSolve[m,v] calculate the solution of a system of linear equations LinearSolve[{{1,2},{0,1}},{3,4}]
EigenValues[m] eigenvalues of a square matrix EigenValues[{{1,2},{2,i}}]
EigenVectors[m] eigenvectors of a square matrix EigenVectors[{{1,2},{2,i}}]

 

Using the standard operation signs one can make additions, multiplications, subtractions, divisions, powers to integer exponent of matrices.

Example.

 

The following operators act on the content of lists.

list operators
operator result example
Append[l,o] given a list identifier l and an item o, puts o at the end of l Append[l,o]
Append[l,l1] given two list identifiers l and l1, appends to l all the items of l1 Append[l,l1]
Insert[l,o,ix] given a list identifier l, the item o and an index ix, inserts o in the position ix of l Insert[l,o,ix]
Insert[l,l1,ix] given two list identifiers l and l1 and an index ix, inserts all the items of l2 in l1 beginning from the position ix Insert[l,l1,ix]
Remove[l,ix] given a list identifier l and an index ix, removes from l the item at the position ix Remove[l,ix]
Remove[l,ix1,ix2] given a list identifier l and two indexes ix1 e ix1, removes from l all the items from the position ix1 to the position ix2 Remove[l,ix1,ix2]
Set[l,o,ix] given a list l, an item o and an index ix, substitutes with o the item at the position ix Set[l,o,ix]
ASort[l] given a list l containing numeric values or strings, sorts l in ascending order ie from the smallest to the largest ASort[1,-4,PI,R,11/3,2e-1,2^5]
DSort[l] given a list l containing numeric values or strings, sorts l in descending order ie from largest to smallest DSort[1,-4,PI,R,11/3,2e-1,2^5]
Frequencies[l] Given a list l containing numeric values, groups the values in ascending order counting how many times they appear in the list. r[x]:=Int[Random[10]]; Frequencies[Values[r,1,100,1]]

 

The following operators generate outputs of financial mathematics.

financial mathematics
operator result example
Percent given a loan and the interest rate, evaluates the interest Percent[100000,4.85]
Payment given the loan amount, the annual interest rate, the term and the number of annual payments, evaluates the amount of the periodic payment Payment[100000,4,10,12]
Interest given the loan amount, the constant periodic payment, the term and the number of annual payments, evaluates the effective annual interest rate Interest[100000,1250,10,12]
Amortization given the loan amount, the annual interest rate, the term and the number of annual constant payments, prints the amortization table Amortization[100000,4,10,12]

 

The following operators rewrite the input strings and the output values for further calculations.

input & output
operator result example
In rewrites the n-th input string In[4]
Out rewrites the n-th output value Out[4]
Clear cancels a previous assignment a=1; Clear["a"]

 

The following operators give calendarial informations.

calendar
operator result example
Today today's date Today
Now the instant time Now
DayOfWeek the day of the week from year, month, day of the month DayOfWeek[1900,1,1]
Easter calculates the Easter date of the given year Easter[2007]

Trigonometry

trigonometry
operator result example
Triangle[a,b,c,α,β,γ] triangle solution Triangle[1,1,0,PI/6,0,0]
DistanceKm[la1,lo1,la2,lo2] distance between two points on the Earth's surface (kilometers) DistanceKm[0°,0°,0°,1']
DistanceNm[la1,lo1,la2,lo2] distance between two points on the Earth's surface (nautical miles) DistanceNm[44°13',0°,44°14',0°]

The operator Triangle allows you to solve a triangle given three of its elements; at least one of them must be a side; angles are input as radians; unknown elements are input as 0.

The last two functions require four arguments expressed by sexagesimal numbers in the following order:

SOUTH latitudes and WEST longitudes require a minus sign.

Distances are calculated as the crow flies along a path on the surface of a theoretical geoid using the Vincenty's method, as applied in a page of Chris Veness.

 

Mathematical expressions

The mathematical expressions must be inputted by typewritten strings, using the keys of a standard keyboard. They can contain numbers given immediately or represented by identifiers of constants, operations signs, built-in functions or user declared functions, parentheses eventually nested and well balanced.

Examples.

 

Grouping marks

The grouping marks are:

 

Storage of a constant value

To store a constant value one must write an arbitrary identifier followed by = and by the value.

Example.

Identifiers are case sensitive.

Identifiers can be reassigned.

 

Declaration of a function

To declare a real function of one or more variables, one must write an arbitrary identifier followed by brackets enclosing one or more variables. The brackets must be followed by := (Pascal like) and by the expression of the function in terms of these variables.

Examples.

Parametric functions can be declared as functions of a single variable expressed by a list of two or more expressions. The list must contain only names of functions

Example.

Declared real functions of one real variable may be analyzed by the following operators.

 

Tables of functions

Real functions of real variable may be tabulated using the operator Table with almost four parameter: the variable, the function, the lower and the upper bounds of the interval. An optional fifth parameter may set the increment of the variable between two successive values. If there isn't a fifth parameter, the increment is calculated by dividing the interval by the value of the field n. of points.

Examples.

Table[x,Sin[x],0,2PI]

Table[x,Sin[x],0,2PI,PI/20]

qsin[x]:=Sin[x]^2; Table[x,qsin[x],-2PI,2PI,PI/20]

Table[x,(x^2-1)/(x^2+1),-4,4]

It is possible to tabulate two or more functions by inserting their names in a list delimited by braces.

Examples.

Table[x,{Sin[x],Cos[x]},0,2PI]

f1[x] := x^2-1; f2[x] := 1-x^2; Table[x,{f1[x],f2[x]},-2,2,0.1]

 

Graphs of functions

Functions can be plotted by using the operator Graph with almost four arguments: the variable, the name of the function, the beginning and the end of the analyzed interval.

Example.

Graph[x,Sin[x],-2PI,2PI]

graph100.gif

You can get in a single plane the graphs of two or more functions, by including their names in a list delimited by curly braces.

Example.

Graph[x,{Sin[x],Cos[x]},-2PI,2PI]

graph101.gif

 

It is possible to get the graph of a function defined by the user.

Example.

sinsq[x]:=Sin[x]^2; Graph[x,sinsq[x],0,2PI]

graph102.gif

It is possible to get the graph of a parametric function of two real variables. For example, after the declaration of the function f[x]:={Cos[x],Sin[x]}, the statement Graph[x,f[x],0,2PI] makes a circle of radius 1.

Examples.

Given the functions f1[x] := Cos[x+PI/4] and f2[x] := Cos[x-PI/4]:

Some other examples.

Graph[x,(x^2-1)/(x^2+1),-4,4]

graph107.gif

Graph[x,{1,(x^2-1)/(x^2+1)},-4,4]

graph108.gif

As you can see in the images of examples, by setting or clearing the check boxes axes, grid and measures, you can change the view, adding or removing the axes, the grid background and the values of abscissas and ordinates.

The red buttons allow you to modify the graph enlarging or reducing it or by moving it leftward, rightward, upward and downward.

The graphs can be dragged within their window. The size of the window can be adapted by dragging its borders.

The save button (the rightmost one of the top row) starts a procedure that allows you to insert the generated graph into an Html page that can be downloaded to your computer.

If you click this button:

In a similar way, you can save the tables produced by the operator Table.

In this case, the save button at the bottom of the table, starts a procedure that allows you to insert the table into an html page that can be downloaded to your computer.

If you click this button:

 

geometric figures

You can draw some plane geometric figures, like segments, polygons, circles, ellipses, arcs of curves, in a Cartesian plane. In order to do this, you must take the following steps:

Examples.

penta=Polygon[(0,0),1,5]; Draw[penta]

graph109.gif

c=Circ[(0,0),1]; sq=Polygon[(0,0),1,4]; Draw[c,sq]

graph110.gif

 

To obtain arcs of curves given by real valued functions, you must take the following steps:

Now this last object can be an argument for the operator Draw.

Example.

lpara=List[x,Sqr[x],-1,1,0.1]; para=Polygonal[lpara]; c=Circ[(0,0),1]; Draw[para,c]

graph111.gif

 

The description of a drawing can be translated or rotated

tri=Polygon[(0,0),1,3]; transl=Translate[tri,(2,1)]; rot=Rotate[tri,45°]; Draw[tri,transl,rot]

graph112.gif

 

Histograms

You can represent two-dimensional histograms using the Histogram operator with argument given by a list of pairs {number, number} or {string, number}. Optionally the list may be preceded by a string with the title.

Example.

b[k] := Binomial[10,k]; Histogram["binomial coefficients",List[k,b[k],0,10,1]]

graph113.gif

tlist=("London",20),("Oslo",15),("Madrid",22);Histogram["temperatures",tlist]

graph114.gif

 


 

last revision: July 2015