Cosa \303\250 Maple Maple (Canada - Universit\303\240 di Waterloo, 1980) \303\250 un Sistema di calcolo simbolico e algebrico, ossia \303\250 un programma interattivo che consente di svolgere calcoli non solo con i numeri ma anche e soprattutto con espressioni simboliche.I simboli possono rappresentare: numeri (interi, razionali, reali, complessi), oggetti matematici ( polinomi, funzioni razionali, sistemi di equazioni), strutture algebriche astratte (gruppi, anelli, algebre) .L'aggettivo "simbolico"indica che il software permette di risolvere problemi matematici esprimendo la risposta sotto forma di formula o trovando un'approssimazione simbolica L'aggettivo "algebrico" indica che il software \303\250 in grado di effettuare calcoli esatti, rispettando le regole algebriche.Inoltre Maple contiene: un grosso numero di soluzioni grafiche per la visualizzazione in 2D e 3D algoritmi numerici per la stima e la risoluzione di problemi in cui non esiste una soluzione esatta un linguaggio di programmazione per la creazione di procedure STRUTTURA DI MAPLE Maple ha una struttura modulare formata da tre parti: 1. Iris (interfaccia grafica ) 2. Kernel (nucleo) 3. Library (libreria esterna) Iris e Kernel costituiscono la parte pi\303\271 piccola del sistema, sono scritti nel linguaggio di programmazione C e si caricano ogni volta che si comincia una sessione di Maple. Iris gestisce: l\342\200\231input di espressioni matematiche (analisi e notificazioni di errori) la visualizzazione di espressioni (\342\200\234prettyprinting\342\200\235) la grafica Il Kernel di Maple: interpreta l\342\200\231input dato dagli utenti esegue le operazioni algebriche di base (aritmetica razionale e aritmetica dei polinomi) contiene alcune procedure algebriche consuete che per una ragione di efficienza, devono essere presenti nel linguaggio del sistema a livello pi\303\271 basso si occupa della gestione dell\342\200\231immagazzinamento di ogni espressione Le conoscenze matematiche di Maple risiedono sotto forma di comandi-funzione nella Library organizzata in packages (pacchetti) contenenti ciascuno procedure e comandi specifici relativi a: algebra lineare, teoria dei numeri, statistica, grafica, ecc.. I packages devono essere aperti all\342\200\231interno del foglio di lavoro di Maple una sola volta e solo nel momento in cui l\342\200\231utente necessita di un determinato comando contenuto in uno di essi, mediante : with(name package) Questa struttura \303\250 importante perch\303\250 Maple usa esclusivamente lo spazio di memoria strettamente necessario.Maple ha due modalit\303\240 di lavoro: modalit\303\240 \342\200\234Document\342\200\235 : ideata per l\342\200\231esecuzione rapida di calcoli , permette di inserire un\342\200\231espressione matematica, valutarla, manipolarla, risolverla o disegnarla in modo rapidissimo (usando semplicemente il tasto destro del mouse)!! modalit\303\240 \342\200\234Worksheet\342\200\235 : ideata per un utilizzo interattivo attraverso comandi e programmazione usando il linguaggio di Maple In ogni documento Maple si possono usare la modalit\303\240 \342\200\234Document\342\200\235 e la modalit\303\240 \342\200\234Worksheet\342\200\235 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Una guida di MapleAlcuni comandi per la Geometria AnaliticaPer lo studio della geometria analitica, i packages principali sono: plots e plottools.Quando si vuole scrivere con Maple un testo, sulla barra degli strumenti deve essere selezionata l'icona Text (da men\303\271 : Insert - Text).Se invece si vuole che Maple elabori quanto scritto, sulla barra degli strumenti deve essere selezionata l'icona Math (clicca sull'icona oppure da men\303\271: Insert - Maple Input).LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=restartQuando si vuole reiniziare una elaborazione in una pagina di Maple non vuota, \303\250 opportuno scrivere il comandorestartIn questo modo durante l'elaborazione non si \303\250 costretti a fare attenzione a come si nominano i luoghi geometrici con cui si vuole lavorare.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=package plotsIl package plots contiene i comandi necessari alla gestione della grafica degli enti della geometria analitica e si carica con LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJnBsb3RzRidGL0YyL0YzUSdub3JtYWxGJ0Y9LUYsNiNRIUYnRj0=il simbolo ":" dopo un comando fa in modo che Maple lo esegua senza modalit\303\240 di visualizzazione. Se invece si scrive con Maple with(plots); ( seguito dal ";") oppure with(plots) , vengono visualizzati i comandi che sono contenuti nel package . In generale si scrive with(name package) e si preme invio. Ad esempio i comandi del package plots:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJnBsb3RzRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkBGPUZAprint(); # input placeholderJSFHI comandi del package plottoolsLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRKnBsb3R0b29sc0YnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZARj1GQA==print(); # input placeholderLa pagina Help per un comando o un package pu\303\262 essere richiamata in qualunque momento con ?name package oppure ?name command. Ad esempio: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiP0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjExMTExMTFlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEtaW1wbGljaXRwbG90RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdGNEYvrestituisce le seguenti informazioni, oltre a degli esempi:
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 Sequenceimplicitplot(expr, x=a..b, y=c(x)..d(x), options)implicitplot(ineq, x=a..b, y=c(x)..d(x), options)implicitplot(f, a..b, c..d, options)implicitplot([expr1,expr2,t], x=a..b, y=c(x)..d(x), options)Parameters
expr-expression or equation depending on x and yineq-inequality depending on x and yf-equation containing procedures or operators representing a function of 2 variablesexpr1,expr2-equations or expressions in x, y and t, polynomial in tx,y,t-variablesa,b,c,d-real constantsc(x),d(x)-expressions that evaluate to real constants for a fixed x valueoptions-(optional) as described in the Options section, or any plot options; see plot/options
DescriptionThe implicitplot command computes the two-dimensional plot of an implicitly defined curve. By default, the curve is computed in Cartesian coordinates.In the first calling sequence, implicitplot(expr, x=a..b, y=c(x)..d(x)), the equation expr must have components that are expressions in the names x and y. The expr parameter can also be an expression instead of an equation, in which case the equation expr = 0 is plotted. The range a..b must evaluate to real constants, and the range c(x)..d(x) must evaluate to real constants for any fixed value of x.In the second calling sequence, implicitplot(ineq, x=a..b, y=c(x)..d(x)), the inequality can depend only upon x and y. If the inequality is strict, the border of the inequality is plotted as a dotted line, while for nonstrict it is plotted as a solid line. There is also a difference in the behavior of the filledregions option (described in the Options section).In the third calling sequence, implicitplot(f, a..b, c..d), the assumption is made that the equation f consists only of procedures or operators taking no more than two arguments. The f parameter can also be a procedure or operator instead of an equation, in which case the equation f = 0 is plotted. Operator notation must be used, that is, the procedure name is given without parameters specified, and the ranges must be given simply in the form a..b and c..d, rather than as equations.In the fourth calling sequence, implicitplot([expr1,expr2,t], x=a..b(x), y=c..d(x)), the expr1 and expr2 must be equations or expressions in the names x,y and t, and must be polynomial with respect to t. This form of call to implicitplot is equivalent to the call implicitplot(resultant(expr1,expr2,t), x=a..b(x), y=c..d(x)), except that the resultant is computed more efficiently avoiding expression growth and excessive round-off error.Because the implicitplot command samples the function being plotted and builds the final image from the sample, it does not, by default, detect discontinuities in the function. Instead, the function is interpolated across the discontinuities. To change this behavior, see the rational and signchange options (described in the Options section).For similar reasons, a sample based method cannot be used to detect isolated points which should be plotted.If expr or f is a set or list (for the first two calling sequences), then its members are plotted together. If it is a list, then particular option values can also be given as lists, with elements corresponding to elements of expr or f. The options that can take lists as values are: color, coords, grid, legend, linestyle, numpoints, style, symbol, symbolsize, thickness, and transparency.OptionsThis section describes options to implicitplot.Any additional arguments are interpreted as options which are specified as equations of the form option = value. Most options available for the plot command can also be used with the implicitplot command. For more information, see plot/options. The options that result in specific behavior when used with implicitplot are described below.The option grid = [m, n] where m and n are positive integers (larger than 1) specifies that the points used initially to plot the 2-D curve lie on an m by n grid of equally spaced points in the ranges a..b and c..d respectively. By default a 26 by 26 grid is used, and thus 676 points are generated. In contrast, the numpoints = k option controls the total number of points, so the grid will have isqrt(k+3)+1 points in each direction.The option gridrefine = l where l is a non-negative integer (default 0) specifies the number of recursive subdivisions to perform on any cells in the initial grid that have been determined to contain part of the curve to be plotted. This allows for a more efficient refinement of the curve, as it only computes function values where necessary. One problem is that for some curves, and some choices of the initial grid, it may not appear as though a cell contains any part of the curve, but implicitplot has some degree of intelligence in this respect, as it uses a quadratic interpolation to detect if some part of the curve may be in a cell before rejecting it. The subdivisions are performed recursively, so if the initial grid is [26,26], setting gridrefine=1 will have the highest grid level as [51,51], setting gridrefine=2 will have the highest grid level as [101,101], etc. The highest grid level for gridrefine=l will be [2^l*m,2^l*n].The option crossingrefine = i where i is a non-negative integer (default 0) provides a facility for improving the interpolation used to determine the location where the curve crosses a cell boundary. Normally a simple linear interpolation is used, but setting crossingrefine to i>0 performs i-1 steps of bisection, and uses a quadratic interpolant to determine the cell boundary crossing. This is most useful for high degree curves where a linear interpolation does not provide a good estimate of the crossing point.The option rational = true/false (default false), when set to true, tells implicitplot to use a rational interpolant to determine the location where the curve crosses a cell boundary. With this option implicitplot is better able to interpolate across a singular curve (for example, this provides a more accurate interpolation for the singular curve of 1/(x^2+y^2-1)). The rational interpolation is more expensive than standard interpolation as it always requires an additional function evaluation for each crossing point.The option signchange = true/false (default true), when set to true, implicitly plots sign changes of the function. This includes, for example, the line y=0 for the input x/y. If this is not desired, and only the zeros of the input function are of interest, then signchange should be set to false. Note that when signchange is set to false, rational is automatically set to true, as it is not generally possible to detect sign changes that are not zeros unless a rational interpolant is used.If the first argument is an expression or a procedure f, the option filledregions = true specifies that the regions defined by f = 0 should be colored. The option coloring = [c1, c2] allows the default colors to be changed, and causes region f < 0 to be given color c1 and region f > 0 to be given color c2. Note that the color of the curve defined by f = 0 now defaults to black, but this can be changed with the color option.If the first argument is an equation, such as f=g, the option filledregions = true specifies that the regions defined by f-g should be colored.If the first argument is an inequality, and filledregions is specified, then only the region that satisfies the inequality will be drawn. Just as for filledregions=false, if the inequality is strict, then the lines for f = 0 will be plotted as dotted lines instead of solid lines.The option resolution = r applies resolution-based smoothing of the output curve to reduce the size of the output data structure, but retain the visual features of the curve up to a resolution of r x r pixels. By default, this value is 0, which means that no smoothing is to be applied. Note that this option cannot be used in combination with filledregions. Specifying resolution = 1000, when used in combination with crossingrefine, can reduce the size of a high detail plot by as much as a factor of 10.The option resultant = fast/stable applies only to the third calling sequence, and specifies the algorithm used to numerically compute the resultant of expr1 and expr2 with respect to t. The default is fast, which uses Euclid's algorithm to compute the numerical resultant for each evaluation. The option stable uses a full Gauss elimination of the Sylvester matrix to compute the resultant for each evaluation. Use of resultant = stable is only really helpful when the input, as polynomials in t, have numerical instability when the resultant is computed using Euclid's algorithm.The option factor = true/false (default false) when set to true tells implicitplot to perform symbolic preprocessing to make the plotting easier, and may be the only way, for simple functions, of plotting the zeros of a function that is greater or equal to zero over the plotting region. Note that this option cannot be used for the resultant form (third calling sequence), operator input (no way to factor) or for inequalities.The option rangeasview = true/false (default false) is simply a convenience option that, when set to true, tells implicitplot to use the specified region (a..b,c..d) as the view option (see view in plot/options). Note that when the vertical range is dependent on x, in the form c(x)..d(x), then the vertical range is ignored for this option.The option outlines = true/false (default false), when set to true, displays the mesh over which the sampling takes place. Note that it is only reasonable to display the mesh when using a fairly coarse grid or a low refinement.The option adaptranges = true/false (default false), when set to true tells implicitplot that if a plot is produced where only a portion of the specified range contains curves, then the plot should be automatically recomputed with smaller ranges, thus providing greater resolution in the output plot. Note that the ranges are determined from the curves produced in the initial plot, so if the initial resolution (as specified by grid and gridrefine) is poor, then parts of the plot may be missed.NotesLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=punti nel piano cartesianoUtilizzando il package plots per avere dei punti del piano cartesiano in formato grafico il comando \303\250 pointplot mentre per richiedere il grafico del punto il comando \303\250 display Ad esempio: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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEoZGlzcGxheUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRIlBGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIjtGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRidGPUZA%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=luoghi geometriciSepre uti\303\262izzando il package plots, volendo gestire un luogo geometrico, ad esempio una retta o una circonferenza, attraverso la relativa equazione, i comandi sono :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(); # input 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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoZGlzcGxheUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRLWdyYWZpY29yZXR0YUYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZARj1GQA==%;Nel comando implicitplot va dunque indicato:l'equazione del luogo, i valori minimo e massimo per le incognite, eventuali opzioni, quali:colore del grafico : color=....stile della linea del grafico: linestyle=.....unit\303\240 di misura sugli assi : scaling=.....LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=intersezioniMaple permette di trovare l'intersezione tra due luoghi geometrici in diversi formati.Nel package plots il comando solve restituisce la soluzione in formato algebrico.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEiP0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjExMTExMTFlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEmc29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRicvJStleGVjdXRhYmxlR0ZMLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJ0Yvsolve - solve one or more equationsCalling Sequencesolve(equations, variables)Parameters
equations-equation or inequality, or set or list of equations or inequalitiesvariables-(optional) name or set or list of names; unknown(s) for which to solve
Basic InformationDescriptionThe solve command solves one or more equations or inequalities for their unknowns.OutputIf the second argument is a name or set of names, then the solutions to a single equation are returned as an expression sequence. If the second argument is a list, then the solutions are returned as a list.If the second argument is a name or set of names, then the solutions to a set or list of equations are returned as sets of equation sequences. If the second argument is a list, then the solutions are returned as a sorted listlist of equations.If the solve command does not find any solutions, then if the second argument is a name or set of names, then the empty sequence (NULL) is returned and if the second argument is a list, then the empty list is returned. This means that there are no solutions, or the solve command cannot find the solutions. In the latter case, a warning is issued and the global variable _SolutionsMayBeLost is set to true.If the output of the solve command is a piecewise-defined expression, then the assuming command can be used to isolate the desired solution(s). If the output is not piecewise-defined, in particular, if the output is constant, assumptions on the independent variables may be ignored. If there are parameters in the input equations, the solve command will use those assumptions in its computations. See examples below.For higher degree polynomial equations, Maple returns implicit solutions in terms of RootOf.Examplessolve( 2*y - (x - 1)^2 = 2, y );solve( x^2 - x = 2025, x );To ignore parameters, specify the variables for which to solve.solve( {(a^2*c^2 - 4*b^2)/b = a^6*b - 4*a^3*b}, {c} );The solve command can solve linear systems.solve( {32*x + 13*y + 42*z = 50, 87*x + 190*y + 112*z = 940, 10*x + 10*y/4 + 10*z = 10}, {x, y, z});The solve command can solve inequations.solve( {x + y < 10, x^2 = 9}, {x, y} );Assumptions on parameters can be used to get more specific solutions. Note also, the form of the output changes when variables are given in a list.solve(x^2=a,[x]) assuming a::negative;solve(b < a*x, [x]) assuming a>1;The explicit solutions to high-degree polynomials can be very large, so Maple may return a solution using RootOf expressions as placeholders.solve(x^4-x^3+1,x);Maple may also use RootOf expressions as placeholders when it cannot find an explicit form for the solution of a non-algebraic equation in one variable.solve( cos(x^2) = 2*cos(x)+x, x );DetailsFor detailed information including:Complete description of all parametersComplete description of functionalityComplete description of outputShortcuts for specifying equations and unknownsControlling the form and number of solutions returnedsee the solve/details help page.See AlsoLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=La sintassi del comando \303\250:solve([equazione1,equazione2],[x,y]);Questo comando per\303\262 non rende visibile il punto :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print(); # input 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%;Se si vuole un formato 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print(); # input 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print(); # input 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print(); # input 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(); # input 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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEoZGlzcGxheUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRJ3B1bnRvUEYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnL0YzUSdub3JtYWxGJ0ZDRj1GQEZD%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=grafico di un segmentoPer avere il grafico di un segmento di estremi dati il comando \303\250 nel package plottools e la sua sintassi \303\250:line([x1,y1],[x2,y2],opzioni):LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==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%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Alcune Procedure per la Geometria AnaliticaUna procedura \303\250 costituita da una sequenza di istruzioni che possono essere eseguite all'interno di una elaborazione Maple semplicemente richiamandone il nome e indicando i valori delle variabili alle quali applicarla.Per scrivere una procedura la sintassi da rispettare \303\250 :nome procedura:=proc(elenco variabili) eventuali opzioni;corpo della procedura, ossia formula o gruppo di istruzioni;end proc:I termini in grassetto sono i nomi riservati ai comandi cui si riferiscono. Vediamo alcuni esempi applicati alla geometria analitica.Rappresentazione grafica della retta passante per due puntiIl comando Maple che restituisce il grafico di un'equazione scritta in forma implicita \303\250:implicitplot(equazione,x=valore min..valore max,y=valore min..valore max,eventuali opzioni per il grafico);Indicati i due punti con A(xa,ya) e B(xb,yb) , sappiamo che l'equazione della retta che passa per A e B si pu\303\262 scrivere nel modo seguente:(y-ya)*(xb-xa) = (x-xa)*(yb-ya)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%;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%;JSFHJSFHRappresentazione grafica dell'asse di un segmentoSapendo che l'asse del segmento di estremi A(xa,ya) e B(xb,yb) \303\250 la retta perpendicolare al segmento AB e passante per il suo punto medio, si pu\303\262 scriverne l'equazione nel modo seguente: (y-(ya+yb)/2)*(yb-ya) = -(x-(xa+xb)/2)*(xb-xa)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(); # input 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%;print(); # input placeholderequivalentemente si pu\303\262 scrivere l'equazione dell'asse del segmento AB ricordando che \303\250 il luogo geometrico dei punti del piano equidistanti da A e da B: (x - xa)^2 + (y - ya)^2 = (x - xb)^2 + (y - yb)^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(); # input 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%;JSFHJSFHEquazione della retta passante per due puntiSe si vuole ottenere l'equazione della retta passante per i punti A(xa,ya) e B(xb,yb), la procedura \303\250: 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%;Per visualizzare l'equazione ottenuta con la procedura :LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVElZXFBQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYrLUkjbW5HRiQ2JFEiMUYnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUY7NiRRIjJGJ0Y+RkAtRjs2JFEiMEYnRj5GQEZmbi8lK2V4ZWN1dGFibGVHRkZGPkY+LUZBNi1RIjtGJ0Y+RkRGR0ZJRktGTUZPRlFGUy9GV1EsMC4yNzc3Nzc4ZW1GJ0ZpbkY+print(); # input 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print(); # input 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print(); # input placeholderComunque \303\250 possibile richiederne il grafico con il comando implicitplot: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%;JSFHJSFHJSFHEquazione dell'asse di un segmentoSe si vuole ottenere l'equazione dell'asse del segmento di estremi A(xa,ya) e B(xb,yb) , la procedura \303\250 la seguente: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 visualizzare l'equazione ottenuta con la procedura :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print(); # input placeholderE' comunque possibile richiederne il grafico con il comando implicitplot: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%;JSFHJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=