Computer algebra system CAS | HP Prime Graphing NW280AAABA guide

60	Computer algebra system (CAS)

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HP Prime Graphing NW280AAABA manual Computer algebra system CAS

Contents

HP Prime Graphing Calculator User Guide Edition1 Part Number NW280-2001 Legal Notices Product Regulatory & Environment Information Edition Printing HistoryJuly Page Contents Plot view Application Library App views Symbolic viewCommon operations in Plot view Zoom Trace Function app 233 Computed statistics Getting started with the Parametric app 271 Getting started with the Polar app 277 Variables Lists Basic integer arithmetic Status messages Preface Manual conventions Function, Polar, Parametric, Ans, etc Getting started Before starting On/off, cancel operations Display Sections of the display Be entered in uppercase when a Uppercase when a key is pressedLowercase when a key is pressed You are working in CAS view, not Navigation Touch gestures Keyboard Context-sensitive menu Entry and edit keys Primary entry and edit keys are Minute, or second symbol accord Comparison operators and BoolEan operators Characters Shift keys Adding text Math keys Math template Math shortcuts Fractions Hexagesimal numbers 236…. Press conce to see 219602 and again to seePressing ca third time will cycle back to Original decimal representation EEX key powers Return home H Enter 4BQ13 s6B23n 3BQ5 Menus To select from a menu Toolbox menus Input formsAlternatively, select the field and tap System-wide settings Home settings Becomes 123.46 Fixed 2 format23E2 in Scientific Becomes 1.23E9 in Engineer Or a+b*i Commands on the Math and CAS Shorthand. The default is to provideMenus are presented descriptively Or in common mathematical YYYY/MM/DD, DD/MM/YYYY, or MM/DD/YYYY Specifying a Home setting Press SH Settings to open Where to start Always one-dimensionalMathematical calculations Choosing an entry type Examples that follow assume that the entry mode is Entering expressionsRPN Reverse Polish Notation. Not available in CAS view Textbook Example Parentheses R23jw14S j8nQ3 h45E Negative numbers Algebraic precedenceE45+Sz Sj85s9 Reusing previous expressions and results Explicit and implied multiplication Large results To reuse the last Using the clipboardResult Sj2E Storing a value in a variableSjS+E Szj AQAcE Szj AaEExample To assign π2 to to the variable a Sharing data Complex numbersR2o3 Ay6E When is tapped HP Prime to another Online Help RPN Reverse Polish Notation Reverse Polish Notation RPNRPN is available in Home view, but not in CAS view History in RPN mode Re-using Sample calculationsResults SzX3 Reverse Polish Notation RPN Swap Manipulating the stackStack Show an item Delete an item Delete all items Computer algebra system CAS CAS view CAS calculations Menu buttons in CAS view are Assigns an object to a variable Settings 2Asj+3Asw2 5Asjw6 Ments Radians or Degrees Standard or Scientific or Engineering Recursive Replacement See also Recursive Evalua Tion above Computer algebra system CAS Computer algebra system CAS Exam Mode Modifying the default configuration Press SH. The Home Settings screen appears TapDon’t want disabled are not selected Press O+ A+ c Creating a new configuration Before, the only base configuration will be Default Exam Activating Exam Mode To activate exam mode Tap If a configuration other than Default Cancelling exam mode Modifying configurationsTo change a configuration Deleting configurations To return to the default configurationTap Exam Mode screen appears Exam Mode An introduction to HP apps Equations Linear SolverSolve Explore equations in one or more real Application Library To delete an app Other options Symbolic view App viewsConfidence level, and select a type Test Symbolic Setup view Plot view Symbolic viewSolve Plot Setup view Numeric view Test selected in Symbolic viewAdvanced View a table of numbers generated by Graphing Symbolic view, and set the zoom factor Numeric Setup viewAdvanced Specify the numbers to be calculated Graphing Quick example Open the app4Szf n2f jE N2f Press SP Set the second θRNG field to 4π by entering Press PPress Pto return to Plot view and see the complete plot Θ column to be 1. You set this up in the Numeric Setup view Common operations in Symbolic viewNumeric View Modify a definition Add a definitionDefinitional building blocks From Home variables Evaluate a dependent definition Select or deselect a definition to exploreF9X=X2+Statistics2Var.PredY6 X2+X+ 2 *X2 Choose a color for plots Delete a definition Symbolic view Summary of menu buttons Common operations in Symbolic Setup view Override system-wide settingsRestore default settings Press SYto open Symbolic Setup view Zoom Common operations in Plot viewZoom factors Zoom options By the X Zoom and Y Zoom settings Zoom settingCenter on Shortcut press w Given the supplied x axis settings. For Graph with the original plot settingsShows a representative piece of the plot Apps, autoscaling rescales both axes Testing a Zoom withSplit-screen Viewing Shown, tap Out Square AutoscaleDecimal Integer Trace Trig To evaluate a definition To turn tracing on or off Configure Plot view Common operations in Plot Setup viewPlot view Summary of menu buttons Parametric Only Polar onlySequence Only Stats 1 Var only Sets the initial range of the x-axis. Note That here are two fields one forPanning and zooming Sets the initial range of the y-axis. Note Graphing methods Restore default settings Common operations in Numeric view Zoom options Zoom keys Zoom menu Evaluating Custom tables Deleting data Start typing a new value Only visible if Numtype is set to Numeric view Summary of menu buttonsSelect Ascending or Descending , Common operations in Numeric Setup view Modifying Numeric Setup Combining Plot and Numeric Views Adding a note to an app Creating an app Fibonacci in this example App functions and variables Asjw5 Tap This opens a menu of app variables Select Statistics 1Var results MeanX Function app Getting started with the Function app Open the Function app Define the expressions Rdw1 jw3EOpen the Function app ISelect Function Set up the plot Plot the functions Trace a graph Change the scale Display Numeric view Set up Numeric view Display the Numeric Setup view SMSetup Press SJClear to reset all the settings to their defaults Explore Numeric viewTo navigate around a table Substituted the values in the X column for x To go directly to a value To access the zoomOptions Analyzing functions Display the Plot view menuTo find a root of the quadratic function =or\ To find an Intersection of twoFunctions Intersection To find the slope of the quadratic function To find the signed area between the two functions Function Variables To findExtremum Quadratic Tap and select Function Select Results and then the variable of interest Named Extremum Summary of FCN operationsSlope Advanced Graphing app Getting started with the Advanced Graphing app Open the app Define the open sentence Jn2+ n5 ISelect Advanced Graphing 128 Advanced Graphing app Advanced Graphing app 129 You can move in any direction within Region. Use this option forInequalities, for example Edge Numeric view Display the Numeric view Explore Numeric view Numeric Setup Trace in Numeric view Sj3n2 Trace EdgeTrace PoI Plot Gallery Exploring a plot from the Plot Gallery Geometry Getting started with the Geometry app Plot Function 3seASsEWith plotfunc on the entry line, enter 3*sinx More Tangent Create a Derivative point Add some calculations AbscissaGB,slopeGC 140 Plot view in detail DerivativePoint D is the point whose ordinate value matches Derivative changes by looking at a plot of it rather than 142 Selecting an ObjectHiding names Moving objects Coloring objects Filling objectsRemoving fill Undoing Clearing an Clearing allObjects Moving about Plot view buttons and keys Key Result in Plot view Symbolic view in detail Re-ordering EntriesHiding an object Tap either To move it down the list or Move it up Can delete an object in Symbolic view Numeric view in detailDeleting an Tap Or press C To delete all objects, press SJ Listing all Enter radiusGC 152 Geometric objects Points More Element 0 . . Notice Line Polygon Ngon Curve Special Circumcircle is the circle That passes through eachTriangle’s three vertices Thus enclosing the triangle Special Locus places Geometric transformations Tap Select Reflection Axis and press E. The object is reflected acrossSymmetry axis defined in step Given scale factor around a given point as center Select Transform Rotation GK,angleGK,GL,GM 164 Geometry functions and commands Symbolic view Cmds menuPoint Barycenter Center DivisionpointElement Inter Isobarycenter MidpointOrthocenter Point Point2d Stop traceErase trace DrawSlp Bisector ExbisectorHalfline Line Medianline ParallelPerpenbisector Medianlinepoint1, point2, point3 Perpendicular SegmentTangent Draws a segment defined by its endpoints Equilateraltriangle HexagonEquilateral triangle0,6 draws an equilateral Equilateral triangle0,6, v draws an equilateral Isoscelestriangle IsopolygonParallelogram IsoscelestriangleGA, GB, angleGC, GA, GB Polygon QuadrilateralRectangle Rhombus Square RighttriangleTriangle Circle CircumcircleConic CircumcircleGA, GB, GC draws the circle Ellipse ExcircleHyperbola Excirclepoint1, point2, point3 Transform IncircleLocus Parabola Inversion ProjectionReflection Draws the orthogonal projection of a point onto a curve Rotation SimilarityTranslation RotateGA, angleGB, GC, GD,GK rotates Measure Plot Numeric view Cmds menu Measure Affix AngleArcLen Area Coordinates DistanceDistance2 Area4-x2/4, x=-4..4 returns 14.666… Equation ExtractmeasureOrdinate Parameq Test RadiusIscollinear Isconcyclic Iselement IsequilateralIsisoceles Isorthogonal Isparallel IsparallelogramIsperpendicular Isrectangle Other Geometry functions IssquareConvexhull Harmonicconjugate Isharmonic IsharmoniccirclebundleIsharmoniclinebundle Isrhombus LineHorz LineVertOpenpolygon Polar Powerpc PoleRadicalaxis Reciprocation Singleinter VectorVertices Verticesabca 194 Getting started with the Spreadsheet app SpreadsheetTo open the Spreadsheet app, press Iand select Spreadsheet 196 Select cell D1 Enter a formula to add up your takings Select cell C3 Enter a label for your total commissionSelect the heading cell for column C, tap and select Select cell C5 Ancostse Enter a label for your fixed costs Basic operations Navigation, selection and gestures Cell naming Cell referencesMethod Enter Cost and tap Entering contentCOST*0.33 and tap Enter Statistics1Var.D1 External functions Select Polynomial Find Roots External references Copy and pasteTo copy one or more cells, select them and press SVCopy Format, both value and format, or both formula and format Referencing variables Using the CAS in spreadsheet calculations = Row2-√Row-1. The only Buttons and keys Handled by the CAS, but only Evaluates itLine is active Changes to Formatting options appear Formatting optionsFont Size Auto or from 10 to 22 point Format Parameters Spreadsheet functions Getting started with the Statistics 1Var app Statistics 1Var appStatistics 1Var Sample data in D1 Symbolic view menu items Menu items you can tap on in Symbolic view areEditing. Tap when done Enters D directly to save you having to press two keys 214 Configure a histogram plot for the data Setup Entering and editing statistical data Edit a data set 1Var app open, return to Home view and enterSpreadsheet.A1A10 D7 E Menu items you can tap on in Numeric view are Delete data Insert data Generating data Sort data values Computed statistics Plotting Plot typesTo plot statistical data Histogram Box-and-Whisker Normal probabilityLine plot Bar graph Setting up the plot Plot Setup view Pareto chartExploring the graph Data in descending Plot view menu items Menu items you can tap on in Plot view are Statistics 2Var app Getting started with the Statistics 2Var appAdvertising minutes Resulting sales $ Dependent, y Statistics 2Var Enter the advertising minutes data in column C1 2E1E3E5E5E4 Statistics 2Var app 225 Setup plot Plot the graph Display the equation Predict values Spreadsheet.A1A10 C7 E Buttons you can tap on in Numeric view are Numeric view menu itemsTap , make your change, and tap Delete data Insert data Sort data values Descending Defining a regression model Fit types Where L is the saturation value Fits the data to a logistic curveFor growth. You can store a Positive real value in L, or-if COV SCOVΣXY Plotting statistical data SerrY Tracing a curve Tracing a scatterTracing order Plot setup Plot view menu itemsPlotting mark Connect Predicting values Home view Troubleshooting a plot Inference app Getting started with the Inference appOpen Inference Symbolic view options Test μ1 μ2, the T-Test on Select the inference method Enter data Test 1 μ from the Type menuSample mean Sample size Population standard deviation Alpha level for the test Display the test results Plot the test results Open the Statistics 1Var app Clear unwanted data Enter data Importing statistics82.5 E 83.1 E 82.6 E 83.7 E 82.4 E 83 E Calculate statistics Open the Inference app Select inference method and type Import the dataTap on the Method field and select Confidence Interval Hypothesis tests DisplayResults Numerically Menu name One-Sample Z-TestInputs Two-Sample Z-Test One-Proportion Z-Test Two-Proportion Z-Test One-Sample T-Test Test Z Test statistic Test Δ pˆ Difference betweenWith the test Z-value This test measures the strength of the evidence for a Test μ1 μ2 Two-Sample T-TestEach sample from a different population, this test Sample 2 standard deviation Sample 1 standard deviationΑ level that you supplied One-Sample Z-Interval Confidence intervalsTwo-Sample Z-Interval One-Proportion Z-Interval Int 1πNumber of successes Sample success count Sample size Confidence level Two-Proportion Z-Interval Menu name Int π1 π2Confidence interval for the difference between Proportions of successes in two populations One-Sample T-Interval Two-Sample T-Interval Result Definition 258 Solve app Getting started with the Solve app One equation Open the Solve appClear the app and define the equation AVjS.AU j+2AAAD Solve the unknown variable Enter known variablesKph over a distance Is approximately 2.4692 m/s2 Where n is the number of the selected equation Plot the equationSelect Auto Scale Select Both sides of En Matches the value of a you calculated above Open the Solve app Define the equations Enter a seed value Several equationsAXj+AYj S.16E AXwAYS. Q1E Limitations Solve the unknown variables Solution information ZeroSign Reversal No values satisfy the selected equation or expression Bad Guesses Constant?Value of the equation is the same at every point sampled Linear Solver app Getting started with the Linear Solver appOpen the Linear Solver app. ISelect Linear Solver Define and solve the equations Coefficients and constants had been entered Menu items Solve a two-by- two system 270 Parametric app Getting started with the Parametric appOpen the Parametric app Parametric Define the functions 8ed? 8fd? Set the angle measure Set up the plot Plot the functions Degrees 274 Tap .The table scrolls to the value you entered 276 Open the Polar app ISelect Polar App opens in Symbolic view Polar appGetting started with the Polar app Open the Polar app 5Szf dn2 fdj Set angle measure Set up the plotDefine the expression 5πcosθ/2cosθ2 Plot the expression Explore the graph 280 Polar app Sequence app Getting started with the Sequence app App opens in Symbolic view Define the Fibonacci sequence + EOpen the Sequence app ISelect Sequence Plot the sequence Select Stairstep from the Seq Plot menu Display Numeric view Explore the table of values Set up the table of values Define the expression Setup the plotAnother example Explicitly-defined sequences RQFand Plot the sequence Explore the table of sequence values Finance app Getting Started with the Finance app 288 Cash flow diagrams Time value of money TVM TVM calculations Another example PMT 292 Calculating amortizations To calculate amortizations Amortization graph Finance app 295 Triangle Solver app Getting started with the Triangle Solver appTapping Open the Triangle Solver app ISelect Specify the known values Choosing triangle types Solve for the unknown values Special cases Triangle Solver app 299 Explorer apps Linear Explorer app Graph mode Between them by tapping or Equation mode Tap to enter Test mode Quadratic Explorer app Open the appQuadratic Explorer Equation mode Its value. When you are ready, tap To see if youTap To see the correct answer and tap Exit Test mode Graphs that are harder match by tapping Respectively Trig Explorer app Trig Explorer Tap To switch to Graph by pressingCursor keys. All four keys Are available. Tap to see the correct answer and tap to exit Test mode Now press the cursor keys to select each parameter Functions and commands All the functions and commands 308 Abbreviations used in this chapter Keyboard functionsNORMALICDFμ,σ,p +,w,s, n ShexE5 returns ALOG3 returns Efg +2*i returns -1-2*i 1returns2returns Math menu Numbers Example XPON123456 returns 5 since 105.0915... equals ArithmeticMaximum Maximum. The greater of two values Modulus Modulo. The remainder of value1/value2 Example ARG3+3*i returns 45 degrees modePercentage x percent of y that is, x/100*y Example Trigonometry Hyperbolic Probability PERM5,2returns Normal Random real number with normal distribution Nμ,σ RANDSEEDvalue NORMALDμ,σ,xNORMALD0.5 and NORMALD0,1,0.5 both return STUDENTn,x Is a real number CHISQUARECDFn,k CHISQUARECDF2,6.1 returnsFISHERCDFn,d,x FISHERCDF5,5,2 returns List Matrix Special CAS menu Algebra Syntax substExpr,Var=value PartfracRatFrac or OptNumera,b Denoma/b DiffExpr,var DiffExpr,var1$k1,var2$k2 CalculusLimitExpr,Var,Val,Dir1, 0 SeriesExpr,Equalvar=limitpoint,Orde r,Dir1,0,-1 SumExpr,Var,Real1, Real2,StepCurlExpr1, Expr2, …, ExprN, Var1, Var2, …, VarN DivergenceExpr1, Expr2, …, ExprN, Var1, Var2, …, VarN GradExpr,LstVar Hessian Returns the Hessian matrix of an expressionHessianExpr,LstVar IbpufVar, uVar, Var, Real1, Real2 PrevalExprFvar,Reala,Realb,Var SumriemannExprXpr,Lstvar1,var2TaylorExpr,Var=Value,Order DivpcPoly1,Poly2,Integer Solve ZerosExpr,Var or zerosExpr1, Expr2,…,Var1, Var2,… Zerosx2-4 returns -2CsolveEq,Var CsolveEq1, Eq2,…, Var CZerosExpr,Var CZerosExpr1, Expr2,…,Var1, Var2,… Rewrite TexpandExpr Exp2powExprPow2expExpr Exp2trigExpr Asin2atanExpr Sin2costanExprAcos2asinExpr Acos2atanExpr Atan2asinExpr Atan2asinatan2*x returnsAtan2acosExpr Tan2sincosExpr TrigcosExpr TrigtanExprAtrig2lnExpr TlinExprTrig Integer GcdIntgr1, Intgr2,… IsPrimeIntegerNextprimeInteger PrevprimeInteger Polynomial IquoIntgr1, Intgr2IremIntgr1, Intgr2 Powmoda, n, p,Expr,Var CoeffPoly, Var, Integer DivisPoly or divisPoly1, Poly2,…FactorsPoly or factorsPoly1, Poly2,… GcdPoly1,Poly2 Poly2symbVector, Var Symb2polyExpr,Var Symb2polyExpr, Var1, Var2,…PcoefVect QuoList1, List2, Var QuoPoly1, Poly2, Var PminMtrx,VarRemList1, List2, Var RemPoly1, Poly2, Var ContentPoly,Var DegreePolyFactorxnPoly SturmabPoly,Var,a,b CyclotomicInteger GbasisPoly1 Poly2…, Var1 Var2…GreducePoly1, Poly2 Poly3 …, Var1 Var2… HermiteInteger LagrangeX1 X2…, Y1 Y2… LaguerreIntegerTchebyshev1Integer Tchebyshev2Integer Plot PlotodeExpr, Var1, Var2, X0, Y0 App menuPlotlistX1, Y1, X2, Y2, … Function app functions Solve app functions Spreadsheet app functionsSOLVEEn,var,guess SOLVEX2-X-2,X,3returns2 FunctionNameinput,optional Parameters =STAT1A25A37=STAT1A25A37,h n As in SUMB7C23 Calculates the arithmetic mean of a range of numbers For example, AVERAGEB7B23 returns the arithmeticSpecify a block of cells, as in AVERAGB7C23 Finance app Second column is treated as the weight of the first Columns are multiplied to generate a data pointSet to Place column headers Place row headers Serr STAT1A25A37 REGRSInput range,model, configurationSTAT1A25A37,h n x σ Example REGRSA25B37,2 PredY PredXPredYmode, x, parameters PredXmode, y, parameters HypZ1mean The one-sample Z-test for a mean HypZ1mean x, n,μ0,σ,α,mode, configurationHypZ1mean0.461368, 50, 0.5, 0.2887, 0.05 HypZ2mean0.461368, 0.522851, 50, 50, 0.2887, 0.2887, 0.05 HypZ1propHypZ1propx,n,π0,α,mode HypZ2prop HypZ1prop21, 50, 0.5, 0.05,1 Mode Specifies which alternative hypothesis to use ≠ μ0 HypT1mean x ,s,n,μ0, α,mode,configurationHypT1mean The one-sample t-test for a mean HypZ2prop21, 26, 50, 50, 0.05 HypT2meanx1,x2,s1,s2, n1,n2, α,pooled,mode, configuration ConfZ1mean x ,n,s, C,configuration ConfZ2mean x1, x2, n1, n2,s1,s2,C, configuration ConfZ1propx,n,C,configurationConfZ1mean0.461368, 50, 0.2887 ConfZ2mean0.461368, 0.522851, 50, 50, 0.2887, 0.2887 ConfT1mean ConfZ2propConfZ1prop21, 50 ConfT2mean x1, x2, s1,s2,n1, n2,C,pooled, configuration Statistics 1Var app functionsConfT1mean0.461368, 0.2776, 50 ConfT2mean0.461368, 0.522851, 0.2776, 0.2943, 50, 50, 0 SetFreq Do1VStatsSetSample Statistics 2Var app functions ResidDo2VStats SetDepend Inference app functions SetIndepDoInference HypZ1mean Critical value of π associated with the critical Z-value Test π valueHypZ2mean x1, x2, n1, n2,σ1,σ2,α,mode HypT1mean OrderTest Δπ value Critical value of the statistic associated with HypT2meanx1,x2,s1,s2, n1,n2, α,pooled,mode ConfZ2mean ConfZ1meanConfZ1prop Two proportions. Returns a list containing in order Finance app functions CalcFVSolves for the future value of an investment or loan CalcFVNbPmt,IPYR,PV,PMTV,PPYR,CPYR,BEG CalcIPYR CalcNbPmtCalcPMT CalcPV Linear Solver app functions Triangle Solver app functionsSolve2x2 Solve3x3 AASangle,angle,side ASAangle,side,angleSASside,angle,side SSAside,side,angle DoSolve Linear Explorer functionsSolveForYIntercept Quadratic Explorer functions Common app functionsSOLVEa, b, c DELTAa, b, c Ctlg menu Function.CHECK1UNCHECKDigit Enter Sequence.UNCHECK2 Percent of y. Returns x/100*y Example Change Percent change from x to y. Returns 100*y-x/x List1.*List2 or Matrix1.*Matrix2 List.Integer or Matrix.IntegerVar=expression 3,4.*3,4,5,6 gives 3,8,15,24 A2qMatrix, Var1, Var2… A2q1,2,4,4,x,y returns x2+6*x*y+4*y2AbcuvPolyA, PolyB, PolyC, Var Abcuvx2+2*x+1,x2-1,x+1 returns 1/2 -1/2 Append Appends an element to a list or vector BasisMatrix CanonicalformQuadraticExpr,VarCanonicalform2*x2-12*x+1 gives 2*x-32-17 CatObject1, Object2,… ColDim Returns the number of columns of a matrix Companion Returns the companion matrix of a polynomial Complexrootx3+8, 0.01 returns ContainsList, Element or containsVector, Element Contains0,1,2,3,2 returnsCopyVarVar1,Var2 CorrelationList or correlationMatrix Returns Enters the mathematical constant e Euler’s number Eigenvals Returns the sequence of eigenvalues of a matrix Eval Evaluates an expression EvalcExpr EvalfExpr,IntegerEvalf2/3 gives Even1251 returns Expr Parses the string String into a number or expression ExprX+10 returns 100, if the variable X has the value FMaxExpr,Var FMax-x2+2*x+1,x givesFMinExpr,Var FMinx2-2*x+1,x gives FsolveExpr,Var,Guess or Interval,Method FunctiondiffFncFunctiondiffsin gives x→cosx GaussExpr,VectVar GramschmidtVector, Function Halftanhyp2expExprTrigHalftanhyp2expsinx+sinhx returns HamdistInteger1, Integer2 IcontentPoly,Var Icontent24x3+6x2-12x+18 givesHead1,2,3 gives HeavisideReal Interval2center Returns the center of an interval Inv Returns the inverse of an expression or matrix JacobisymbolInteger1, Integer2 Jacobisymbol132,5 givesIPartReal or iPartList IPart4.3 returns Lin Returns an expression with the exponentials linearized Lname Returns a list of the variables in an expression Logb Returns the logarithm of base b of a Lvar Returns a list of variables used in an expression Mat2list Returns a list containing the elements of a matrix MeanList1, List2 or meanMatrix Mean1,2,3,1,2,3 gives 7/3MedianList1, List2 or medianMatrix Median1,2,3,5,10,4 gives ModgcdPoly1,Poly2 Modgcdx4-1,x-12 givesMRowExpr, Matrix, Integer MultcconjugateExpr NDerivfx,x,h returns fx+h-fx-h*0.5/h NormalExprNormal2*x*2 gives 4*x NormalizeVector or normalizeComplex PI Inserts π PIECEWISE⎪ PlotparamfVar+i*gVar, Var= Interval Plotparamcost+i*sint, t=0..2*π plots the unit circlePlotpolarExpr,Var=Interval Plotpolarπ/2x, x=-π..π plots a partial spiral PoleCrcle,Line Polecircle0, 1, line1+i, 2 returns point1/2,1/2POLYCOEFVector or POLYCOEFList POLYCOEF-1, 1 returns 1, 0 PolygonscatterplotMatrix PolynomialregressionList1, List2, IntegerPolynomialregression1, 2, 3, 4, 1, 4, 9, 16,3 returns 0 1 0 POLYROOTPoly or POLYROOTVector PowerregressionList1, List2 Powerregression1, 2, 3, 4, 1, 4, 9, 16 returns 2Powerpccircle0,1+i,3+i gives Prepend1,2,3 gives 3,1,2 Purge Unassigns a variable name Quote Returns an expression unevaluated ⎠ returns Reducedconicx2+2*x-2*y+1 returns RefMatrixRemoveElement, Vector or removeElement, List Remove6,1 2 6 7 returns 1 2 Residue Returns the residue of an expression at a value Restart Purges all the variables RowDim Returns the number of rows of a matrix Example Gives Signature Returns the signature of a permutation Sqrt Returns the square root of an expression Sto Stores a real or string in a variable Sylvester Returns the Sylvester matrix of two polynomials Transpose Returns a matrix transposed without conjugation Type Returns the type of an expression e.g. list, string When Used to introduce a conditional statement Returns the square of an expression Inserts the imaginary number Creating your own functionsExpr Function field, enter the function. eAA+fABAC Variables AaE Working with Home variablesResult is written to history Multiply a by AAxotwAS. Sq1o2 o3 E Working with user variables Working with app variablesExample 3 You can also store objects in variables More about the Vars menu Qualifying variables Home variables are accessed by pressing aand Tapping Home variables App variables Function app variablesNumStart NumType NumStep NumZoom NumIndep AAngle ADigits AComplex AFormat Geometry app variables Results variables Category Names Symbolic Plot Spreadsheet app variablesSolve app variables ColWidth RowHeight NumXStart Advanced Graphing app variablesNumYStart NumType NumXStep NumXZoom NumYStep NumYZoom Statistics 1Var app variables NbItem MinValMedVal MaxVal Statistics 2Var app variables Corr CoefDetSCov ΣCov SerrY Inference app variablesContains the sum of the dependent values Y CritScore CritVal1CritVal2 Prob Parametric app variables NumStart NumType NumStep NumZoom Polar app variables Finance app variablesΘmin Recenter NumIndep NumType NumStart NumZoom NumStep Linear Solver app variables Triangle Solver app variablesLinear Explorer app variables Quadratic Explorer app variables Sequence app variables Trig Explorer app variablesCategory Names Modes Units and constants UnitsUnit categories Length Acceleration Unit calculations PrefixesUnits menu includes an entry that is not a unit Palette of prefixes +5 SF Unit tools MKSA8.175cm/s returns .08175m*s-1 UFACTOR100C,1A returns 100A*s Physical constantsUSIMPLIFY5kg*m2/s2 returns 5J Value or measurement? List of constants Avogadro, NA 450 Lists Create a list in the List Catalog = or \ List Editor List Editor ButtonsKeys =or \ To insert an element To edit a listA list Deleting lists Lists in Home viewTo delete a list To createa list To store a list Aj7To display a list To display one List functions To send a listData on page 44 for instructions 2,3 returns 5,10,15 Make List SortMenu format Aajo Reverse Concatenate Position Size Aj5E Aj5 E Finding statistical values for lists Aj1EAj1 Ad1E Beginning on page 211, for the meaning of each statistic Vectors MatricesMatrices Creating and storing matrices POLYROOT1,0,-1,0M1 Editor Working with matricesMatrix Editor To create a matrix in the Matrix Editor View Matrices in HomeTo store a matrix To display a matrix Matrix arithmetic R1o2To send a matrix Matrixnamerow,column E3 E HAQ1 +To multiply Divide by a scalar AQ1k5 AQ1sAAQ1kQ Solving systems of linear equations Q1 n AQ2 2E3E Tap in cell R1, C3 E 1E1E Q1E4EQ1 Commands Matrix functions and commandsSns AQ1E Matrix functions Argument conventionsTRN matrix TRN ⎜ Rref matrix Rref3,2,3,4 IDENMATsize JordanBlockExpr,n 0 JordanBlock7,3 returns 0 7 1 0 0Hilbertn Cos1 -sin1sin1 cos1 Rownorm ⎜ Specnorm ⎜ Specrad ⎜Cond Rank EIGENVALmatrix 37228… -0.37228…Eigenvv matrix Eigenvv Choleskymatrix Example CAS viewCholesky ⎜ IhermiteMtrxA HessenbergMtrxA 278IsmithMtrxA Ismith ⎜ LSQmatrix1, matrix2 LSQP*A=L*U LUmatrix QRmatrix A,var1,var2 SCHURmatrixExample Schur ⎛⎜ 1 2 ⎞⎟ returns SVD ⎝ 4649… 0.3659… Cross 1 2 , 3 4 returnsDOT 1 2 , 3 4 returns L2normVect MaxnormVect or Mtrx ExamplesMaxnorm 1 2 3 -4 returns + y z = 5 2x y = 2y + z = 488 Features. See below Opens the selected note forEditing Begins a new note, Rename renames the selected note To create a note from the Notes CatalogOpen the Note Catalog To create a note for an app Keys Are adding or editing a note Make the next character upper-case With lowercase locked, make next character uppercase Text formatting Mathematical InsertingExpressions Sharing notes HP Prime Programs Command Structure Programming in HP PPLPixon xposition, yposition Pixon xposition, yposition ,color Program Catalog Program Structure CommentsExport Myprogam Begin END Open Program Catalog Program Catalog buttons and keys =or S\ Creating a new program Myprogram Program Editor Or S=and Checks the current program for errorsStrings Drawing Matrix App Functions Integer More Press Jto return to the main menu Begin and END For N from 1 to 3 do Run a Program Tap Myprogram to expand the menu and select Myprogram Debug a Program Multi-functionPrograms Parameters Program Catalog, select Edit a program Copy a program or part of a program 510 To share a program HP Prime programming languageVariables and visibility Export Radius Export Getradius Begin Inputradius END Programming in HP PPL 513 Program Rolldie ProgramExport Rolldien Return 1+RANDINTN-1 L2roll+1 L2roll RolldieROLLDIEn Return 1+RANDINTn-1 END User Keyboard Customizing key presses User modeBegin Return 1+RANDINTN-1 END Re-assigning keys Key names Internal name of keys and key states KDiv App programs KAMath Using dedicated program functions Redefining the View menu Resets or Initializes an appStarts an app View text, function Customizing an app Tap Enter a name for the new app such as DiceSimulation Dicesimvars Rolldie Export SIDES,ROLLS Export DiceSimulationBegin END View Roll Dice,ROLLMANY Sides Begin RepeatSIDES= Floorsides If SIDES2 then Until Sides =4 STARTVIEW7,1 END STARTVIEW1,1 END STARTVIEW0,1 ENDExport ROLLS,SIDES Export Dicesimvars Begin Sides END Program commands Roll Dice Commands under the Tmplt menu Block Begin END Syntax Begin command1 command2… commandN ENDBranch Export SQM1X Begin Return END Loop Default commands ENDCase Export Maxfactorsn Begin MSGBOXMax of + max + factors for +resultMAXFACTORS100 Export Drawpattern Begin END Wait RectExport ISPERFECTn +1 d END Return sum==n END Export Perfectnums BeginExport Sides Export Getsides Begin Repeat INPUTSIDES,Die Sides,N = ,Enter num sides,2 Variable FunctionExport Syntax Export var1, var2, …, varn Syntax Export FunctionName Commands under the Cmds menu Strings Char Syntax CHARvector or CHARinteger StringF1, when F1X Cosx = Cosx 666666666667String INSTRINGvanilla,van returns Instring banana,na returns Drawing Ymax Pixels and Cartesian Getpix Syntax GETPIXG, x, y GETPIXPG, x, yGrobh Syntax Grobhg Grobhpg INVERTPG, x1, y1, x2, y2 GrobwpgPIXOFFPG, x, y Pixon Syntax PIXONG, x, y ,color PIXONPG, x, y ,color Export BOX Begin Rect RECTP40,90,#0 Wait END Export Piseries Begin Local sign K=2 A=4 sign=−1 Rect TEXTOUTPN=,0,0Textoutppi APPROX=,0,30 Repeat +sign*4/2*K-1 a Sign*-1 sign K+1 K Until ENDAddcol Syntax ADDCOLmatrixname, vector, columnnumber Addrow Syntax ADDROWmatrixname, vector, rownumber Replace Syntax REPLACEname, start, object Scale Syntax SCALEname, value, rownumberScaleadd Syntax Scaleadd name, value, row1, row2 SUB Syntax SUB name, start, end App Functions Commands Bitand Syntax BITANDint1, int2, … intn →R Syntax B→R#integerm Bitsl Syntax BITSLint1 ,int2Getbase Syntax GETBASE#integerm Getbits Syntax GETBITS#integer Example GETBITS#22122 returns #20h or →B Syntax R→BintegerSetbits Syntax SETBITS#integerm ,bits Choose Syntax CHOOSEvar, title, item1, item2,…,itemn Editmat Syntax EDITMATmatrixvar Taps Example EDITMATM1 edits matrix M1 Getkey Syntax Getkey Export Sides Export Getsides Input Syntax INPUTvar ,title, label, help, resetBegin INPUTSIDES,D ie Sides,N = ,Enter num sides,2 END Msgbox Syntax MSGBOXexpression or string ,okcancel? Export Areacalc Begin Programming in HP PPL 553 Executes the function or returns the variable using MoreCAS Syntax CAS.function or CAS.variable Execon Syntax EXECON&expr, List1, list2,… Example ITERATEX2, X, 2, 3 returns Example →HMS54.8763 returns 5452′34.68″EXECON&23+&1,1,5,16,4,5,6,7 returns 7,12 Variables and Programs Programming in HP PPL 557 App variables Plot view variablesAxes Cursor GridLines Hmin/HmaxHwidth Labels Nmin/Nmax Recenter S1mark-S5markSeqPlot Θmin/θmax Tstep Θstep Polar Tmin/TmaxXtick Ytick Xmin/Xmax Symbolic view variables Ymin/YmaxXzoom Yzoom H1...H5 F0...F9H1Type...H5Type S1...S5 R0...R9S1Type...S5Type X0, Y0...X9,Y9 TypeU0...U9 Numeric view variables C0...C9D0...D9 NumIndep  NumStep where n  NumXStep where n NumYStep where n  NumType-forAutomatic default  NumType-forBuildYourOwn  NumXZoom where n  NumYZoom where nInference app variables Alpha Conf Mean1 Mean2 Mean1  Mean2  Pooled-for not pooled default Pooled Pooled-for pooled Difference of two means or two proportions, sets Variables Finance appCPYR NbPmt IPYRNbPmt PMTV Triangle Linear Solver app variablesSolver app SideC AngleAAngleB AngleC Settings Home HComplex DateTime Language Entry BaseBits Signed Symbolic SetupAAngle AComplex AFormat  AFormat 580 Basic integer arithmetic Default base Changing the default base Binary, Octal, Decimal or Hex Examples of integer arithmetic Mixed-base arithmetic Integer manipulation Base functions These are described in Integer, beginning on Glossary Catalog Matrix Two-dimensional array of real or Record using the Program EditorVector One-dimensional array of real or Symbolic, and Symbolic Setup 590 Troubleshooting To resetCalculator not responding If the calculator does not turn on Operating limits Status messages Correct. Look up the function Name in the index to find itsProper syntax Apps, matrices, lists, notes, or 594 Product regulatory information Federal Communications Commission noticeModifications Cables 596 European Union Regulatory Notice 598 Substances ChemicalParliament and the Council. a chemical information 600 Index CAS 54 Menu 324-347 settings 30, 55 view370-371 Functions 118-122, 348 variables 366-369 299-301 606 Zoom 88-94 points Polar app 70, 277-280 variables Samples 514-516, 524-527 structure Solve app 70, 259-266 functions 349 limitations 264 messages 215 App 109, 558-579 CAS Types of 89-90