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HP Prime Graphing NW280AAABA manual Recursive Replacement

Models: Prime Graphing NW280AAABA

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Setting

Purpose (Cont.)

Complex Use √

Select this to allow complex results in variables.

If checked, second order polyno- mials are factorized in complex mode or in real mode if the dis- criminant is positive.

Use i	If checked, the calculator is in
	complex mode and complex solu-
	tions will be displayed when they
	exist. If not checked, the calculator
	is in real mode and only real solu-
	tions will be displayed. For exam-
	ple, factors(x4–1) yields
	(x–1),(x+1),(x+i),(x–i) in complex
	mode and
	(x–1),(x+1),(x2+1) in real mode.
Principal	If checked, the principal solutions
	to trigonometric functions will be
	displayed. If not checked, the gen-
	eral solutions to trigonometric func-
	tions will be displayed.
Increasing	If checked, polynomials will be
	displayed with increasing powers
	(for example, –4+x+3x2+x3). If not
	checked, polynomials will be dis-
	played with decreasing powers
	(for example, x3+3x2+x–4).

Page 2

Setting	Purpose

Recursive	Specify the maximum number of
Evaluation	embedded variables allowed in
	an interactive evaluation. See also
	Recursive Replacement
	below.

Computer algebra system (CAS)

Page 61

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HP Prime Graphing NW280AAABA manual Recursive Replacement

Contents

User Guide HP Prime Graphing CalculatorProduct Regulatory & Environment Information Edition1 Part Number NW280-2001 Legal NoticesEdition Printing HistoryJuly Page Contents Plot view Application Library App views Symbolic viewCommon operations in Plot view Zoom Trace Function app Computed statistics 233Getting started with the Polar app 277 Getting started with the Parametric app 271Variables Lists Status messages Basic integer arithmeticManual conventions PrefaceFunction, Polar, Parametric, Ans, etc Before starting Getting startedOn/off, cancel operations Display Sections of the display Uppercase when a key is pressed Be entered in uppercase when aLowercase when a key is pressed You are working in CAS view, notNavigation Touch gestures Keyboard Context-sensitive menu Primary entry and edit keys are Entry and edit keysComparison operators and Bool Minute, or second symbol accordEan operators CharactersShift keys Adding text Math template Math keysMath shortcuts 236…. Press conce to see 219602 and again to see Fractions Hexagesimal numbersPressing ca third time will cycle back to Original decimal representationReturn home H Enter 4BQ13 s6B23n 3BQ5 EEX key powersTo select from a menu MenusToolbox menus Input formsAlternatively, select the field and tap Home settings System-wide settingsFixed 2 format Becomes 123.4623E2 in Scientific Becomes 1.23E9 in EngineerOr a+b*i Shorthand. The default is to provide Commands on the Math and CASMenus are presented descriptively Or in common mathematicalMM/DD/YYYY YYYY/MM/DD, DD/MM/YYYY, orPress SH Settings to open Specifying a Home settingAlways one-dimensional Where to startMathematical calculations Choosing an entry typeEntering expressions Examples that follow assume that the entry mode isRPN Reverse Polish Notation. Not available in CAS view TextbookR23jw14S j8nQ3 h45E Example ParenthesesAlgebraic precedence Negative numbersE45+Sz Sj85s9Explicit and implied multiplication Large results Reusing previous expressions and resultsTo 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 HP Prime to another When is tappedOnline Help RPN Reverse Polish Notation Reverse Polish Notation RPNRPN is available in Home view, but not in CAS view History in RPN mode Sample calculations Re-usingResults SzX3Reverse Polish Notation RPN Swap Manipulating the stackStack Show an item Delete an item Delete all items CAS view Computer algebra system CASMenu buttons in CAS view are Assigns an object to a variable CAS calculations2Asj+3 SettingsAsw2 5Asjw6Standard or Scientific or Engineering Ments Radians or DegreesRecursive Replacement Tion above See also Recursive EvaluaComputer algebra system CAS Computer algebra system CAS Exam Mode Press SH. The Home Settings screen appears Tap Modifying the default configurationDon’t want disabled are not selected Press O+ A+ cBefore, the only base configuration will be Default Exam Creating a new configurationActivating Exam Mode Tap If a configuration other than Default To activate exam modeCancelling 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 App views Symbolic viewConfidence level, and select a type TestSymbolic 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 Open the app Quick example4Szf n2f jE N2fPress 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 Select or deselect a definition to explore Evaluate a dependent definitionF9X=X2+Statistics2Var.PredY6 X2+X+ 2 *X2Delete a definition Choose a color for plotsSymbolic view Summary of menu buttons Override system-wide settings Common operations in Symbolic Setup viewRestore default settings Press SYto open Symbolic Setup viewZoom Common operations in Plot viewZoom factors Zoom options Zoom setting By the X Zoom and Y Zoom settingsCenter on Shortcut press wGraph with the original plot settings Given the supplied x axis settings. ForShows a representative piece of the plot Apps, autoscaling rescales both axesZoom with Testing aSplit-screen ViewingOut Shown, tapAutoscale SquareDecimal IntegerTrig TraceTo evaluate a definition To turn tracing on or off Configure Plot view Common operations in Plot Setup viewPlot view Summary of menu buttons Polar only Parametric OnlySequence Only Stats 1 Var onlyThat here are two fields one for Sets the initial range of the x-axis. NotePanning and zooming Sets the initial range of the y-axis. NoteGraphing methods Common operations in Numeric view Restore default settingsZoom options Zoom keys Zoom menu Evaluating Deleting data Custom tablesStart typing a new value Only visible if Numtype is set to Numeric view Summary of menu buttonsSelect Ascending or Descending , Modifying Numeric Setup Common operations in Numeric Setup viewAdding a note to an app Combining Plot and Numeric ViewsCreating an app Fibonacci in this example Asjw5 App functions and variablesSelect Statistics 1Var results MeanX Tap This opens a menu of app variablesGetting started with the Function app Function appRdw1 jw3E Open the Function app Define the expressionsOpen the Function app ISelect FunctionSet up the plot Plot the functions Trace a graph Change the scale Display the Numeric Setup view SMSetup Display Numeric view Set up Numeric viewExplore Numeric view Press SJClear to reset all the settings to their defaultsTo navigate around a table Substituted the values in the X column for xTo go directly to a value To access the zoomOptions Display the Plot view menu Analyzing functionsTo find a root of the quadratic function =or\Intersection of two To find anFunctions IntersectionTo find the slope of the quadratic function To find the signed area between the two functions To find Function VariablesExtremum QuadraticFunction Select Results and then the variable of interest Tap and selectNamed Extremum Summary of FCN operationsSlope Advanced Graphing app Getting started with the Advanced Graphing app Jn2 Open the app Define the open sentence+ n5 ISelect Advanced Graphing128 Advanced Graphing app Advanced Graphing app 129 Region. Use this option for You can move in any direction withinInequalities, for example EdgeNumeric view Display the Numeric view Explore Numeric view Trace in Numeric view Numeric SetupSj3n2 Trace EdgeTrace PoI Exploring a plot from the Plot Gallery Plot GalleryGetting started with the Geometry app GeometryPlot Function 3seASsEWith plotfunc on the entry line, enter 3*sinx More Tangent Derivative point Create aAbscissaGB,slopeGC Add some calculations140 Derivative Plot view in detailPoint D is the point whose ordinate value matches Derivative changes by looking at a plot of it rather than142 Object Selecting anHiding names Moving objectsFilling objects Coloring objectsRemoving fill UndoingClearing all Clearing anObjects Moving aboutPlot view buttons and keys Key Result in Plot view Symbolic view in detail Entries Re-orderingHiding an object Tap either To move it down the list or Move it upNumeric view in detail Can delete an object in Symbolic viewDeleting an Tap Or press C To delete all objects, press SJEnter radiusGC Listing all152 Points Geometric objectsMore Element 0 . . Notice Line Ngon PolygonSpecial CurveThat passes through each Circumcircle is the circleTriangle’s three vertices Thus enclosing the triangleSpecial Locus places Geometric transformations Axis and press E. The object is reflected across Tap Select ReflectionSymmetry axis defined in step Given scale factor around a given point as centerGK,angleGK,GL,GM Select Transform Rotation164 Symbolic view Cmds menu Geometry functions and commandsPoint BarycenterDivisionpoint CenterElement InterMidpoint IsobarycenterOrthocenter PointStop trace Point2dErase trace DrawSlpExbisector BisectorHalfline LineParallel MedianlinePerpenbisector Medianlinepoint1, point2, point3Segment PerpendicularTangent Draws a segment defined by its endpointsHexagon EquilateraltriangleEquilateral triangle0,6 draws an equilateral Equilateral triangle0,6, v draws an equilateralIsopolygon IsoscelestriangleParallelogram IsoscelestriangleGA, GB, angleGC, GA, GBQuadrilateral PolygonRectangle RhombusSquare RighttriangleTriangle Circumcircle CircleConic CircumcircleGA, GB, GC draws the circleExcircle EllipseHyperbola Excirclepoint1, point2, point3Incircle TransformLocus ParabolaProjection InversionReflection Draws the orthogonal projection of a point onto a curveSimilarity RotationTranslation RotateGA, angleGB, GC, GD,GK rotatesMeasure Plot Measure Numeric view Cmds menuAngle AffixArcLen AreaDistance CoordinatesDistance2 Area4-x2/4, x=-4..4 returns 14.666…Extractmeasure EquationOrdinate ParameqRadius TestIscollinear IsconcyclicIsequilateral IselementIsisoceles IsorthogonalIsparallelogram IsparallelIsperpendicular IsrectangleIssquare Other Geometry functionsConvexhull HarmonicconjugateIsharmoniccirclebundle IsharmonicIsharmoniclinebundle IsrhombusLineVert LineHorzOpenpolygon PolarPole PowerpcRadicalaxis ReciprocationVector SingleinterVertices Verticesabca194 Getting started with the Spreadsheet app SpreadsheetTo open the Spreadsheet app, press Iand select Spreadsheet 196 Select cell C3 Enter a label for your total commission Select cell D1 Enter a formula to add up your takingsSelect the heading cell for column C, tap and select Select cell C5Enter a label for your fixed costs AncostseNavigation, selection and gestures Basic operationsCell naming Cell referencesMethod Enter Cost and tap Entering contentCOST*0.33 and tap Enter Statistics1Var.D1 Select Polynomial Find Roots External functionsCopy and paste External referencesTo copy one or more cells, select them and press SVCopy Format, both value and format, or both formula and formatReferencing variables = Row2-√Row-1. The only Using the CAS in spreadsheet calculationsHandled by the CAS, but only Evaluates it Buttons and keysLine is active Changes toFormatting 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 Menu items you can tap on in Symbolic view are Symbolic view menu itemsEditing. Tap when done Enters D directly to save you having to press two keys214 Entering and editing statistical data Configure a histogram plot for the data Setup1Var app open, return to Home view and enter Edit a data setSpreadsheet.A1A10 D7 E Menu items you can tap on in Numeric view areDelete data Insert data Generating data Sort data values Computed statistics Plot types PlottingTo plot statistical data HistogramNormal probability Box-and-WhiskerLine plot Bar graphPareto chart Setting up the plot Plot Setup viewExploring the graph Data in descendingMenu items you can tap on in Plot view are Plot view menu itemsGetting started with the Statistics 2Var app Statistics 2Var appAdvertising minutes Resulting sales $ Dependent, yEnter the advertising minutes data in column C1 2E1E3E5E5E4 Statistics 2VarStatistics 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 Descending Delete data Insert data Sort data valuesFit types Defining a regression modelFits the data to a logistic curve Where L is the saturation valueFor growth. You can store a Positive real value in L, or-ifCOV SCOVΣXY SerrY Plotting statistical dataTracing a curve Tracing a scatterTracing order Plot view menu items Plot setupPlotting mark ConnectHome view Predicting valuesTroubleshooting a plot Getting started with the Inference app Inference appOpen InferenceTest μ1 μ2, the T-Test on Symbolic view optionsTest 1 μ from the Type menu Select the inference method Enter dataSample mean Sample size Population standard deviation Alpha level for the testDisplay 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 Select inference method and type Import the data Calculate statistics Open the Inference appTap on the Method field and select Confidence IntervalDisplay Hypothesis testsResults NumericallyMenu name One-Sample Z-TestInputs Two-Sample Z-Test One-Proportion Z-Test Two-Proportion Z-Test Test Z Test statistic Test Δ pˆ Difference between One-Sample T-TestWith the test Z-value This test measures the strength of the evidence for aTest 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 Int 1π One-Proportion Z-IntervalNumber of successes Sample success count Sample size Confidence levelMenu name Int π1 π2 Two-Proportion Z-IntervalConfidence interval for the difference between Proportions of successes in two populationsTwo-Sample T-Interval One-Sample T-IntervalResult Definition 258 Getting started with the Solve app Solve appOpen the Solve app One equationClear the app and define the equation AVjS.AU j+2AAADSolve the unknown variable Enter known variablesKph over a distance Is approximately 2.4692 m/s2 Plot the equation Where n is the number of the selected equationSelect Auto Scale Select Both sides of En Matches the value of a you calculated aboveOpen the Solve app Define the equations Enter a seed value Several equationsAXj+AYj S.16E AXwAYS. Q1E Solve the unknown variables LimitationsZero Solution informationSign ReversalNo values satisfy the selected equation or expression Bad Guesses Constant?Value of the equation is the same at every point sampled Getting started with the Linear Solver app Linear Solver appOpen the Linear Solver app. ISelect Linear SolverCoefficients and constants had been entered Define and solve the equationsSolve a two-by- two system Menu items270 Getting started with the Parametric app Parametric appOpen the Parametric app Parametric8ed? 8fd? Define the functionsDegrees Set the angle measure Set up the plot Plot the functions274 Tap .The table scrolls to the value you entered 276 Polar app Open the Polar app ISelect Polar App opens in Symbolic viewGetting started with the Polar app Open the Polar app5Szf dn2 fdj Set angle measure Set up the plotDefine the expression 5πcosθ/2cosθ2 Plot the expression Explore the graph 280 Polar app Getting started with the Sequence app Sequence app+ E App opens in Symbolic view Define the Fibonacci sequenceOpen the Sequence app ISelect SequenceSelect Stairstep from the Seq Plot menu Plot the sequenceDisplay Numeric view Explore the table of values Define the expression Setup the plot Set up the table of valuesAnother example Explicitly-defined sequences RQFandPlot the sequence Explore the table of sequence values Getting Started with the Finance app Finance app288 Cash flow diagrams Time value of money TVM PMT TVM calculations Another example292 To calculate amortizations Calculating amortizationsAmortization graph Finance app 295 Getting started with the Triangle Solver app Triangle Solver appTapping Open the Triangle Solver app ISelectSpecify the known values Solve for the unknown values Choosing triangle typesSpecial cases Triangle Solver app 299 Linear Explorer app Explorer appsBetween them by tapping or Graph modeTest mode Equation mode Tap to enterOpen the app Quadratic Explorer appQuadratic ExplorerIts value. When you are ready, tap To see if you Equation modeTap To see the correct answer and tap Exit Test mode Graphs that are harder match by tapping RespectivelyTrig Explorer Trig Explorer appGraph by pressing Tap To switch toCursor keys. All four keys Are available.Now press the cursor keys to select each parameter Tap to see the correct answer and tap to exit Test modeAll the functions and commands Functions and commands308 Abbreviations used in this chapter Keyboard functionsNORMALICDFμ,σ,p Shex +,w,s, nE5 returns ALOG3 returnsEfg +2*i returns -1-2*i 1returns2returns Numbers Math menuExample 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 Probability HyperbolicNormal Random real number with normal distribution Nμ,σ PERM5,2returnsNORMALDμ,σ,x RANDSEEDvalueNORMALD0.5 and NORMALD0,1,0.5 both return STUDENTn,xIs a real number CHISQUARECDF2,6.1 returns CHISQUARECDFn,kFISHERCDFn,d,x FISHERCDF5,5,2 returnsList Special MatrixAlgebra CAS menuPartfracRatFrac or Opt Syntax substExpr,Var=valueNumera,b Denoma/bDiffExpr,var DiffExpr,var1$k1,var2$k2 CalculusLimitExpr,Var,Val,Dir1, 0 SumExpr,Var,Real1, Real2,Step SeriesExpr,Equalvar=limitpoint,Orde r,Dir1,0,-1CurlExpr1, Expr2, …, ExprN, Var1, Var2, …, VarN DivergenceExpr1, Expr2, …, ExprN, Var1, Var2, …, VarNHessian Returns the Hessian matrix of an expression GradExpr,LstVarHessianExpr,LstVar IbpufVar, uVar, Var, Real1, Real2SumriemannExprXpr,Lstvar1,var2 PrevalExprFvar,Reala,Realb,VarTaylorExpr,Var=Value,Order DivpcPoly1,Poly2,IntegerSolve Zerosx2-4 returns -2 ZerosExpr,Var or zerosExpr1, Expr2,…,Var1, Var2,…CsolveEq,Var CsolveEq1, Eq2,…, Var CZerosExpr,Var CZerosExpr1, Expr2,…,Var1, Var2,…Rewrite Exp2powExpr TexpandExprPow2expExpr Exp2trigExprSin2costanExpr Asin2atanExprAcos2asinExpr Acos2atanExprAtan2asinatan2*x returns Atan2asinExprAtan2acosExpr Tan2sincosExprTrigtanExpr TrigcosExprAtrig2lnExpr TlinExprTrigInteger IsPrimeInteger GcdIntgr1, Intgr2,…NextprimeInteger PrevprimeIntegerIquoIntgr1, Intgr2 PolynomialIremIntgr1, Intgr2 Powmoda, n, p,Expr,VarDivisPoly or divisPoly1, Poly2,… CoeffPoly, Var, IntegerFactorsPoly or factorsPoly1, Poly2,… GcdPoly1,Poly2Poly2symbVector, Var Symb2polyExpr,Var Symb2polyExpr, Var1, Var2,…PcoefVect QuoList1, List2, Var QuoPoly1, Poly2, Var PminMtrx,VarRemList1, List2, Var RemPoly1, Poly2, Var DegreePoly ContentPoly,VarFactorxnPoly SturmabPoly,Var,a,bGbasisPoly1 Poly2…, Var1 Var2… CyclotomicIntegerGreducePoly1, Poly2 Poly3 …, Var1 Var2… HermiteIntegerLaguerreInteger LagrangeX1 X2…, Y1 Y2…Tchebyshev1Integer Tchebyshev2IntegerPlot PlotodeExpr, Var1, Var2, X0, Y0 App menuPlotlistX1, Y1, X2, Y2, … Function app functions Spreadsheet app functions Solve app functionsSOLVEEn,var,guess SOLVEX2-X-2,X,3returns2=STAT1A25A37 FunctionNameinput,optional Parameters=STAT1A25A37,h n As in SUMB7C23For example, AVERAGEB7B23 returns the arithmetic Calculates the arithmetic mean of a range of numbersSpecify a block of cells, as in AVERAGB7C23 Finance appColumns are multiplied to generate a data point Second column is treated as the weight of the firstSet to Place column headers Place row headers SerrSTAT1A25A37 REGRSInput range,model, configurationSTAT1A25A37,h n x σ Example REGRSA25B37,2 PredX PredYPredYmode, x, parameters PredXmode, y, parametersHypZ1mean 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 HypZ1prop21, 50, 0.5, 0.05,1 HypZ2propHypT1mean x ,s,n,μ0, α,mode,configuration Mode Specifies which alternative hypothesis to use ≠ μ0HypT1mean The one-sample t-test for a mean HypZ2prop21, 26, 50, 50, 0.05ConfZ1mean x ,n,s, C,configuration HypT2meanx1,x2,s1,s2, n1,n2, α,pooled,mode, configurationConfZ1propx,n,C,configuration ConfZ2mean x1, x2, n1, n2,s1,s2,C, configurationConfZ1mean0.461368, 50, 0.2887 ConfZ2mean0.461368, 0.522851, 50, 50, 0.2887, 0.2887ConfT1mean ConfZ2propConfZ1prop21, 50 Statistics 1Var app functions ConfT2mean x1, x2, s1,s2,n1, n2,C,pooled, configurationConfT1mean0.461368, 0.2776, 50 ConfT2mean0.461368, 0.522851, 0.2776, 0.2943, 50, 50, 0SetFreq Do1VStatsSetSample Resid Statistics 2Var app functionsDo2VStats SetDependSetIndep Inference app functionsDoInference HypZ1meanCritical value of π associated with the critical Z-value Test π valueHypZ2mean x1, x2, n1, n2,σ1,σ2,α,mode Order HypT1meanTest Δπ value Critical value of the statistic associated withHypT2meanx1,x2,s1,s2, n1,n2, α,pooled,mode ConfZ2mean ConfZ1meanConfZ1prop Two proportions. Returns a list containing in order CalcFV Finance app functionsSolves for the future value of an investment or loan CalcFVNbPmt,IPYR,PV,PMTV,PPYR,CPYR,BEGCalcNbPmt CalcIPYRCalcPMT CalcPVTriangle Solver app functions Linear Solver app functionsSolve2x2 Solve3x3ASAangle,side,angle AASangle,angle,sideSASside,angle,side SSAside,side,angleDoSolve Linear Explorer functionsSolveForYIntercept Common app functions Quadratic Explorer functionsSOLVEa, b, c DELTAa, b, cFunction.CHECK1 Ctlg menuUNCHECKDigit Enter Sequence.UNCHECK2Change Percent change from x to y. Returns 100*y-x/x Percent of y. Returns x/100*y ExampleList.Integer or Matrix.Integer List1.*List2 or Matrix1.*Matrix2Var=expression 3,4.*3,4,5,6 gives 3,8,15,24A2q1,2,4,4,x,y returns x2+6*x*y+4*y2 A2qMatrix, Var1, Var2…AbcuvPolyA, PolyB, PolyC, Var Abcuvx2+2*x+1,x2-1,x+1 returns 1/2 -1/2Append Appends an element to a list or vector CanonicalformQuadraticExpr,Var BasisMatrixCanonicalform2*x2-12*x+1 gives 2*x-32-17 CatObject1, Object2,…ColDim Returns the number of columns of a matrix Complexrootx3+8, 0.01 returns Companion Returns the companion matrix of a polynomialContains0,1,2,3,2 returns ContainsList, Element or containsVector, ElementCopyVarVar1,Var2 CorrelationList or correlationMatrixReturns Enters the mathematical constant e Euler’s number Eval Evaluates an expression Eigenvals Returns the sequence of eigenvalues of a matrixEvalfExpr,Integer EvalcExprEvalf2/3 gives Even1251 returnsExprX+10 returns 100, if the variable X has the value Expr Parses the string String into a number or expressionFMax-x2+2*x+1,x gives FMaxExpr,VarFMinExpr,Var FMinx2-2*x+1,x givesFunctiondiffFnc FsolveExpr,Var,Guess or Interval,MethodFunctiondiffsin gives x→cosx GaussExpr,VectVarHalftanhyp2expExprTrig GramschmidtVector, FunctionHalftanhyp2expsinx+sinhx returns HamdistInteger1, Integer2Icontent24x3+6x2-12x+18 gives IcontentPoly,VarHead1,2,3 gives HeavisideRealInv Returns the inverse of an expression or matrix Interval2center Returns the center of an intervalJacobisymbol132,5 gives JacobisymbolInteger1, Integer2IPartReal or iPartList IPart4.3 returnsLin Returns an expression with the exponentials linearized Logb Returns the logarithm of base b of a Lname Returns a list of the variables in an expressionMat2list Returns a list containing the elements of a matrix Lvar Returns a list of variables used in an expressionMean1,2,3,1,2,3 gives 7/3 MeanList1, List2 or meanMatrixMedianList1, List2 or medianMatrix Median1,2,3,5,10,4 givesModgcdx4-1,x-12 gives ModgcdPoly1,Poly2MRowExpr, Matrix, Integer MultcconjugateExprNormalExpr NDerivfx,x,h returns fx+h-fx-h*0.5/hNormal2*x*2 gives 4*x NormalizeVector or normalizeComplexPIECEWISE⎪ PI Inserts πPlotparamcost+i*sint, t=0..2*π plots the unit circle PlotparamfVar+i*gVar, Var= IntervalPlotpolarExpr,Var=Interval Plotpolarπ/2x, x=-π..π plots a partial spiralPolecircle0, 1, line1+i, 2 returns point1/2,1/2 PoleCrcle,LinePOLYCOEFVector or POLYCOEFList POLYCOEF-1, 1 returns 1, 0PolynomialregressionList1, List2, Integer PolygonscatterplotMatrixPolynomialregression1, 2, 3, 4, 1, 4, 9, 16,3 returns 0 1 0 POLYROOTPoly or POLYROOTVectorPowerregression1, 2, 3, 4, 1, 4, 9, 16 returns 2 PowerregressionList1, List2Powerpccircle0,1+i,3+i gives Prepend1,2,3 gives 3,1,2Purge Unassigns a variable name Quote Returns an expression unevaluated ⎠ returns RefMatrix Reducedconicx2+2*x-2*y+1 returnsRemoveElement, Vector or removeElement, List Remove6,1 2 6 7 returns 1 2Restart Purges all the variables Residue Returns the residue of an expression at a valueExample Gives RowDim Returns the number of rows of a matrixSignature Returns the signature of a permutation Sqrt Returns the square root of an expression Sto Stores a real or string in a variable Transpose Returns a matrix transposed without conjugation Sylvester Returns the Sylvester matrix of two polynomialsType Returns the type of an expression e.g. list, string Returns the square of an expression When Used to introduce a conditional statementInserts 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 Home variables are accessed by pressing aand TappingFunction app variables App variablesNumStart NumType NumStep NumZoom NumIndep AAngle ADigits AComplex AFormatResults variables Geometry app variablesSpreadsheet app variables Category Names Symbolic PlotSolve app variables ColWidth RowHeightNumXStart Advanced Graphing app variablesNumYStart NumType NumXStep NumXZoom NumYStep NumYZoom Statistics 1Var app variables MinVal NbItemMedVal MaxValStatistics 2Var app variables CoefDet CorrSCov ΣCovSerrY Inference app variablesContains the sum of the dependent values Y CritVal1 CritScoreCritVal2 ProbNumStart NumType NumStep NumZoom Parametric app variablesFinance app variables Polar app variablesΘmin Recenter NumIndep NumType NumStart NumZoom NumStepTriangle Solver app variables Linear Solver app variablesLinear Explorer app variables Quadratic Explorer app variablesSequence app variables Trig Explorer app variablesCategory Names Modes Units Units and constantsUnit categories Length AccelerationPrefixes Unit calculationsUnits menu includes an entry that is not a unit Palette of prefixes+5 SF MKSA8.175cm/s returns .08175m*s-1 Unit toolsUFACTOR100C,1A returns 100A*s Physical constantsUSIMPLIFY5kg*m2/s2 returns 5J Value or measurement? Avogadro, NA List of constants450 Create a list in the List Catalog Lists= or \ List Editor Buttons List EditorKeys =or \To insert an element To edit a listA list Lists in Home view Deleting listsTo delete a list To createa listAj7 To store a listTo display a list To display oneTo send a list List functionsData on page 44 for instructions 2,3 returns 5,10,15Sort Make ListMenu format AajoReverse Concatenate Position Size Aj5 E Aj5EAj1E Finding statistical values for listsAj1 Ad1EBeginning on page 211, for the meaning of each statistic Vectors MatricesMatrices POLYROOT1,0,-1,0M1 Creating and storing matricesEditor Working with matricesMatrix Editor To create a matrix in the Matrix Editor View Matrices in HomeTo store a matrix To display a matrix R1o2 Matrix arithmeticTo send a matrix Matrixnamerow,columnHAQ1 + E3 ETo multiply Divide by a scalarAQ1k5 AQ1sAAQ1kQ Q1 n AQ2 Solving systems of linear equations2E3E Tap in cell R1, C3 E 1E1E Q1E4EQ1 Commands Matrix functions and commandsSns AQ1E Argument conventions Matrix functionsTRN matrix TRN ⎜Rref Rref matrix3,2,3,4 IDENMATsize0 JordanBlock7,3 returns 0 7 1 0 0 JordanBlockExpr,nHilbertn Cos1 -sin1sin1 cos1Rownorm ⎜ Specrad ⎜ Specnorm ⎜Cond Rank37228… -0.37228… EIGENVALmatrixEigenvv matrix EigenvvExample CAS view CholeskymatrixCholesky ⎜ IhermiteMtrxA278 HessenbergMtrxAIsmithMtrxA Ismith ⎜LSQ LSQmatrix1, matrix2P*A=L*U LUmatrixSCHURmatrix QRmatrix A,var1,var2Example Schur ⎛⎜ 1 2 ⎞⎟ returns SVD ⎝Cross 1 2 , 3 4 returns 4649… 0.3659…DOT 1 2 , 3 4 returns L2normVectMaxnormVect or Mtrx ExamplesMaxnorm 1 2 3 -4 returns + y z = 5 2x y = 2y + z = 488 Opens the selected note for Features. See belowEditing 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 Are adding or editing a note KeysWith lowercase locked, make next character uppercase Make the next character upper-caseText formatting Mathematical InsertingExpressions Sharing notes Programming in HP PPL HP Prime Programs Command StructurePixon xposition, yposition Pixon xposition, yposition ,colorProgram Structure Comments Program CatalogExport Myprogam Begin ENDProgram Catalog buttons and keys Open Program Catalog=or S\ Myprogram Creating a new programProgram 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 Tap Myprogram to expand the menu and select Myprogram Run a ProgramMulti-function Debug a ProgramPrograms ParametersProgram 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 Program RolldieExport Rolldien Return 1+RANDINTN-1Rolldie L2roll+1 L2rollROLLDIEn Return 1+RANDINTn-1 ENDUser Keyboard Customizing key presses User modeBegin Return 1+RANDINTN-1 END Re-assigning keys Internal name of keys and key states Key namesKDiv KAMath App programsResets or Initializes an app Using dedicated program functions Redefining the View menuStarts an app View text, functionCustomizing an app DiceSimulation Tap Enter a name for the new app such asExport SIDES,ROLLS Export DiceSimulation Dicesimvars RolldieBegin END View Roll Dice,ROLLMANYBegin Repeat SidesSIDES= Floorsides If SIDES2 then Until Sides =4 STARTVIEW7,1 ENDSTARTVIEW0,1 END STARTVIEW1,1 ENDExport ROLLS,SIDES Export Dicesimvars Begin Sides ENDRoll Dice Program commandsBegin END Syntax Begin command1 command2… commandN END Commands under the Tmplt menu BlockBranch Export SQM1X Begin Return ENDLoop Default commands ENDCase MSGBOXMax of + max + factors for +result Export Maxfactorsn BeginMAXFACTORS100 Export Drawpattern BeginEND Wait RectExport ISPERFECTn Export Perfectnums Begin +1 d END Return sum==n ENDExport Sides Export Getsides Begin Repeat INPUTSIDES,Die Sides,N = ,Enter num sides,2Function VariableExport Syntax Export var1, var2, …, varn Syntax Export FunctionNameChar Syntax CHARvector or CHARinteger Commands under the Cmds menu Strings666666666667 StringF1, when F1X Cosx = CosxString INSTRINGvanilla,van returns Instring banana,na returnsDrawing Ymax Pixels and Cartesian GETPIXPG, x, y Getpix Syntax GETPIXG, x, yGrobh Syntax Grobhg GrobhpgINVERTPG, x1, y1, x2, y2 GrobwpgPIXOFFPG, x, y PIXONPG, x, y ,color Pixon Syntax PIXONG, x, y ,colorWait END Export BOX Begin Rect RECTP40,90,#0Local sign K=2 A=4 sign=−1 Rect TEXTOUTPN=,0,0 Export Piseries BeginTextoutppi APPROX=,0,30 Repeat +sign*4/2*K-1 aUntil END Sign*-1 sign K+1 KAddcol Syntax ADDCOLmatrixname, vector, columnnumber Addrow Syntax ADDROWmatrixname, vector, rownumberScale Syntax SCALEname, value, rownumber Replace Syntax REPLACEname, start, objectScaleadd Syntax Scaleadd name, value, row1, row2 SUB Syntax SUB name, start, endApp Functions Bitand Syntax BITANDint1, int2, … intn Commands→R Syntax B→R#integerm Bitsl Syntax BITSLint1 ,int2Getbase Syntax GETBASE#integerm Example GETBITS#22122 returns #20h or →B Syntax R→Binteger Getbits Syntax GETBITS#integerSetbits Syntax SETBITS#integerm ,bits Choose Syntax CHOOSEvar, title, item1, item2,…,itemnTaps Example EDITMATM1 edits matrix M1 Getkey Syntax Getkey Editmat Syntax EDITMATmatrixvarExport Sides Export Getsides Input Syntax INPUTvar ,title, label, help, resetBegin INPUTSIDES,D ie Sides,N = ,Enter num sides,2 END Export Areacalc Begin Msgbox Syntax MSGBOXexpression or string ,okcancel?Programming in HP PPL 553 More Executes the function or returns the variable usingCAS 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 Plot view variables App variablesAxes CursorHmin/Hmax GridLinesHwidth LabelsRecenter S1mark-S5mark Nmin/NmaxSeqPlot Θmin/θmaxTstep Θstep Polar Tmin/TmaxXtick Ytick Xmin/Xmax Ymin/Ymax Symbolic view variablesXzoom YzoomH1...H5 F0...F9H1Type...H5Type S1...S5 R0...R9S1Type...S5Type X0, Y0...X9,Y9 TypeU0...U9 C0...C9 Numeric view variablesD0...D9 NumIndep NumXStep where n  NumStep where n NumYStep where n  NumType-forAutomatic default  NumType-forBuildYourOwn NumYZoom where n  NumXZoom where nInference app variables Alpha ConfMean2 Mean1 Mean1  Mean2Pooled  Pooled-for not pooled default Pooled-for pooled Difference of two means or two proportions, setsVariables Finance appCPYR IPYR NbPmtNbPmt PMTVTriangle Linear Solver app variablesSolver app AngleA SideCAngleB AngleCHome SettingsDate HComplexTime LanguageBase EntryBits SignedSetup SymbolicAAngle AComplex AFormat AFormat580 Basic integer arithmetic Default base Binary, Octal, Decimal or Hex Changing the default baseMixed-base arithmetic Examples of integer arithmeticInteger manipulation These are described in Integer, beginning on Base functionsGlossary Catalog Record using the Program Editor Matrix Two-dimensional array of real orVector One-dimensional array of real or Symbolic, and Symbolic Setup590 To reset TroubleshootingCalculator not responding If the calculator does not turn onStatus messages Operating limitsName in the index to find its Correct. Look up the functionProper syntax Apps, matrices, lists, notes, or594 Federal Communications Commission notice Product regulatory informationModifications Cables596 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 Samples 514-516, 524-527 structure Zoom 88-94 points Polar app 70, 277-280 variables215 Solve app 70, 259-266 functions 349 limitations 264 messagesApp 109, 558-579 CAS Types of 89-90