Examples of integer arithmetic

The operands in integer arithmetic can be of the same base or of mixed bases.

Integer calculation	Decimal equivalent

#10000b+#10100b	16 + 20 = 36
=#100100b
#71o–#10100b =	57 – 20 = 37
#45o
#4Dh * #11101b = #8B9h	77 × 29 = 2233
#32Ah/#5o = #A2h	810/5 = 162

Mixed-base arithmetic

With one exception, where you have operands of different bases, the result of the calculation is presented in the base of the first operand. The example at the right shows two equivalent calculations: the first multiplies 410 by 5710 and the

second multiplies 5710 by 410. Obviously the results too are mathematically equivalent. However, each is presented in the base of the operand entered first: 16 in the first case and 8 in the second.

The exception is if an operand is not marked as an integer by preceding it with #. In these cases, the result is presented in base 10.

584	Basic integer arithmetic

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Image 590

HP Prime Graphing NW280AAABA manual Examples of integer arithmetic, Mixed-base arithmetic

Contents

HP Prime Graphing Calculator User Guide Edition1 Part Number NW280-2001 Legal Notices Product Regulatory & Environment Information July Printing HistoryEdition Page Contents Common operations in Plot view Zoom Trace Application Library App views Symbolic viewPlot view 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 Lowercase when a key is pressed Be entered in uppercase when aUppercase 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 Ean operators Minute, or second symbol accordComparison operators and Bool Characters Shift keys Adding text Math keys Math template Math shortcuts Pressing ca third time will cycle back to Fractions Hexagesimal numbers236…. Press conce to see 219602 and again to see Original decimal representation EEX key powers Return home H Enter 4BQ13 s6B23n 3BQ5 Menus To select from a menu Alternatively, select the field and tap Input formsToolbox menus System-wide settings Home settings 23E2 in Scientific Becomes 123.46Fixed 2 format Becomes 1.23E9 in Engineer Or a+b*i Menus are presented descriptively Commands on the Math and CASShorthand. The default is to provide Or in common mathematical YYYY/MM/DD, DD/MM/YYYY, or MM/DD/YYYY Specifying a Home setting Press SH Settings to open Mathematical calculations Where to startAlways one-dimensional Choosing an entry type RPN Reverse Polish Notation. Not available in CAS view Examples that follow assume that the entry mode isEntering expressions Textbook Example Parentheses R23jw14S j8nQ3 h45E E45+Sz Negative numbersAlgebraic precedence Sj85s9 Reusing previous expressions and results Explicit and implied multiplication Large results Result Using the clipboardTo reuse the last SjS+E Storing a value in a variableSj2E Example To assign π2 to to the variable a Szj AaESzj AQAcE R2o3 Ay6E Complex numbersSharing data When is tapped HP Prime to another Online Help RPN is available in Home view, but not in CAS view Reverse Polish Notation RPNRPN Reverse Polish Notation History in RPN mode Results Re-usingSample calculations SzX3 Reverse Polish Notation RPN Stack Manipulating the stackSwap 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 Asw2 Settings2Asj+3 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 Don’t want disabled are not selected Modifying the default configurationPress SH. The Home Settings screen appears Tap 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 To change a configuration Modifying configurationsCancelling exam mode Tap Exam Mode screen appears To return to the default configurationDeleting configurations Exam Mode An introduction to HP apps Solve Explore equations in one or more real Linear SolverEquations Application Library To delete an app Other options Confidence level, and select a type Symbolic viewApp views Test Symbolic Setup view Solve Symbolic viewPlot view Plot Setup view Advanced View a table of numbers generated by Graphing Test selected in Symbolic viewNumeric view Advanced Specify the numbers to be calculated Graphing Numeric Setup viewSymbolic view, and set the zoom factor 4Szf n2f jE Quick exampleOpen the app N2f Press Pto return to Plot view and see the complete plot Press PPress SP Set the second θRNG field to 4π by entering Numeric View Common operations in Symbolic viewΘ column to be 1. You set this up in the Numeric Setup view Definitional building blocks Add a definitionModify a definition From Home variables F9X=X2+Statistics2Var.PredY6 Evaluate a dependent definitionSelect or deselect a definition to explore X2+X+ 2 *X2 Choose a color for plots Delete a definition Symbolic view Summary of menu buttons Restore default settings Common operations in Symbolic Setup viewOverride system-wide settings Press SYto open Symbolic Setup view Zoom factors Zoom options Common operations in Plot viewZoom Center on By the X Zoom and Y Zoom settingsZoom setting Shortcut press w Shows a representative piece of the plot Given the supplied x axis settings. ForGraph with the original plot settings Apps, autoscaling rescales both axes Split-screen Testing aZoom with Viewing Shown, tap Out Decimal SquareAutoscale Integer Trace Trig To evaluate a definition To turn tracing on or off Plot view Summary of menu buttons Common operations in Plot Setup viewConfigure Plot view Sequence Only Parametric OnlyPolar only Stats 1 Var only Panning and zooming Sets the initial range of the x-axis. NoteThat here are two fields one for 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 Select Ascending or Descending , Numeric view Summary of menu buttonsStart typing a new value Only visible if Numtype is set to 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 ISelect Open the Function app Define the expressionsRdw1 jw3E 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 To navigate around a table Press SJClear to reset all the settings to their defaultsExplore Numeric view Substituted the values in the X column for x Options To access the zoomTo go directly to a value To find a root of the quadratic function Analyzing functionsDisplay the Plot view menu =or\ Functions To find anIntersection of two Intersection To find the slope of the quadratic function To find the signed area between the two functions Extremum Function VariablesTo find Quadratic Tap and select Function Select Results and then the variable of interest Slope Summary of FCN operationsNamed Extremum Advanced Graphing app Getting started with the Advanced Graphing app + n5 Open the app Define the open sentenceJn2 ISelect Advanced Graphing 128 Advanced Graphing app Advanced Graphing app 129 Inequalities, for example You can move in any direction withinRegion. Use this option for Edge Numeric view Display the Numeric view Explore Numeric view Numeric Setup Trace in Numeric view Trace PoI Trace EdgeSj3n2 Plot Gallery Exploring a plot from the Plot Gallery Geometry Getting started with the Geometry app With plotfunc on the entry line, enter 3*sinx 3seASsEPlot Function More Tangent Create a Derivative point Add some calculations AbscissaGB,slopeGC 140 Point D is the point whose ordinate value matches Plot view in detailDerivative Derivative changes by looking at a plot of it rather than 142 Hiding names Selecting anObject Moving objects Removing fill Coloring objectsFilling objects Undoing Objects Clearing anClearing all Moving about Plot view buttons and keys Key Result in Plot view Symbolic view in detail Hiding an object Re-orderingEntries Tap either To move it down the list or Move it up Deleting an Can delete an object in Symbolic viewNumeric view in detail 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 Triangle’s three vertices Circumcircle is the circleThat passes through each Thus enclosing the triangle Special Locus places Geometric transformations Symmetry axis defined in step Tap Select ReflectionAxis and press E. The object is reflected across Given scale factor around a given point as center Select Transform Rotation GK,angleGK,GL,GM 164 Point Geometry functions and commandsSymbolic view Cmds menu Barycenter Element CenterDivisionpoint Inter Orthocenter IsobarycenterMidpoint Point Erase trace Point2dStop trace DrawSlp Halfline BisectorExbisector Line Perpenbisector MedianlineParallel Medianlinepoint1, point2, point3 Tangent PerpendicularSegment Draws a segment defined by its endpoints Equilateral triangle0,6 draws an equilateral EquilateraltriangleHexagon Equilateral triangle0,6, v draws an equilateral Parallelogram IsoscelestriangleIsopolygon IsoscelestriangleGA, GB, angleGC, GA, GB Rectangle PolygonQuadrilateral Rhombus Triangle RighttriangleSquare Conic CircleCircumcircle CircumcircleGA, GB, GC draws the circle Hyperbola EllipseExcircle Excirclepoint1, point2, point3 Locus TransformIncircle Parabola Reflection InversionProjection Draws the orthogonal projection of a point onto a curve Translation RotationSimilarity RotateGA, angleGB, GC, GD,GK rotates Measure Plot Numeric view Cmds menu Measure ArcLen AffixAngle Area Distance2 CoordinatesDistance Area4-x2/4, x=-4..4 returns 14.666… Ordinate EquationExtractmeasure Parameq Iscollinear TestRadius Isconcyclic Isisoceles IselementIsequilateral Isorthogonal Isperpendicular IsparallelIsparallelogram Isrectangle Convexhull Other Geometry functionsIssquare Harmonicconjugate Isharmoniclinebundle IsharmonicIsharmoniccirclebundle Isrhombus Openpolygon LineHorzLineVert Polar Radicalaxis PowerpcPole Reciprocation Vertices SingleinterVector Verticesabca 194 To open the Spreadsheet app, press Iand select Spreadsheet SpreadsheetGetting started with the Spreadsheet app 196 Select the heading cell for column C, tap and select Select cell D1 Enter a formula to add up your takingsSelect cell C3 Enter a label for your total commission Select cell C5 Ancostse Enter a label for your fixed costs Basic operations Navigation, selection and gestures Method Cell referencesCell naming COST*0.33 and tap Entering contentEnter Cost and tap Enter Statistics1Var.D1 External functions Select Polynomial Find Roots To copy one or more cells, select them and press SVCopy External referencesCopy and paste Format, both value and format, or both formula and format Referencing variables Using the CAS in spreadsheet calculations = Row2-√Row-1. The only Line is active Buttons and keysHandled by the CAS, but only Evaluates it Changes to Font Size Auto or from 10 to 22 point Formatting optionsFormatting options appear Format Parameters Spreadsheet functions Statistics 1Var Statistics 1Var appGetting started with the Statistics 1Var app Sample data in D1 Editing. Tap when done Symbolic view menu itemsMenu items you can tap on in Symbolic view are 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 Spreadsheet.A1A10 D7 E Edit a data set1Var app open, return to Home view and enter Menu items you can tap on in Numeric view are Delete data Insert data Generating data Sort data values Computed statistics To plot statistical data PlottingPlot types Histogram Line plot Box-and-WhiskerNormal probability Bar graph Exploring the graph Setting up the plot Plot Setup viewPareto chart Data in descending Plot view menu items Menu items you can tap on in Plot view are Advertising minutes Resulting sales $ Statistics 2Var appGetting started with the Statistics 2Var app 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 Tap , make your change, and tap Numeric view menu itemsButtons you can tap on in Numeric view are Delete data Insert data Sort data values Descending Defining a regression model Fit types For growth. You can store a Where L is the saturation valueFits the data to a logistic curve Positive real value in L, or-if ΣXY SCOVCOV Plotting statistical data SerrY Tracing order Tracing a scatterTracing a curve Plotting mark Plot setupPlot view menu items Connect Predicting values Home view Troubleshooting a plot Open Inference appGetting started with the Inference app Inference Symbolic view options Test μ1 μ2, the T-Test on Sample mean Sample size Select the inference method Enter dataTest 1 μ from the Type menu Population standard deviation Alpha level for the test Display the test results Plot the test results 82.5 E 83.1 E 82.6 E 83.7 E 82.4 E 83 E Importing statisticsOpen the Statistics 1Var app Clear unwanted data Enter data Tap on the Method field and select Calculate statistics Open the Inference appSelect inference method and type Import the data Confidence Interval Results Hypothesis testsDisplay Numerically Inputs One-Sample Z-TestMenu name Two-Sample Z-Test One-Proportion Z-Test Two-Proportion Z-Test With the test Z-value One-Sample T-TestTest Z Test statistic Test Δ pˆ Difference between This test measures the strength of the evidence for a Each sample from a different population, this test Two-Sample T-TestTest μ1 μ2 Α level that you supplied Sample 1 standard deviationSample 2 standard deviation Two-Sample Z-Interval Confidence intervalsOne-Sample Z-Interval Number of successes One-Proportion Z-IntervalInt 1π Sample success count Sample size Confidence level Confidence interval for the difference between Two-Proportion Z-IntervalMenu name Int π1 π2 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 Clear the app and define the equation One equationOpen the Solve app AVjS.AU j+2AAAD Kph over a distance Is approximately 2.4692 m/s2 Enter known variablesSolve the unknown variable Select Auto Scale Select Both sides of En Where n is the number of the selected equationPlot the equation Matches the value of a you calculated above AXj+AYj S.16E AXwAYS. Q1E Several equationsOpen the Solve app Define the equations Enter a seed value Limitations Solve the unknown variables Sign Solution informationZero Reversal Value of the equation is the same at every point sampled Bad Guesses Constant?No values satisfy the selected equation or expression Open the Linear Solver app. ISelect Linear Solver appGetting started with the Linear Solver app Linear Solver Define and solve the equations Coefficients and constants had been entered Menu items Solve a two-by- two system 270 Open the Parametric app Parametric appGetting started with 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 Getting started with the Polar app Open the Polar app ISelect Polar App opens in Symbolic viewPolar app Open the Polar app Define the expression 5πcosθ/2cosθ2 Set angle measure Set up the plot5Szf dn2 fdj Plot the expression Explore the graph 280 Polar app Sequence app Getting started with the Sequence app Open the Sequence app ISelect App opens in Symbolic view Define the Fibonacci sequence+ E Sequence Plot the sequence Select Stairstep from the Seq Plot menu Display Numeric view Explore the table of values Another example Explicitly-defined sequences Set up the table of valuesDefine the expression Setup the plot 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 Tapping Triangle Solver appGetting started with the Triangle Solver app 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 Quadratic Explorer appOpen the app Explorer Tap To see the correct answer and tap Exit Test mode Equation modeIts value. When you are ready, tap To see if you Graphs that are harder match by tapping Respectively Trig Explorer app Trig Explorer Cursor keys. All four keys Tap To switch toGraph by pressing 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 NORMALICDFμ,σ,p Keyboard functionsAbbreviations used in this chapter E5 returns +,w,s, nShex ALOG3 returns Efg 2returns 1returns+2*i returns -1-2*i Math menu Numbers Maximum Maximum. The greater of two values ArithmeticExample XPON123456 returns 5 since 105.0915... equals Percentage x percent of y that is, x/100*y Example Example ARG3+3*i returns 45 degrees modeModulus Modulo. The remainder of value1/value2 Trigonometry Hyperbolic Probability PERM5,2returns Normal Random real number with normal distribution Nμ,σ NORMALD0.5 and NORMALD0,1,0.5 both return RANDSEEDvalueNORMALDμ,σ,x STUDENTn,x Is a real number FISHERCDFn,d,x CHISQUARECDFn,kCHISQUARECDF2,6.1 returns FISHERCDF5,5,2 returns List Matrix Special CAS menu Algebra Numera,b Syntax substExpr,Var=valuePartfracRatFrac or Opt Denoma/b LimitExpr,Var,Val,Dir1, 0 CalculusDiffExpr,var DiffExpr,var1$k1,var2$k2 CurlExpr1, Expr2, …, ExprN, Var1, Var2, …, VarN SeriesExpr,Equalvar=limitpoint,Orde r,Dir1,0,-1SumExpr,Var,Real1, Real2,Step DivergenceExpr1, Expr2, …, ExprN, Var1, Var2, …, VarN HessianExpr,LstVar GradExpr,LstVarHessian Returns the Hessian matrix of an expression IbpufVar, uVar, Var, Real1, Real2 TaylorExpr,Var=Value,Order PrevalExprFvar,Reala,Realb,VarSumriemannExprXpr,Lstvar1,var2 DivpcPoly1,Poly2,Integer Solve CsolveEq,Var CsolveEq1, Eq2,…, Var ZerosExpr,Var or zerosExpr1, Expr2,…,Var1, Var2,…Zerosx2-4 returns -2 CZerosExpr,Var CZerosExpr1, Expr2,…,Var1, Var2,… Rewrite Pow2expExpr TexpandExprExp2powExpr Exp2trigExpr Acos2asinExpr Asin2atanExprSin2costanExpr Acos2atanExpr Atan2acosExpr Atan2asinExprAtan2asinatan2*x returns Tan2sincosExpr Atrig2lnExpr TrigcosExprTrigtanExpr TlinExprTrig Integer NextprimeInteger GcdIntgr1, Intgr2,…IsPrimeInteger PrevprimeInteger IremIntgr1, Intgr2 PolynomialIquoIntgr1, Intgr2 Powmoda, n, p,Expr,Var FactorsPoly or factorsPoly1, Poly2,… CoeffPoly, Var, IntegerDivisPoly or divisPoly1, Poly2,… GcdPoly1,Poly2 PcoefVect Symb2polyExpr,Var Symb2polyExpr, Var1, Var2,…Poly2symbVector, Var RemList1, List2, Var RemPoly1, Poly2, Var PminMtrx,VarQuoList1, List2, Var QuoPoly1, Poly2, Var FactorxnPoly ContentPoly,VarDegreePoly SturmabPoly,Var,a,b GreducePoly1, Poly2 Poly3 …, Var1 Var2… CyclotomicIntegerGbasisPoly1 Poly2…, Var1 Var2… HermiteInteger Tchebyshev1Integer LagrangeX1 X2…, Y1 Y2…LaguerreInteger Tchebyshev2Integer Plot PlotlistX1, Y1, X2, Y2, … App menuPlotodeExpr, Var1, Var2, X0, Y0 Function app functions SOLVEEn,var,guess Solve app functionsSpreadsheet app functions SOLVEX2-X-2,X,3returns2 =STAT1A25A37,h n FunctionNameinput,optional Parameters=STAT1A25A37 As in SUMB7C23 Specify a block of cells, as in AVERAGB7C23 Calculates the arithmetic mean of a range of numbersFor example, AVERAGEB7B23 returns the arithmetic Finance app Set to Second column is treated as the weight of the firstColumns are multiplied to generate a data point Place column headers Place row headers Serr STAT1A25A37,h n x σ REGRSInput range,model, configurationSTAT1A25A37 Example REGRSA25B37,2 PredYmode, x, parameters PredYPredX PredXmode, y, parameters HypZ1mean0.461368, 50, 0.5, 0.2887, 0.05 HypZ1mean x, n,μ0,σ,α,mode, configurationHypZ1mean The one-sample Z-test for a mean HypZ1propx,n,π0,α,mode HypZ1propHypZ2mean0.461368, 0.522851, 50, 50, 0.2887, 0.2887, 0.05 HypZ2prop HypZ1prop21, 50, 0.5, 0.05,1 HypT1mean The one-sample t-test for a mean Mode Specifies which alternative hypothesis to use ≠ μ0HypT1mean x ,s,n,μ0, α,mode,configuration HypZ2prop21, 26, 50, 50, 0.05 HypT2meanx1,x2,s1,s2, n1,n2, α,pooled,mode, configuration ConfZ1mean x ,n,s, C,configuration ConfZ1mean0.461368, 50, 0.2887 ConfZ2mean x1, x2, n1, n2,s1,s2,C, configurationConfZ1propx,n,C,configuration ConfZ2mean0.461368, 0.522851, 50, 50, 0.2887, 0.2887 ConfZ1prop21, 50 ConfZ2propConfT1mean ConfT1mean0.461368, 0.2776, 50 ConfT2mean x1, x2, s1,s2,n1, n2,C,pooled, configurationStatistics 1Var app functions ConfT2mean0.461368, 0.522851, 0.2776, 0.2943, 50, 50, 0 SetSample Do1VStatsSetFreq Do2VStats Statistics 2Var app functionsResid SetDepend DoInference Inference app functionsSetIndep HypZ1mean HypZ2mean x1, x2, n1, n2,σ1,σ2,α,mode Test π valueCritical value of π associated with the critical Z-value Test Δπ value HypT1meanOrder Critical value of the statistic associated with HypT2meanx1,x2,s1,s2, n1,n2, α,pooled,mode ConfZ1prop ConfZ1meanConfZ2mean Two proportions. Returns a list containing in order Solves for the future value of an investment or loan Finance app functionsCalcFV CalcFVNbPmt,IPYR,PV,PMTV,PPYR,CPYR,BEG CalcPMT CalcIPYRCalcNbPmt CalcPV Solve2x2 Linear Solver app functionsTriangle Solver app functions Solve3x3 SASside,angle,side AASangle,angle,sideASAangle,side,angle SSAside,side,angle SolveForYIntercept Linear Explorer functionsDoSolve SOLVEa, b, c Quadratic Explorer functionsCommon app functions DELTAa, b, c UNCHECKDigit Ctlg menuFunction.CHECK1 Enter Sequence.UNCHECK2 Percent of y. Returns x/100*y Example Change Percent change from x to y. Returns 100*y-x/x Var=expression List1.*List2 or Matrix1.*Matrix2List.Integer or Matrix.Integer 3,4.*3,4,5,6 gives 3,8,15,24 AbcuvPolyA, PolyB, PolyC, Var A2qMatrix, Var1, Var2…A2q1,2,4,4,x,y returns x2+6*x*y+4*y2 Abcuvx2+2*x+1,x2-1,x+1 returns 1/2 -1/2 Append Appends an element to a list or vector Canonicalform2*x2-12*x+1 gives 2*x-32-17 BasisMatrixCanonicalformQuadraticExpr,Var CatObject1, Object2,… ColDim Returns the number of columns of a matrix Companion Returns the companion matrix of a polynomial Complexrootx3+8, 0.01 returns CopyVarVar1,Var2 ContainsList, Element or containsVector, ElementContains0,1,2,3,2 returns 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 Evalf2/3 gives EvalcExprEvalfExpr,Integer Even1251 returns Expr Parses the string String into a number or expression ExprX+10 returns 100, if the variable X has the value FMinExpr,Var FMaxExpr,VarFMax-x2+2*x+1,x gives FMinx2-2*x+1,x gives Functiondiffsin gives x→cosx FsolveExpr,Var,Guess or Interval,MethodFunctiondiffFnc GaussExpr,VectVar Halftanhyp2expsinx+sinhx returns GramschmidtVector, FunctionHalftanhyp2expExprTrig HamdistInteger1, Integer2 Head1,2,3 gives IcontentPoly,VarIcontent24x3+6x2-12x+18 gives HeavisideReal Interval2center Returns the center of an interval Inv Returns the inverse of an expression or matrix IPartReal or iPartList JacobisymbolInteger1, Integer2Jacobisymbol132,5 gives 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 MedianList1, List2 or medianMatrix MeanList1, List2 or meanMatrixMean1,2,3,1,2,3 gives 7/3 Median1,2,3,5,10,4 gives MRowExpr, Matrix, Integer ModgcdPoly1,Poly2Modgcdx4-1,x-12 gives MultcconjugateExpr Normal2*x*2 gives 4*x NDerivfx,x,h returns fx+h-fx-h*0.5/hNormalExpr NormalizeVector or normalizeComplex PI Inserts π PIECEWISE⎪ PlotpolarExpr,Var=Interval PlotparamfVar+i*gVar, Var= IntervalPlotparamcost+i*sint, t=0..2*π plots the unit circle Plotpolarπ/2x, x=-π..π plots a partial spiral POLYCOEFVector or POLYCOEFList PoleCrcle,LinePolecircle0, 1, line1+i, 2 returns point1/2,1/2 POLYCOEF-1, 1 returns 1, 0 Polynomialregression1, 2, 3, 4, 1, 4, 9, 16,3 returns 0 1 0 PolygonscatterplotMatrixPolynomialregressionList1, List2, Integer POLYROOTPoly or POLYROOTVector Powerpccircle0,1+i,3+i gives PowerregressionList1, List2Powerregression1, 2, 3, 4, 1, 4, 9, 16 returns 2 Prepend1,2,3 gives 3,1,2 Purge Unassigns a variable name Quote Returns an expression unevaluated ⎠ returns RemoveElement, Vector or removeElement, List Reducedconicx2+2*x-2*y+1 returnsRefMatrix 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 Expr Creating your own functionsInserts the imaginary number Function field, enter the function. eAA+fABAC Variables Result is written to history Multiply a by Working with Home variablesAaE Example 3 You can also store objects in variables Working with user variables Working with app variablesAAxotwAS. Sq1o2 o3 E More about the Vars menu Qualifying variables Home variables are accessed by pressing aand Tapping Home variables NumStart NumType NumStep NumZoom NumIndep App variablesFunction app variables AAngle ADigits AComplex AFormat Geometry app variables Results variables Solve app variables Category Names Symbolic PlotSpreadsheet app variables ColWidth RowHeight NumYStart NumType NumXStep NumXZoom NumYStep NumYZoom Advanced Graphing app variablesNumXStart Statistics 1Var app variables MedVal NbItemMinVal MaxVal Statistics 2Var app variables SCov CorrCoefDet ΣCov Contains the sum of the dependent values Y Inference app variablesSerrY CritVal2 CritScoreCritVal1 Prob Parametric app variables NumStart NumType NumStep NumZoom Θmin Recenter Polar app variablesFinance app variables NumIndep NumType NumStart NumZoom NumStep Linear Explorer app variables Linear Solver app variablesTriangle Solver app variables Quadratic Explorer app variables Category Names Modes Trig Explorer app variablesSequence app variables Unit categories Units and constantsUnits Length Acceleration Units menu includes an entry that is not a unit Unit calculationsPrefixes Palette of prefixes +5 SF Unit tools MKSA8.175cm/s returns .08175m*s-1 USIMPLIFY5kg*m2/s2 returns 5J Physical constantsUFACTOR100C,1A returns 100A*s Value or measurement? List of constants Avogadro, NA 450 Lists Create a list in the List Catalog = or \ Keys List EditorList Editor Buttons =or \ A list To edit a listTo insert an element To delete a list Deleting listsLists in Home view To createa list To display a list To store a listAj7 To display one Data on page 44 for instructions List functionsTo send a list 2,3 returns 5,10,15 Menu format Make ListSort Aajo Reverse Concatenate Position Size Aj5E Aj5 E Aj1 Finding statistical values for listsAj1E Ad1E Beginning on page 211, for the meaning of each statistic Matrices MatricesVectors Creating and storing matrices POLYROOT1,0,-1,0M1 Matrix Editor Working with matricesEditor To create a matrix in the Matrix Editor To store a matrix Matrices in HomeView To display a matrix To send a matrix Matrix arithmeticR1o2 Matrixnamerow,column To multiply E3 EHAQ1 + Divide by a scalar AQ1kQ AQ1sAAQ1k5 Solving systems of linear equations Q1 n AQ2 4EQ1 1E1E Q1E2E3E Tap in cell R1, C3 E Sns AQ1E Matrix functions and commandsCommands TRN matrix Matrix functionsArgument conventions TRN ⎜ 3,2,3,4 Rref matrixRref IDENMATsize Hilbertn JordanBlockExpr,n0 JordanBlock7,3 returns 0 7 1 0 0 Cos1 -sin1sin1 cos1 Rownorm ⎜ Cond Specnorm ⎜Specrad ⎜ Rank Eigenvv matrix EIGENVALmatrix37228… -0.37228… Eigenvv Cholesky ⎜ CholeskymatrixExample CAS view IhermiteMtrxA IsmithMtrxA HessenbergMtrxA278 Ismith ⎜ P*A=L*U LSQmatrix1, matrix2LSQ LUmatrix Example Schur ⎛⎜ 1 2 ⎞⎟ returns QRmatrix A,var1,var2SCHURmatrix SVD ⎝ DOT 1 2 , 3 4 returns 4649… 0.3659…Cross 1 2 , 3 4 returns L2normVect Maxnorm 1 2 3 -4 returns ExamplesMaxnormVect or Mtrx + y z = 5 2x y = 2y + z = 488 Editing Features. See belowOpens the selected note for Begins a new note, Open the Note Catalog To create a note from the Notes CatalogRename renames the selected note 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 Expressions InsertingMathematical Sharing notes Pixon xposition, yposition HP Prime Programs Command StructureProgramming in HP PPL Pixon xposition, yposition ,color Export Myprogam Begin Program CatalogProgram Structure Comments END Open Program Catalog Program Catalog buttons and keys =or S\ Creating a new program Myprogram Strings Drawing Matrix App Functions Integer More Or S=and Checks the current program for errorsProgram Editor 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 Programs Debug a ProgramMulti-function Parameters Program Catalog, select Edit a program Copy a program or part of a program 510 Variables and visibility HP Prime programming languageTo share a program Export Radius Export Getradius Begin Inputradius END Programming in HP PPL 513 Export Rolldien Program RolldieProgram Return 1+RANDINTN-1 ROLLDIEn L2roll+1 L2rollRolldie Return 1+RANDINTn-1 END Begin Return 1+RANDINTN-1 END User modeUser Keyboard Customizing key presses Re-assigning keys Key names Internal name of keys and key states KDiv App programs KAMath Starts an app Using dedicated program functions Redefining the View menuResets or Initializes an app View text, function Customizing an app Tap Enter a name for the new app such as DiceSimulation Begin END Dicesimvars RolldieExport SIDES,ROLLS Export DiceSimulation View Roll Dice,ROLLMANY SIDES= Floorsides If SIDES2 then SidesBegin Repeat Until Sides =4 STARTVIEW7,1 END Export ROLLS,SIDES Export Dicesimvars Begin STARTVIEW1,1 ENDSTARTVIEW0,1 END Sides END Program commands Roll Dice Branch Commands under the Tmplt menu BlockBegin END Syntax Begin command1 command2… commandN END Export SQM1X Begin Return END Case Default commands ENDLoop MAXFACTORS100 Export Maxfactorsn BeginMSGBOXMax of + max + factors for +result Export Drawpattern Begin Export ISPERFECTn RectEND Wait Export Sides Export Getsides Begin Repeat +1 d END Return sum==n ENDExport Perfectnums Begin INPUTSIDES,Die Sides,N = ,Enter num sides,2 Export Syntax Export var1, var2, …, varn VariableFunction Syntax Export FunctionName Commands under the Cmds menu Strings Char Syntax CHARvector or CHARinteger String StringF1, when F1X Cosx = Cosx666666666667 INSTRINGvanilla,van returns Instring banana,na returns Drawing Ymax Pixels and Cartesian Grobh Syntax Grobhg Getpix Syntax GETPIXG, x, yGETPIXPG, x, y Grobhpg PIXOFFPG, x, y GrobwpgINVERTPG, x1, y1, x2, y2 Pixon Syntax PIXONG, x, y ,color PIXONPG, x, y ,color Export BOX Begin Rect RECTP40,90,#0 Wait END Textoutppi APPROX=,0,30 Repeat Export Piseries BeginLocal sign K=2 A=4 sign=−1 Rect TEXTOUTPN=,0,0 +sign*4/2*K-1 a Addcol Syntax ADDCOLmatrixname, vector, columnnumber Sign*-1 sign K+1 KUntil END Addrow Syntax ADDROWmatrixname, vector, rownumber Scaleadd Syntax Scaleadd name, value, row1, row2 Replace Syntax REPLACEname, start, objectScale Syntax SCALEname, value, rownumber SUB Syntax SUB name, start, end App Functions Commands Bitand Syntax BITANDint1, int2, … intn Getbase Syntax GETBASE#integerm Bitsl Syntax BITSLint1 ,int2→R Syntax B→R#integerm Setbits Syntax SETBITS#integerm ,bits Getbits Syntax GETBITS#integerExample GETBITS#22122 returns #20h or →B Syntax R→Binteger Choose Syntax CHOOSEvar, title, item1, item2,…,itemn Editmat Syntax EDITMATmatrixvar Taps Example EDITMATM1 edits matrix M1 Getkey Syntax Getkey Begin INPUTSIDES,D ie Sides,N = ,Enter num sides,2 END Input Syntax INPUTvar ,title, label, help, resetExport Sides Export Getsides Msgbox Syntax MSGBOXexpression or string ,okcancel? Export Areacalc Begin Programming in HP PPL 553 CAS Syntax CAS.function or CAS.variable Executes the function or returns the variable usingMore Execon Syntax EXECON&expr, List1, list2,… EXECON&23+&1,1,5,16,4,5,6,7 returns 7,12 Example →HMS54.8763 returns 5452′34.68″Example ITERATEX2, X, 2, 3 returns Variables and Programs Programming in HP PPL 557 Axes App variablesPlot view variables Cursor Hwidth GridLinesHmin/Hmax Labels SeqPlot Nmin/NmaxRecenter S1mark-S5mark Θmin/θmax Xtick Ytick Xmin/Xmax Θstep Polar Tmin/TmaxTstep Xzoom Symbolic view variablesYmin/Ymax Yzoom H1Type...H5Type F0...F9H1...H5 S1Type...S5Type R0...R9S1...S5 U0...U9 TypeX0, Y0...X9,Y9 D0...D9 Numeric view variablesC0...C9 NumIndep  NumYStep where n  NumStep where n NumXStep where n  NumType-forAutomatic default  NumType-forBuildYourOwn Inference app variables  NumXZoom where n NumYZoom where n Alpha Conf  Mean1 Mean1Mean2  Mean2  Pooled-for pooled  Pooled-for not pooled defaultPooled Difference of two means or two proportions, sets CPYR Finance appVariables NbPmt NbPmtIPYR PMTV Solver app Linear Solver app variablesTriangle AngleB SideCAngleA AngleC Settings Home Time HComplexDate Language Bits EntryBase Signed AAngle SymbolicSetup 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 Vector One-dimensional array of real or Matrix Two-dimensional array of real orRecord using the Program Editor Symbolic, and Symbolic Setup 590 Calculator not responding TroubleshootingTo reset If the calculator does not turn on Operating limits Status messages Proper syntax Correct. Look up the functionName in the index to find its Apps, matrices, lists, notes, or 594 Modifications Product regulatory informationFederal Communications Commission notice Cables 596 European Union Regulatory Notice 598 Parliament and the Council. a chemical information ChemicalSubstances 600 Index 370-371 Menu 324-347 settings 30, 55 viewCAS 54 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