Polynomial | HP 33s Scientific manual

Program Lines:		Description
(In RPN mode)

	! %	First initial guess.
-+.		Second initial guess.
	/	Specifies routine to solve.
	# %	Solves for a real root.
!		Gets synthetic division coefficients for next lower order
		polynomial.

Generates DIVIDE BY 0 error if no real root found. Checksum and length: 15FE 54

º65¸ ª -+. ! ! ! º µ . º6@ º ! @ ! !. ¶ !-

Starts quadratic solution routine. Exchanges a0 and a1.

a1/2.

–a1/2.

Saves – a1/2.

Stores real part if complex root. (a1/2)2.

a0.

(a1/2)2 – ao. Initializes flag 0. Discriminant (d) < 0

Sets flag 0 if d < 0 (complex roots).

Stores imaginary part if complex root. Complex roots?

Returns if complex roots.

Calculates – a1/2	–	d
Calculates – a1/2	+	d

Mathematics Programs 15–23

Page 245

Image 245

Contents

Hp 33s scientific calculator Printing History Contents Clearing the X-Register RPN The Automatic Memory Stack Storing Data into Variables How You Can Use Equations Summary of Equation Operations Fractions in Programs Solving an Equation Complex Stack Complex Operations ContentsFor More Information Accuracy of Integration Programming Data Input and Output 12-4 Entering a Program 12-5 12-412-6 12-7 13-2 13-113-3 Branching GTO 13-4 Part 3. Appendixes and Reference Managing Calculator Memory ContentsVector Operations 15-1 15-12 Round-Off Error Contents Resetting the Calculator Clearing MemoryDisabling Operations Neutral Operations About ALG Conditions That Prolong Calculation Time UnderflowHow the Integral Is Evaluated Page Basic Operation PartPage Getting Started Adjusting Display ContrastImportant Preliminaries Turning the Calculator On and Off 2Getting Started Highlights of the Keyboard and DisplayShifted Keys Cursor Keys Alpha Keys 4Getting Started Silver Paint KeysBackspacing and Clearing Are described in Using Menus on page 1-7. If Keyboard-entry modeEquation-entry mode ¾ when number entry is complete 6Getting Started HP 33s Menus Chapter Name Using MenusProgramming Instructions Numeric Functions 8Getting Started Other functionsDescription To use a menu function KeysDisplay Exiting Menus To select RPN mode RPN mode ALG modeTo select ALG mode RPN and ALG Keys First Line Second Line Display and Annunciators 12Getting Started HP 33s Annunciators Meaning Chapter2 3 RAD or §,¨ Making Numbers Negative Keying in NumbersExponents of Ten Keys Display Description Other Exponent Functions Understanding Digit EntryKeying in Exponents of Ten Range of Numbers and Overflow Doing ArithmeticKeys Display 16Getting Started Two-Number Functions One-Number Functions, \, , Qor T Key in the number. You dont need to press ‘ Periods and Commas in Numbers Controlling the Display Format‘3 z D, , \, ,Q Scientific Format Number of Decimal PlacesFixed-Decimal Format % 20Getting Started SHOWing Full 12-Digit PrecisionEngineering Format ALL Format KeysDisplayDescription FractionsEntering Fractions 22Getting Started DisplayDescription MessagesDisplaying Fractions Checking Available Memory Calculator MemoryClearing All of Memory 24Getting Started RPN The Automatic Memory Stack RPN The Automatic Memory StackWhat the Stack Is 2RPN The Automatic Memory Stack X and Y-Registers are in the DisplayClearing the X-Register Rµ Roll Up Reviewing the Stack¶ Roll Down 4RPN The Automatic Memory Stack Arithmetic How the Stack Does ItExchanging the X- and Y-Registers in the Stack Lost How Enter Works How Clear x Works Using a Number Twice in a Row6RPN The Automatic Memory Stack Filling the stack with a constant Last X Register , \, , Qor T Correcting Mistakes with Last8RPN The Automatic Memory Stack Wrong One-Number Function › Reusing Numbers with LastMistake 96.704 + 10RPN The Automatic Memory Stack Work from the Parentheses Out Chain Calculations in RPN mode 12RPN The Automatic Memory Stack Exercises SolutionOrder of Calculation 16.3805x5 = 181.0000 ‘14 ‘ More Exercises14RPN The Automatic Memory Stack ⋅ 0.8 ⎟ 12.5 − 0.73 = Page Storing Data into Variables Storing Data into Variables 2Storing Data into Variables Storing and Recalling NumbersTo recall a copy of a number from a variable to the display Example Storing Numbers To review the values at any or all non-zero variables Viewing a Variable without Recalling ItReviewing Variables in the VAR Catalog Arithmetic with Stored Variables Clearing VariablesStorage Arithmetic 4Storing Data into Variables Result 3 That is, x Recall Arithmetic 6Storing Data into Variables Exchanging x with Any VariableLzE Variable Page Real-Number Functions Real-Number FunctionsExponential and Logarithmic Functions Quotient and Remainder of Division Power FunctionsTo Calculate Press 2Real-Number Functions To Calculate Press Result TrigonometryEntering π Trigonometric Functions Setting the Angular ModeOption Description Annunciator 4Real-Number Functions Programming Note NzR Percentage Functions Hyperbolic Functions6Real-Number Functions ‘x Q 16.12 ‘ 15.76 T . 8Real-Number Functions Physics ConstantsConst Menu Items Description Value To insert a constant Conversion FunctionsItems Description Value To convert between rectangular and polar coordinates Coordinate Conversions10Real-Number Functions Example Conversion with Vectors Example Polar to Rectangular Conversion 12Real-Number Functions Time ConversionsTo convert between decimal fractions and minutes-seconds Example Converting Time Formats Unit Conversions Angle ConversionsTo Convert Press Displayed Results To convert an angle between degrees and radians Factorial Probability FunctionsGamma Probability Display KeysExample Combinations of People 16Real-Number Functions Parts of Numbers Names of Functions Page Entering Fractions Fractions 2Fractions Fractions in the DisplayDisplay Rules Entered Value Internal Value Displayed Fraction Accuracy Indicators 4Fractions Changing the Fraction DisplayLonger Fractions Choosing a Fraction Format Setting the Maximum Denominator To Get This Fraction Format Change These Flags Examples of Fraction DisplaysFraction How 2.77 Is Displayed Format 6Fractions Denominator Fixed Rounding FractionsFraction Number Entered and Fraction Displayed Format ¼ 8Fractions Fractions in Equations Fractions in Programs Page How You Can Use Equations Entering and Evaluating EquationsEntering and Evaluating Equations Example Calculating with an Equation 2Entering and Evaluating Equations ZNzZLL Key Operation Enters and leaves Equation modeSummary of Equation Operations Variables in Equations Entering Equations into the Equation List4Entering and Evaluating Equations To enter an equation Functions in Equations Numbers in Equations Parentheses in Equations Displaying and Selecting EquationsLR d ZLC z ——— Editing and Clearing EquationsTo view a long equation To select an equation 8Entering and Evaluating Equations Evaluating Equations Types of Equations 10Entering and Evaluating Equations Type of Equation Result for ‘Fx ¼ To evaluate an equation Example Evaluating an Equation with Enter Using Enter for Evaluation Responding to Equation Prompts Using XEQ for Evaluation12Entering and Evaluating Equations Example Evaluating an Equation with XEQ Operator Precedence Syntax of Equations‘5 g „ To display digits hidden by the prompt, press 14Entering and Evaluating Equations Order Operation ExampleEquations Meaning Σxy Equation Functions 16Entering and Evaluating Equations Operation Equation functionExample Perimeter of a Trapezoid Perimeter = a + b + h Cos π / n HLA ’.25 zLN zLD 2 zR NqLN `qONqLN `‘Example Area of a Polygon Area = Verifying Equations Syntax Errors18Entering and Evaluating Equations Example Checksum and Length of an Equation Solving an Equation Solving EquationsSolving Equations Markup ⋅ Cost = Price ZLT › LD dLV2Solving Equations Example Solving the Equation of Linear Motion Value ZL T HL P z4Solving Equations Example Solving the Ideal Gas Law Equation Understanding and Controlling Solve LV q 6Solving Equations Verifying the Result Choosing Initial Guesses for Solve Interrupting a Solve Calculation 8Solving Equations Example Using Guesses to Find a Root ZL H 40 H 10Solving Equations For More Information Page Integrating Equations Integrating Equations 2Integrating Equations Integrating Equations ≥ FNJ0 x = π1 ≥0π cos x sin t dt Value ≥ 0π f t = ≥ t 4Integrating EquationsExample Sine Integral Accuracy of Integration Interpreting Accuracy Specifying Accuracy6Integrating Equations Example Specifying Accuracy Example Changing the Accuracy Its uncertainty indicates 8Integrating Equations Complex Stack Operations with Complex Numbers+ iy To enter a complex number To do an operation with one complex number Complex Operations2Operations with Complex Numbers To do an arithmetic operation with two complex numbers Functions for One Complex Number, z To Calculate Press 4Operations with Complex Numbers ‘2 ‘ ‘4 2 5 ‘ 2 3 ‘ Using Complex Numbers in Polar Notation‘2 Example Vector Addition 6Operations with Complex Numbers Operations with Complex Numbers Page Base Menu Base Conversions and ArithmeticMenu label Description Base Conversions and Arithmetic 10-2Base Conversions and Arithmetic Arithmetic in Bases 2, 8, Keys Display Negative Numbers Representation of Numbers˜˜ 10-4Base Conversions and Arithmetic 7FFFFFFFF Range of Numbers 10-6Base Conversions and Arithmetic Windows for Long Binary Numbers Statistical Operations Statistical OperationsEntering Statistical Data Entering One-Variable Data Correcting Errors in Data EntryEntering Two-Variable Data 11-2Statistical Operations ‘20 Initial x, y Corrected x, y400 Mean Statistical CalculationsStatistics Menus Key Description 11-4Statistical Operations · Example Weighted Mean Two VariablesPrice per Part Number of Parts y Population Standard Deviation Sample Standard DeviationUº 11-6Statistical Operations σº Linear RegressionKeys DisplayDescription Linear Regression Menu Example Curve Fitting 11-8Statistical OperationsNitrogen Applied Grain Yield 70, y Limitations on Precision of Data Summation Statistics Summation Values and the Statistics Registers11-10Statistical Operations Normalizing Close, Large Numbers Statistics Registers in Calculator Memory Access to the Statistics RegistersExample Viewing the Statistics Registers # ™ ´º¸/ ™ ´¸/ ™ ´º/ ™ ´¸/ ™ ´º/ ‡ 11-12Statistical Operations Programming Page Simple Programming RPN mode 5 !Nz ALG mode 5 !zN‘Simple Programming Example a Simple Program RPN mode RPN mode ALG modeDisplay Description 12-2Simple Programming Designing a Program Selecting a ModeProgram Boundaries LBL and RTN Program Labels Data Input and Output Using RPN, ALG and Equations in ProgramsStrengths of RPN Operations ALG Operations To enter a program into memory Entering a Program To enter an equation in a program line Keys That Clear12-6Simple Programming Example Entering a Labeled Program RPN modeFunction Names in Programs ZLR HN 12-8Simple Programming Example Entering a Program with an Equation Running a Program Testing a ProgramExecuting a Program XEQ NzX 12-10Simple Programming Example Testing a Program @ Using Input for Entering DataEntering and Displaying Data To use the Input function in a program 12-12Simple Programming To respond to a prompt Using View for Displaying Data Example INPUT, VIEW, and Messages in a Program Using Equations to Display Messages12-14Simple Programming LR z › LH NzLR ›p = 2π R2 + 2π RH = 2π R R + H 12-16Simple Programming Displaying Information without Stopping Stopping or Interrupting a Program Error StopsProgramming a Stop or Pause STOP, PSE Interrupting a Running Program 12-18Simple Programming Editing a ProgramTo delete a program line To insert a program line Viewing Program Memory Program Memory Catalog of Programs MEM Memory UsageClearing One or More Programs 12-20Simple Programming To clear all programs from memory Checksum Nonprogrammable Functions Selecting a Base Mode in a ProgramProgramming with Base V Polynomial Expressions and Horners Method Decimal mode set Hexadecimal mode setNumbers Entered in Program Lines Ax4 + Bx3 + Cx2 + Dx + E 12-24Simple Programming Keys Display ALG mode‰X Checksum and length E41A Page Programming Techniques Programming TechniquesRoutines in Programs 13-2Programming Techniques Calling Subroutines XEQ, RTN Example a Nested Subroutine Nested Subroutines A2 + B2 Branching GTO13-4Programming Techniques Programmed GTO Instruction Using GTO from the Keyboard 13-6Programming Techniques Conditional Instructions Test Menus Tests of Comparison x?y, x?0 Flags Program Lines Description RPN mode13-8Programming Techniques !- % ! ! ! º¸@ ! Set FlagFraction-Control Flags Status Clear 13-10Programming Techniques Annunciators for Set Flags Using FlagsFlags Menu Menu Key Description 13-12Programming Techniques Example Using Flags $ @ $ $ @ $ Program Lines Description RPN mode Example Controlling the Fraction Display 13-14Programming Techniques Program Lines Description 13-16Programming Techniques Loops . ! º6¸@ ! #$ ! Conditional Loops GTO ! ! Loop-Control Number Loops with Counters DSE, ISG13-18Programming Techniques $ $ $ ! $ 13-20Programming Techniques Indirectly Addressing Variables and LabelsVariable If i contains Then i will address Indirect Address 13-22Programming Techniques Program Control withExample Choosing Subroutines With ! L Program lines If i holds Then XEQi calls- L & %1L2 Example Loop Control With 13-24Programming Techniques Equations with 1L2 L Page Solving a Program Solving and Integrating ProgramsSolving and Integrating Programs To solve a programmed function V= N x R x T Example Program Using ALG14-2Solving and Integrating Programs Pressure ⋅ volume. Pressure ⋅ volume 14-4Solving and Integrating Programs Example Program Using EquationLP z LV ’ LN z LR z LT ‘ @ @ ‘10 !@ # / 14-6Solving and Integrating Programs Using Solve in a Program/ label #variable Example Solve in a Program To integrate a programmed function Program Lines In RPN modeIntegrating a Program To write a program for ≥ FN 14-8Solving and Integrating Programs / label Using Integration in a ProgramSin Example ≥ FN in a Program 14-10Solving and Integrating Programs≥ G variable Restrictions on Solving and Integrating Page Vector Operations Mathematics ProgramsMathematics Programs = R cosP = arctan V1 = X i + Y j + Z k V2=U i + V j + W k 15-2Mathematics Programs= XU + YV + ZW Program Listing X2 + Y2 + Z2 and P 15-4Mathematics Programs Program Lines Description ALG mode Goes to the vector-addition routine 15-6Mathematics Programs Program Instructions Flags UsedRemarks Variables Used 15-8Mathematics Programs XR @ 15-10Mathematics Programs 07 g !@ 125 g @ AX + DY + GZ = J BX + EY + HZ = K CX + FY + IZ = L Solutions of Simultaneous Equations15-12Mathematics Programs % 15-14Mathematics Programs Mathematics Programs 15-16Mathematics Programs Flags Used Scratch 15-18Mathematics Programs @ 15-20Mathematics Programs Polynomial Root Finder@ @ @ X2 + J + Lx + K + M = Where J = a3/2 = y0 /2X2 + J Lx + K M = ⋅ the sign of JK a1/2 15-22Mathematics Programs Polynomial ! 15-24Mathematics Programs B0 =a04a0 a32 a12 Checksum and length C7A6B2= -a2 B1 = a3a1 4a0 JK. a1 15-26Mathematics Programs + L + M 15-28Mathematics Programs Order Terms and Coefficients 15-30Mathematics Programs %/ 15-32Mathematics Programs Coordinate Transformations Old coordinate System 15-34Mathematics Programs Checksum and length 8C82 Remark 15-36Mathematics Programs Ÿ @ 15-38Mathematics Programs Statistics Programs Statistics ProgramsCurve Fitting 16-2Statistics Programs = B + MIn Description 16-4Statistics Programs #$ #$ 16-6Statistics Programs 16-8Statistics Programs %@ 37.9 g &@ XS%@ 40.5 g &@ value 104.5 g %@ 38.6 g &@ / / %@ 16-10Statistics Programs/ Normal and Inverse-Normal Distributions Logarithmic Exponential Power 16-12Statistics Programs Function ª º ª -+. H % ! 16-14Statistics Programs XS@ Variable used temporarily to pass the value S ⋅ 2 π toInverse program 16-16Statistics Programs 2f − Grouped Standard Deviation 16-18Statistics Programs Updates ƒxi 2fi in register Increments or decrements N 16-20Statistics Programs / Group%@ @ XU/ %@ 13 g @ / %@ 16-22Statistics Programs%@ %@ Miscellaneous Programs and Equations Miscellaneous Programs and EquationsTime Value of Money QLI ›LF z …LN `›LI 17-2Miscellaneous Programs and Equations Solve instructions 17-4Miscellaneous Programs and Equations Keys Display Description RPN modešas Retains 5750 in B calculates monthly interest rate 17-6Miscellaneous Programs and Equations Prime Number Generator LBL Y #$ 17-8Miscellaneous Programs and Equations No test is made to ensure that the input is greater than 17-10Miscellaneous Programs and Equations Appendixes and Reference Page Support, Batteries, and Service A-1 Support, Batteries ServiceCalculator Support Answers to Common Questions Changing the Batteries 2Support, Batteries, and ServiceEnvironmental Limits To install batteries Support, Batteries, and Service A-3 4Support, Batteries, and Service Testing Calculator OperationDo not mutilate, puncture, or dispose of batteries Fire. The batteries can burst or explode ™Ÿ˜—š Support, Batteries, and Service A-5Self-Test 6Support, Batteries, and Service Warranty Europe Country Telephone numbers ServiceSupport, Batteries, and Service A-7 America Country Telephone numbers 8Support, Batteries, and ServiceAsia Pacific Country Telephone numbers Canada Support, Batteries, and Service A-9Regulatory Information Japan 10Support, Batteries, and Service User Memory and the Stack User Memory and the StackManaging Calculator Memory 2User Memory and the Stack Resetting the Calculator Category DefaultClearing Memory Disabling Operations Status of Stack LiftNeutral Operations 4User Memory and the Stack EQN FDISP Vlabel nnnn € θ ,r Status of the Last X Register6User Memory and the Stack ALG Summary C-1 ALG SummaryAbout ALG Doing Two-number Arithmetic in ALG Power FunctionsSimple Arithmetic 2ALG Summary ALG Summary C-3 Percentage Calculations‘27 Q… Quotient and Remainder Of Division Permutations and Combinations16.12 T 4ALG Summary ALG Summary C-5 Keys Display Description 6ALG Summary Reviewing the Stack ALG Summary C-7 Coordinate Conversions 8ALG Summary Integrating an EquationQ3 z ALG Summary C-9 Operations with Complex NumbersTo view the result of complex operations Complex Operations 10ALG Summary 2 ›3 `` Q2 › ALG Summary C-11 ºy4 ÃË2Ë5 ¹cº  ºy3 ÃË  12ALG Summary Initial x, y Corrected x, y ALG Summary C-13 20 Page More about Solving D-1 More about SolvingHow Solve Finds a Root Function Whose Roots Can Be Found 2More about Solving Example An Equation With One Root Interpreting ResultsMore about Solving D-3 Example An Equation with Two Roots 4More about Solving / More about Solving D-5/ -%. `’1.5 LX 6More about Solving Example Discontinuous Function More about Solving D-7 − 1= 8More about Solving When Solve Cannot Find a Root Example a Relative Minimum More about Solving D-9 Example An Asymptote 10More about Solving #LX q LX ›3 ``… ⎟ x + 0.3 − 0.5 =More about Solving D-11 Example Find the root of the equation Example a Local Flat Region 12More about Solving!1%ª1%-22 More about Solving D-13 Round-Off Error 14More about Solving Underflow More about Integration More about IntegrationHow the Integral Is Evaluated 2More about Integration Conditions That Could Cause Incorrect Results ≥0∞ xe −x dx LX ` LX z‡ 4More about Integration More about Integration 6More about Integration Conditions That Prolong Calculation Time . 8More about Integration More about Integration Page Messages F-1 Messages Or program. This might take a while 2Messages # variable Messages F-3 Self-Test Messages 4Messages Operation Index G-1 Operation IndexName Keys and Description j ˜or —h 2Operation Index Polar to rectangular coordinates Operation Index G-3 4Operation Index P Operation Index G-5 M GComplex Change sign 6Operation Index›Complex …Complex Subtraction Operation Index G-7 RHyperbolic 8Operation IndexVRadians to degrees DSE variable Mvariable Natural exponential Operation Index G-9Wlabel ?Fractional part GTO label Vlabel 10Operation Indexlabel Nnnn Operation Index G-11 ”I”Input variable ‰variable Integer part ISG variable Lvariable LBL label •label 12Operation IndexNatural logarithm Common logarithm Permutations of n items Operation Index G-13FPause WDegrees to radians 14Operation Index Operation Index G-15 16Operation Index Operation Index G-17 18Operation Index ≠0? 13-7 Operation Index G-19If x=0, skips the next program Line ≤0? 13-7 11-10 Given an x-value 20Operation Index Power Returns y raised to the xth power Index-1 Index Index-2 Index-3 Index-4 Index-5 Index-6 Index-7 Index-8 Index-9 Index-10 Index-11 RPN Index-12 Index-13 View Index-14 Index-15

HP 33s Scientific manual Polynomial

Models: 33s Scientific

Program Lines:

Description

(In RPN mode)

polynomial.

Mathematics Programs 15–23