Rational Polynomials Grapher

By Jangwon Lee

Introduction

This application summarizes polynomials provided by the user. It gives valuable information such as the x and y intercepts, inflection points, and concave/convex regions, and it also graphs the polynomial onto the GUI. It would be used by calc 1 and 2 students, as well as anyone who's curious about polynomials.

I created this project because I wanted to create tools that help students understand difficult mathematical concepts. I also wanted to try graphing arbitrary curves and felt that my calculus knowledge would help me do just that.

Features

The application will give take in a rational polynomial provided by the user and output both a graph and a summary of it. The application will return values in symbolic form when possible (i.e. fractions and square roots) and decimal approximations otherwise (up to 6 decimal places).

List of traits summarized:

• List of x intercepts (i.e. zeroes of the polynomial)
• The y intercept
• List of critical points (minimums, maximums, and neither)
• List of inflection points

There are other features that the users can enjoy, though mostly from the command line.

List of features:

• Evaluate the function at a specific point
• Integrate and derive the function
• Create and save new polynomials
• Load and modify existing polynomials
• Create polynomials from a list of zeroes (a different kind of object)
• Turn ordinary polynomials into factorized rational polynomials (if possible)

Restrictions

Here are some list of restrictions:

• User can specify rational values (i.e. natural numbers, fractions) as coefficients and are restricted to specifying for positive powers.
• When integrating a function, the user must specify the big C.
• While the application tries to show as much of the graph as possible, the users are limited to viewing a specific part of the graph and can neither pan nor zoom.

User Stories

List of User Stories:

• As a high school student, I want to see where all the x/y intercepts are, and in symbolic form when possible.
  • NOTE: the implementation doesn't yet support non-rational intercepts
• As a college student, I want to see all the critical and inflection points.
• As a college student, I want to just quickly get the derivative of the function.
• As a user, I want to just check the values of the function at specific point f(a).
• As a marker/tester, I want a list of polynomials loaded in by default that I could test with.
• As a student, I want to save a list of polynomials first before looking at each one.
• As a math tutor, I want to be able to quickly generate and plot the polynomials so that I can teach my students math concepts visually.
  • Drawing a lot of tiny lines used over implementing Bezier curves.

Instructions for Grader

• Visual component and summary are all included by default as long as the user loads in a polynomial.
• To create or load a polynomial, go under Files menu and Load from list (Ctrl-L) or create new (Ctrl-N). (LOAD FUNCTION)
• To save the one currently loaded, click Save to file (Ctrl-S). (SAVE FUNCTION)
• You can also add new terms to the existing polynomial in the Edit menu (Ctrl-T). (NOTE: this is your action 1)
• You can even view the derivative of current polynomial or reset it. (NOTE: these also some of the extra actions)

Phase 4: Task 2

Mon Nov 28 14:48:38 PST 2022
Created a new polynomial 0

Mon Nov 28 14:48:43 PST 2022
Created a new polynomial x^3 + x

Mon Nov 28 14:48:47 PST 2022
Added 2x^2 to polynomial (now x^3 + 2x^2 + x)

Mon Nov 28 14:48:52 PST 2022
Derived polynomial (now 3x^2 + 4x + 1)

Mon Nov 28 14:48:53 PST 2022
Reset polynomial to zero polynomial

Phase 4: Task 3

If I were to do any additional refactoring, I would start off by separating the math utilities class into a new MathUtils namespace. This would more explicitly separate out the concern so that the class files in model only need to worry about use cases directly related to the polynomial.

I would also reduce coupling by preventing the Roots class from calling functions in Polynomial class by creating a separate Factory class that creates the list of Roots. This new PolynomialsFactory class will also contain some functions from the Polynomial class.

Lastly, I would while also move out the many private classes in the PolynomialGuiApp into separate class files.

Additional Notes

While the project accurately fills a use case, it's still a prototype. Here are some ways I hope to be able to improve the project:

• Improve the string input parser such that it's able to more robustly handle user inputs.
  • Automatically accept decimals with finite decimal places and convert to fraction.
• Accept logs and exponential functions (new function type).
• Accept sins and cosines.
• Add integration support.