DuckieDai Quartic Zero Tester Python Program

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algebra · MIT License

Overview

Test a proposed zero of a quartic and show the cubic quotient when synthetic division has zero remainder.

Usage

Inputs

Quartic coefficients a, b, c, d, and e
Proposed zero, as a number or fraction

Outputs

Zero-test result and remainder
Cubic quotient coefficients when the remainder is zero

Units: Inputs represent a quartic polynomial a*x^4 + b*x^3 + c*x^2 + d*x + e.

Assumptions and limitations

Assumptions

Decimal remainders within 1E-7 display as zero.

Constraints

Fractions must have a nonzero denominator.

Known failures

Floating-point rounding can classify values close to zero differently than exact symbolic arithmetic.

Compatibility and review

Review status: Tested on a TI calculator
Tested on: Creator-owned TI-84 Plus CE Python calculator; exact .py transferred and launched individually
What happened: Passed: creator tested the exact program on a personal TI 84 Plus CE Python calculator and confirmed the quartic zero test and cubic quotient workflow.
Dependencies: No imports
Suggested calculator name: P2Q4 — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Browser preview

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Simulation boundary: This preview uses a reviewed browser adapter. It does not execute the downloaded Python and does not prove TI-Python or calculator compatibility.

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Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

"""DuckieDai Quartic Zero Tester for TI-84 Plus CE Python."""


def duckiedai_intro(program_name, wait=True):
    title = program_name[:16]
    empty = 16 - len(title)
    left = empty // 2
    right = empty - left

    print("+----------------------+")
    print("|   " + " " * left + title + " " * right + "   |")
    print("|                      |")
    print("|       __             |")
    print("|   ___(o )>  quack!   |")
    print("|   \\ <_. )           |")
    print("|    `---'             |")
    print("|     by DuckieDai     |")
    print("+----------------------+")
    print("Loading...")

    if wait:
        input("Press enter to start ")
        print("\n" * 8)


def clear_screen():
    print("\n" * 8)


def clean_num(n):
    if abs(n - round(n)) < 0.0000001:
        return int(round(n))
    return round(n, 6)


def number(prompt):
    while True:
        try:
            text = input(prompt)

            if "/" in text:
                parts = text.split("/")

                if len(parts) != 2:
                    raise ValueError

                top = float(parts[0])
                bottom = float(parts[1])

                if bottom == 0:
                    print("Cannot divide by 0")
                    continue

                return top / bottom

            return float(text)

        except ValueError:
            print("Enter a number")
            print("or fraction")


def run_test():
    clear_screen()

    print("ENTER QUARTIC")
    print("ax^4+bx^3+cx^2")
    print("+dx+e")
    print("")

    a = number("x^4: ")
    b = number("x^3: ")
    c = number("x^2: ")
    d = number("x: ")
    e = number("Const: ")

    print("")
    zero = number("Test zero: ")

    first = a
    second = b + first * zero
    third = c + second * zero
    fourth = d + third * zero
    remainder = e + fourth * zero

    if abs(remainder) < 0.0000001:
        remainder = 0

    clear_screen()

    print("ZERO TEST")
    print("---------")
    print("Test:", clean_num(zero))
    print("R:", clean_num(remainder))
    print("")

    if remainder == 0:
        print("TRUE!")
        print("IT IS A ZERO")
    else:
        print("FALSE")
        print("NOT A ZERO")

    input("\nPress enter ")

    if remainder != 0:
        return

    clear_screen()

    print("CUBIC QUOTIENT")
    print("--------------")
    print(clean_num(first), "x^3")
    print(clean_num(second), "x^2")
    print(clean_num(third), "x")
    print(clean_num(fourth))

    print("")
    print("Use these in")
    print("Cubic Zero Tester")


duckiedai_intro("Quartic Zero")

while True:
    run_test()

    print("")
    again = input("Again? y/n: ")

    if again.lower() != "y":
        break


clear_screen()
print("DuckieDai says: done!")

"""DuckieDai Quartic Zero Tester for TI-84 Plus CE Python."""
def duckiedai_intro(program_name, wait=True):
title = program_name[:16]
empty = 16 - len(title)
left = empty // 2
right = empty - left
print("+----------------------+")
print("| " + " " * left + title + " " * right + " |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n" * 8)
def clear_screen():
print("\n" * 8)
def clean_num(n):
if abs(n - round(n)) < 0.0000001:
return int(round(n))
return round(n, 6)
def number(prompt):
while True:
try:
text = input(prompt)
if "/" in text:
parts = text.split("/")
if len(parts) != 2:
raise ValueError
top = float(parts[0])
bottom = float(parts[1])
if bottom == 0:
print("Cannot divide by 0")
continue
return top / bottom
return float(text)
except ValueError:
print("Enter a number")
print("or fraction")
def run_test():
clear_screen()
print("ENTER QUARTIC")
print("ax^4+bx^3+cx^2")
print("+dx+e")
print("")
a = number("x^4: ")
b = number("x^3: ")
c = number("x^2: ")
d = number("x: ")
e = number("Const: ")
print("")
zero = number("Test zero: ")
first = a
second = b + first * zero
third = c + second * zero
fourth = d + third * zero
remainder = e + fourth * zero
if abs(remainder) < 0.0000001:
remainder = 0
clear_screen()
print("ZERO TEST")
print("---------")
print("Test:", clean_num(zero))
print("R:", clean_num(remainder))
print("")
if remainder == 0:
print("TRUE!")
print("IT IS A ZERO")
else:
print("FALSE")
print("NOT A ZERO")
input("\nPress enter ")
if remainder != 0:
return
clear_screen()
print("CUBIC QUOTIENT")
print("--------------")
print(clean_num(first), "x^3")
print(clean_num(second), "x^2")
print(clean_num(third), "x")
print(clean_num(fourth))
print("")
print("Use these in")
print("Cubic Zero Tester")
duckiedai_intro("Quartic Zero")
while True:
run_test()
print("")
again = input("Again? y/n: ")
if again.lower() != "y":
break
clear_screen()
print("DuckieDai says: done!")

Filename: P2Q4.py
Size: 2757 bytes
SHA-256: 787e375cae1455448b49baf1011343e1fc64cb6a0643ea66865c3c9cf025409c

Transfer and launch

Confirm that your calculator is the Python-capable model named above. Check that its OS and Python App versions match the reviewed record.
Download the .py source above and verify its SHA-256 digest if your computer provides that option.
Use TI Connect CE to send the Python file to a compatible calculator. P2Q4 is a suggested name; you may choose another valid, unique calculator name.
Open the Python App, select the program, and check sample inputs before relying on other results.

Read the complete installation, launch, troubleshooting, and removal guide.

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Version history

1.0.0 — current version, published 2026-09-27. Download this reviewed version

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