DuckieDai Descartes' Rule Solver Python Program

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algebra · MIT License

Overview

Count sign changes in f(x) and f(-x) to list the possible numbers of positive and negative real zeros.

Tested on a TI calculator
Version 1.0.1
2612 bytes
No imports

Download DESCART.py Read the source How to install

Before you run it

TI-84 Plus CE Python · tested on OS 5.8.3, Python App 5.8.3.0048
TI Connect CE .py conversion to a Python AppVar in RAM; physically tested one program at a time
Zero coefficients are ignored when counting sign changes.
Descartes' Rule gives possible counts, not the actual zeros.
A negative degree is not a valid polynomial input.

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Source code

Download .py

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"""DuckieDai Descartes Rule Solver 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("| hiddenwordscanner.com|")
    print("+----------------------+")
    print("Loading...")
    if wait:
        input("Press enter to start ")
        print("\n" * 8)


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


def count_changes(values):
    signs = []
    for value in values:
        if value > 0:
            signs.append(1)
        elif value < 0:
            signs.append(-1)
    changes = 0
    for i in range(1, len(signs)):
        if signs[i] != signs[i - 1]:
            changes += 1
    return changes


def possible_zeros(changes):
    answers = []
    while changes >= 0:
        answers.append(changes)
        changes -= 2
    return answers


def show_answers(title, answers):
    clear_screen()
    print(title)
    print("-------------")
    for i in range(len(answers)):
        if i > 0:
            print(",", end="")
        print(answers[i], end="")
    print("")
    input("\nPress enter ")


def run_test():
    clear_screen()
    print("DESCARTES RULE")
    print("Enter polynomial")
    print("")
    degree = int(input("Degree: "))
    coeffs = []
    power = degree
    while power >= 0:
        if power == 0:
            value = float(input("Const: "))
        elif power == 1:
            value = float(input("x coef: "))
        else:
            value = float(input("x^" + str(power) + ": "))
        coeffs.append(value)
        power -= 1
    pos_changes = count_changes(coeffs)
    neg_coeffs = []
    power = degree
    for value in coeffs:
        neg_coeffs.append(-value if power % 2 == 1 else value)
        power -= 1
    neg_changes = count_changes(neg_coeffs)
    show_answers("POSITIVE ZEROS", possible_zeros(pos_changes))
    show_answers("NEGATIVE ZEROS", possible_zeros(neg_changes))
    clear_screen()
    print("SIGN CHANGES")
    print("------------")
    print("Positive:", pos_changes)
    print("Negative:", neg_changes)


duckiedai_intro("Descartes Rule")
while True:
    run_test()
    print("")
    if input("Again? y/n: ").lower() != "y":
        break
clear_screen()
print("DuckieDai says: done!")

"""DuckieDai Descartes Rule Solver 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("| hiddenwordscanner.com|")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n" * 8)
def clear_screen():
print("\n" * 8)
def count_changes(values):
signs = []
for value in values:
if value > 0:
signs.append(1)
elif value < 0:
signs.append(-1)
changes = 0
for i in range(1, len(signs)):
if signs[i] != signs[i - 1]:
changes += 1
return changes
def possible_zeros(changes):
answers = []
while changes >= 0:
answers.append(changes)
changes -= 2
return answers
def show_answers(title, answers):
clear_screen()
print(title)
print("-------------")
for i in range(len(answers)):
if i > 0:
print(",", end="")
print(answers[i], end="")
print("")
input("\nPress enter ")
def run_test():
clear_screen()
print("DESCARTES RULE")
print("Enter polynomial")
print("")
degree = int(input("Degree: "))
coeffs = []
power = degree
while power >= 0:
if power == 0:
value = float(input("Const: "))
elif power == 1:
value = float(input("x coef: "))
else:
value = float(input("x^" + str(power) + ": "))
coeffs.append(value)
power -= 1
pos_changes = count_changes(coeffs)
neg_coeffs = []
power = degree
for value in coeffs:
neg_coeffs.append(-value if power % 2 == 1 else value)
power -= 1
neg_changes = count_changes(neg_coeffs)
show_answers("POSITIVE ZEROS", possible_zeros(pos_changes))
show_answers("NEGATIVE ZEROS", possible_zeros(neg_changes))
clear_screen()
print("SIGN CHANGES")
print("------------")
print("Positive:", pos_changes)
print("Negative:", neg_changes)
duckiedai_intro("Descartes Rule")
while True:
run_test()
print("")
if input("Again? y/n: ").lower() != "y":
break
clear_screen()
print("DuckieDai says: done!")

Filename: DESCART.py
Size: 2612 bytes
SHA-256: e310762456142a6f658562caf34388eeabfb84a2c14e2a70a6bb199a1659018b

Usage

Inputs

Polynomial degree
Coefficient of every power from the leading term through the constant

Outputs

Possible positive-real-zero counts
Possible negative-real-zero counts
Sign-change totals

Units: Coefficients are real numbers.

Assumptions and limitations

Assumptions

Zero coefficients are ignored when counting sign changes.

Constraints

Descartes' Rule gives possible counts, not the actual zeros.

Known failures

A negative degree is not a valid polynomial input.

Compatibility and review

Review status: Tested on a TI calculator
Tested on: Owner-tested TI-84 Plus CE Python calculator; exact branded .py transferred and launched individually
What happened: Passed: owner tested the exact 1.0.1 branded source bytes on a TI 84 Plus CE Python calculator.
Dependencies: No imports
Suggested calculator name: DESCART — 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.

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. DESCART 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.

Availability does not mean a teacher, school, or exam permits this program. Follow the applicable rules.

Version history

1.0.1 — current version, published 2026-10-02. Download this reviewed version
1.0.0 — superseded by 1.0.1, published 2026-09-28. Download this reviewed version

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