DuckieDai Cubic Inequality Solver Python Program

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algebra · MIT License

Overview

Solve a cubic inequality by finding its rational zeros with their multiplicities, then reading the sign of each interval.

Owner-tested on a TI calculator
Version 1.0.0
3648 bytes
No imports

Download wcsol.py Read the source How to install

Before you run it

TI-84 Plus CE Python · No calculator OS or Python App version has been verified.
TI Connect CE .py transfer to the Python App; the owner's transfer details were not recorded
The leading coefficient a is nonzero.
Every zero of the cubic is rational.
Zeros are found with the Rational Zero Theorem, so a cubic with an irrational or complex zero reports Could not factor.

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Source code

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"""DuckieDai Cubic Inequality 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 factors(n):
    n=abs(n)
    if n==0:
        return [0]
    f=[]
    for i in range(1,n+1):
        if n%i==0:
            f.append(i)
    return f


def frac(x):
    for d in range(1,101):
        n=round(x*d)
        if abs(x-n/d)<0.000001:
            if d==1:
                return str(n)
            return str(n)+"/"+str(d)
    return str(round(x,4))


def divide(c,r):
    q=[c[0]]
    for i in range(1,len(c)-1):
        q.append(c[i]+q[-1]*r)
    rem=c[-1]+q[-1]*r
    return q,rem


duckiedai_intro("Cubic Inequality")

a=int(input("a: "))
b=int(input("b: "))
c=int(input("c: "))
d=int(input("d: "))

print("1 >0")
print("2 >=0")
print("3 <0")
print("4 <=0")
op=input("Choice: ")

coef=[a,b,c,d]

# Rational Zero Theorem candidates
cand=[]

if d==0:
    cand.append(0)

p=factors(d)
q=factors(a)

for x in p:
    for y in q:
        if y!=0:
            r=x/y
            if r not in cand:
                cand.append(r)
            if -r not in cand:
                cand.append(-r)

roots=[]
mult=[]

# Find roots and multiplicities
for r in cand:
    count=0

    while len(coef)>1:
        new,rem=divide(coef,r)

        if abs(rem)<0.000001:
            count+=1
            coef=new
        else:
            break

    if count>0:
        roots.append(r)
        mult.append(count)

if len(coef)>1:
    print("Could not factor")
else:

    # sort roots
    for i in range(len(roots)):
        for j in range(i+1,len(roots)):
            if roots[i]>roots[j]:
                roots[i],roots[j]=roots[j],roots[i]
                mult[i],mult[j]=mult[j],mult[i]

    n=len(roots)

    print("Roots:")
    for i in range(n):
        print(frac(roots[i]),"mult",mult[i])

    # Interval signs
    signs=[0]*(n+1)

    if a>0:
        signs[n]=1
    else:
        signs[n]=-1

    for i in range(n-1,-1,-1):
        signs[i]=signs[i+1]

        if mult[i]%2==1:
            signs[i]=-signs[i]

    if op=="1" or op=="2":
        want=1
    else:
        want=-1

    include=(op=="2" or op=="4")

    print("Solution:")

    found=False

    for i in range(n+1):

        if signs[i]==want:
            found=True

            if i==0:
                left="-inf"
                lb="("
            else:
                left=frac(roots[i-1])
                if include:
                    lb="["
                else:
                    lb="("

            if i==n:
                right="inf"
                rb=")"
            else:
                right=frac(roots[i])
                if include:
                    rb="]"
                else:
                    rb=")"

            print(lb+left+","+right+rb)

    # Include isolated zeros for >= or <=
    if include:
        for i in range(n):
            if signs[i]!=want and signs[i+1]!=want:
                found=True
                s=frac(roots[i])
                print("["+s+","+s+"]")

    if not found:
        print("EMPTY SET")

"""DuckieDai Cubic Inequality 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 factors(n):
n=abs(n)
if n==0:
return [0]
f=[]
for i in range(1,n+1):
if n%i==0:
f.append(i)
return f
def frac(x):
for d in range(1,101):
n=round(x*d)
if abs(x-n/d)<0.000001:
if d==1:
return str(n)
return str(n)+"/"+str(d)
return str(round(x,4))
def divide(c,r):
q=[c[0]]
for i in range(1,len(c)-1):
q.append(c[i]+q[-1]*r)
rem=c[-1]+q[-1]*r
return q,rem
duckiedai_intro("Cubic Inequality")
a=int(input("a: "))
b=int(input("b: "))
c=int(input("c: "))
d=int(input("d: "))
print("1 >0")
print("2 >=0")
print("3 <0")
print("4 <=0")
op=input("Choice: ")
coef=[a,b,c,d]
# Rational Zero Theorem candidates
cand=[]
if d==0:
cand.append(0)
p=factors(d)
q=factors(a)
for x in p:
for y in q:
if y!=0:
r=x/y
if r not in cand:
cand.append(r)
if -r not in cand:
cand.append(-r)
roots=[]
mult=[]
# Find roots and multiplicities
for r in cand:
count=0
while len(coef)>1:
new,rem=divide(coef,r)
if abs(rem)<0.000001:
count+=1
coef=new
else:
break
if count>0:
roots.append(r)
mult.append(count)
if len(coef)>1:
print("Could not factor")
else:
# sort roots
for i in range(len(roots)):
for j in range(i+1,len(roots)):
if roots[i]>roots[j]:
roots[i],roots[j]=roots[j],roots[i]
mult[i],mult[j]=mult[j],mult[i]
n=len(roots)
print("Roots:")
for i in range(n):
print(frac(roots[i]),"mult",mult[i])
# Interval signs
signs=[0]*(n+1)
if a>0:
signs[n]=1
else:
signs[n]=-1
for i in range(n-1,-1,-1):
signs[i]=signs[i+1]
if mult[i]%2==1:
signs[i]=-signs[i]
if op=="1" or op=="2":
want=1
else:
want=-1
include=(op=="2" or op=="4")
print("Solution:")
found=False
for i in range(n+1):
if signs[i]==want:
found=True
if i==0:
left="-inf"
lb="("
else:
left=frac(roots[i-1])
if include:
lb="["
else:
lb="("
if i==n:
right="inf"
rb=")"
else:
right=frac(roots[i])
if include:
rb="]"
else:
rb=")"
print(lb+left+","+right+rb)
# Include isolated zeros for >= or <=
if include:
for i in range(n):
if signs[i]!=want and signs[i+1]!=want:
found=True
s=frac(roots[i])
print("["+s+","+s+"]")
if not found:
print("EMPTY SET")

Filename: wcsol.py
Size: 3648 bytes
SHA-256: 793d3d805b839c643fe2a3c4892559264ec1224cdb2870f5c0bda9bb18a48513

Usage

Inputs

Integer coefficients a, b, c, and d for ax^3 + bx^2 + cx + d
One menu choice: 1 greater than zero, 2 greater than or equal, 3 less than zero, 4 less than or equal

Outputs

Each rational zero as a whole number or fraction, with its multiplicity
Solution intervals, including single points for the or-equal choices when a repeated zero touches the axis
EMPTY SET when nothing satisfies the inequality
Could not factor when the cubic does not split completely into rational zeros

Units: Polynomial coefficients; no physical units.

Assumptions and limitations

Assumptions

The leading coefficient a is nonzero.
Every zero of the cubic is rational.

Constraints

Zeros are found with the Rational Zero Theorem, so a cubic with an irrational or complex zero reports Could not factor.
A zero is accepted when its synthetic-division remainder is within 0.000001 of zero.
The search tries every factor of d over every factor of a, so very large coefficients take longer.

Known failures

A cubic such as x^3 - 2 has no complete rational factoring and reports Could not factor.
An a value of zero is not a cubic and is outside the supported input domain.
A menu choice other than 1 to 4 is treated as choice 3.
Non-integer input uses the calculator Python input error path.

Compatibility and review

Review status: Owner-tested on a TI calculator
Tested on: Owner reports personally testing this program on a TI-84 Plus CE Python calculator; the test date, OS version, and Python App version were not recorded
What happened: Owner reported pass on the calculator before the DuckieDai opening screen and website line were added. The steps after the opening screen are unchanged and were compared with the owner's file on desktop; this exact file has not yet been rerun on a calculator.
Dependencies: No imports
Suggested calculator name: WCSOL — 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. This release has no verified calculator OS or Python App version; treat transfer and execution as unverified until independently tested.
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. WCSOL 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

1.0.0 — current version, published 2026-10-03. Download this reviewed version

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