DuckieDai Inequality From Roots Python Program

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algebra · MIT License

Overview

Solve a polynomial inequality from zeros you already know: enter each distinct zero with its multiplicity and the leading sign, and read the solution intervals.

Owner-tested on a TI calculator
Version 1.0.0
2795 bytes
No imports

Download cubsolv.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
Every real zero of the polynomial is entered once with its correct multiplicity.
Any factor without real zeros is positive, so the leading sign describes the far right of the graph.
The program does not find zeros; use a zero finder or factoring first.

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Source code

Download .py

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"""DuckieDai Inequality From Roots 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 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 getroot():
    print("1 whole")
    print("2 fraction")
    t=input("Type: ")

    if t=="2":
        num=int(input("numerator: "))
        den=int(input("denominator: "))
        return num/den
    else:
        return float(input("value: "))


duckiedai_intro("Ineq From Roots")

n=int(input("Distinct roots: "))

roots=[]
mult=[]

for i in range(n):
    print("Root",i+1)
    roots.append(getroot())
    mult.append(int(input("multiplicity: ")))

# Sort roots and multiplicities together
for i in range(n):
    for j in range(i+1,n):
        if roots[i]>roots[j]:
            roots[i],roots[j]=roots[j],roots[i]
            mult[i],mult[j]=mult[j],mult[i]

print("Leading sign:")
print("1 positive")
print("-1 negative")
lead=int(input("Sign: "))

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

sign=[0]*(n+1)

if lead>0:
    sign[n]=1
else:
    sign[n]=-1

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

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

want=1

if op=="3" or op=="4":
    want=-1

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

print("Solution:")

found=False

for i in range(n+1):

    if sign[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)

if include:
    for i in range(n):

        leftok=sign[i]==want
        rightok=sign[i+1]==want

        if not leftok and not rightok:
            found=True
            s=frac(roots[i])
            print("["+s+","+s+"]")

if not found:
    print("EMPTY SET")

"""DuckieDai Inequality From Roots 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 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 getroot():
print("1 whole")
print("2 fraction")
t=input("Type: ")
if t=="2":
num=int(input("numerator: "))
den=int(input("denominator: "))
return num/den
else:
return float(input("value: "))
duckiedai_intro("Ineq From Roots")
n=int(input("Distinct roots: "))
roots=[]
mult=[]
for i in range(n):
print("Root",i+1)
roots.append(getroot())
mult.append(int(input("multiplicity: ")))
# Sort roots and multiplicities together
for i in range(n):
for j in range(i+1,n):
if roots[i]>roots[j]:
roots[i],roots[j]=roots[j],roots[i]
mult[i],mult[j]=mult[j],mult[i]
print("Leading sign:")
print("1 positive")
print("-1 negative")
lead=int(input("Sign: "))
print("1 >0")
print("2 >=0")
print("3 <0")
print("4 <=0")
op=input("Choice: ")
sign=[0]*(n+1)
if lead>0:
sign[n]=1
else:
sign[n]=-1
for i in range(n-1,-1,-1):
sign[i]=sign[i+1]
if mult[i]%2==1:
sign[i]=-sign[i]
want=1
if op=="3" or op=="4":
want=-1
include=(op=="2" or op=="4")
print("Solution:")
found=False
for i in range(n+1):
if sign[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)
if include:
for i in range(n):
leftok=sign[i]==want
rightok=sign[i+1]==want
if not leftok and not rightok:
found=True
s=frac(roots[i])
print("["+s+","+s+"]")
if not found:
print("EMPTY SET")

Filename: cubsolv.py
Size: 2795 bytes
SHA-256: 8a167b5abfe8bbc72c6bcda3efe79c2f62b42ac29a05d09fdd0c303456753463

Usage

Inputs

How many distinct zeros the polynomial has
Each zero as a decimal or as a numerator and denominator, with its multiplicity
Leading sign: 1 for positive, -1 for negative
One menu choice: 1 greater than zero, 2 greater than or equal, 3 less than zero, 4 less than or equal

Outputs

Solution intervals written with fractions where possible
Single points for the or-equal choices when an even-multiplicity zero touches the axis
EMPTY SET when nothing satisfies the inequality

Units: Polynomial zeros and coefficients; no physical units.

Assumptions and limitations

Assumptions

Every real zero of the polynomial is entered once with its correct multiplicity.
Any factor without real zeros is positive, so the leading sign describes the far right of the graph.

Constraints

The program does not find zeros; use a zero finder or factoring first.
Signs flip at odd multiplicities and stay the same at even multiplicities.

Known failures

A fraction with a zero denominator stops with a division-by-zero error.
A negative count of zeros stops with an index error.
A menu choice other than 1 to 4 is treated as choice 1.
Non-numeric 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: CUBSOLV — 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. CUBSOLV 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 2026-10-03. Download this reviewed version

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