TI-84 Plus CE Python Edition Scripts

"""
PROGRAM 4: CONVERT FORMS
Rect <-> Polar conversion
TI-84 CE Python v5.8.3
"""

try:
    from ti_system import *
except:
    pass

import math

while True:
    print("\nFORM CONVERTER")
    print("="*25)
    print("1: Rect -> Polar")
    print("2: Polar -> Rect")
    print("3: Exit")
    
    choice = input("\nChoice (1/2/3): ")
    
    if choice == "3":
        print("\nGoodbye!")
        break
    
    if choice == "1":
        # Rectangular to Polar
        print("\nEnter a + jb:")
        a = float(input("Real part a: "))
        b = float(input("Imag part b: "))
        
        # Display input
        if b >= 0:
            print("\nInput: %.3f + j%.3f" % (a, b))
        else:
            print("\nInput: %.3f - j%.3f" % (a, abs(b)))
        
        # Convert
        r = math.sqrt(a**2 + b**2)
        theta = math.degrees(math.atan2(b, a))
        
        # Display result
        print("\nPolar form:")
        print("r = %.4f" % r)
        print("theta = %.2f deg" % theta)
        print("\n= %.4f at %.2f deg" % (r, theta))
    
    elif choice == "2":
        # Polar to Rectangular
        print("\nEnter r at theta:")
        r = float(input("Magnitude r: "))
        theta = float(input("Angle theta (deg): "))
        
        # Display input
        print("\nInput: %.3f at %.2f deg" % (r, theta))
        
        # Convert
        rad = math.radians(theta)
        a = r * math.cos(rad)
        b = r * math.sin(rad)
        
        # Display result
        print("\nRectangular form:")
        print("a = %.4f" % a)
        print("b = %.4f" % b)
        
        if b >= 0:
            print("\n= %.4f + j%.4f" % (a, b))
        else:
            print("\n= %.4f - j%.4f" % (a, abs(b)))
    
    else:
        print("\nInvalid choice!")
    
    input("\nPress Enter for another...")

"""
FLEXIBLE COMPLEX MATRIX SOLVER
Any size: 2x2, 2x3, 3x4, 4x4, etc.
TI-84 CE Python v5.8.3
"""

try:
    from ti_system import *
except:
    pass

import math

def c_add(z1, z2):
    return [z1[0]+z2[0], z1[1]+z2[1]]

def c_sub(z1, z2):
    return [z1[0]-z2[0], z1[1]-z2[1]]

def c_mul(z1, z2):
    a, b = z1[0], z1[1]
    c, d = z2[0], z2[1]
    return [a*c-b*d, a*d+b*c]

def c_div(z1, z2):
    a, b = z1[0], z1[1]
    c, d = z2[0], z2[1]
    denom = c*c + d*d
    if denom < 1e-20:
        return [0, 0]
    return [(a*c+b*d)/denom, (b*c-a*d)/denom]

def c_mag(z):
    return math.sqrt(z[0]**2 + z[1]**2)

def c_to_polar(z):
    r = math.sqrt(z[0]**2 + z[1]**2)
    theta = math.degrees(math.atan2(z[1], z[0]))
    return [r, theta]

def c_show_rect(name, z):
    if z[1] >= 0:
        print("%s= %.3f+j%.3f" % (name, z[0], z[1]))
    else:
        print("%s= %.3f-j%.3f" % (name, z[0], abs(z[1])))

def c_show_polar(name, z):
    p = c_to_polar(z)
    print("%s= %.3f at %.2f deg" % (name, p[0], p[1]))

def c_show_both(name, z):
    if z[1] >= 0:
        print("%s= %.3f+j%.3f" % (name, z[0], z[1]))
    else:
        print("%s= %.3f-j%.3f" % (name, z[0], abs(z[1])))
    p = c_to_polar(z)
    print("  = %.3f at %.2f deg" % (p[0], p[1]))

print("FLEXIBLE MATRIX SOLVER")
print("="*25)
print("Solve: Ax = b")

# Get output format preference
print("\nOutput format:")
print("1: Rectangular (a+jb)")
print("2: Polar (r at theta)")
print("3: Both forms")
fmt = input("Choice (1/2/3): ")

# Get matrix dimensions
rows = int(input("\nRows (equations): "))
cols = int(input("Cols (unknowns): "))

if rows < 2 or rows > 5:
    print("Rows must be 2-5")
    input("\nPress Enter")
    exit()

if cols < 2 or cols > 5:
    print("Cols must be 2-5")
    input("\nPress Enter")
    exit()

print("\nSolve %dx%d system" % (rows, cols))

if rows != cols:
    print("Note: Over/under-determined")
    print("Will find best solution")

# Get matrix A
A = []
for i in range(rows):
    row = []
    for j in range(cols):
        print("\nA[%d][%d]:" % (i+1, j+1))
        r = float(input("Real: "))
        im = float(input("Imag: "))
        row.append([r, im])
    row.append([0, 0])  # placeholder for b
    A.append(row)

# Get vector b
print("\nVector b:")
for i in range(rows):
    print("\nb%d:" % (i+1))
    r = float(input("Real: "))
    im = float(input("Imag: "))
    A[i][cols] = [r, im]

print("\nSolving...")

# Gaussian elimination with RREF
# Handle rectangular matrices
min_dim = min(rows, cols)

for i in range(min_dim):
    # Find pivot in column i
    max_row = i
    max_val = 0
    for k in range(i, rows):
        val = c_mag(A[k][i])
        if val > max_val:
            max_val = val
            max_row = k
    
    # Check if column is zero
    if max_val < 1e-10:
        print("\nWarning: Column %d zero" % (i+1))
        continue
    
    # Swap rows
    A[i], A[max_row] = A[max_row], A[i]
    
    # Scale pivot row
    pivot = A[i][i]
    for j in range(cols+1):
        A[i][j] = c_div(A[i][j], pivot)
    
    # Eliminate column in all other rows
    for k in range(rows):
        if k != i:
            factor = A[k][i]
            for j in range(cols+1):
                temp = c_mul(factor, A[i][j])
                A[k][j] = c_sub(A[k][j], temp)

# Extract solution
print("\nSOLUTION:")

# Choose display function based on user choice
if fmt == "1":
    c_show = c_show_rect
elif fmt == "2":
    c_show = c_show_polar
else:
    c_show = c_show_both

# For square or overdetermined systems
if rows >= cols:
    for i in range(cols):
        if i < rows:
            x = A[i][cols]
            c_show("x%d " % (i+1), x)
        else:
            print("x%d = Free variable" % (i+1))
    
    # Check if overdetermined system is consistent
    if rows > cols:
        print("\nConsistency check:")
        consistent = True
        for i in range(cols, rows):
            if c_mag(A[i][cols]) > 0.01:
                print("Row %d: Inconsistent" % (i+1))
                consistent = False
        if consistent:
            print("✓ System consistent")

# For underdetermined systems
else:
    for i in range(rows):
        x = A[i][cols]
        c_show("x%d " % (i+1), x)
    for i in range(rows, cols):
        print("x%d = Free (set to 0)" % (i+1))
    print("\nNote: Infinite solutions")
    print("Free vars can be any value")

print("\n✓ Done!")

input("\nPress Enter to exit")