Adventures in Python: Combinations and Permutations

Adventures in Python: Combinations and Permutations

This program offers the user a choice of one of three calculations:

1.  Combinations, no repeats

2.  Permutations

3.  Combinations, with repeats

The program demonstrates how a menu is made.  Equality is tested with two equal signs (==).  A single equal sign (=) represents assignment for the Python.

The math.factorial function uses integers.

#  Program 005: Combinations, Permutations, Repeated Combination

#  Demonstration of the If structure

import math

# factorial is only for integers

# choices

# we will need to format the choice variable as an integer (number)

print("Make your choice:")

print("1.  Combination")

print("2.  Permutation")

print("3.  Repeated Combination")

choice = int(input("Choice: "))

# error condition, also input routine

if choice < 1 or choice > 3:

    print("Not a valid choice")

else:

    n = int(input("n = "))

    r = int(input("r = "))

    nf = math.factorial(n)

    rf = math.factorial(r)

    df = math.factorial(n-r)

# calculation test.  Equality is tested using 2 equal signs

if choice == 1:

    calc = nf/(df*rf)

    print("Combinations = ",calc)

if choice == 2:

    calc = nf/df

    print("Permutations = ",calc)

if choice == 3:

    calc = math.factorial(n+r-1)/(rf*math.factorial(n-1))

    print("Combinations = ",calc)

Example: n = 52, r = 5

Make your choice:

1.  Combination

2.  Permutation

3.  Repeated Combination

Choice: 1

n = 52

r = 5

Combinations =  2598960.0

>>>

Make your choice:

1.  Combination

2.  Permutation

3.  Repeated Combination

Choice: 2

n = 52

r = 5

Permutations =  311875200.0

>>>

Make your choice:

1.  Combination

2.  Permutation

3.  Repeated Combination

Choice: 3

n = 52

r = 5

Combinations =  3819816.0

Eddie

This blog is property of Edward Shore, 2017.

Programming Languages: TI-85 vs. TI-84 CE Plus

Programming Languages:  TI-85 vs. TI-84 CE Plus

I purchased a 1995 edition of the TI-85 at a Pasadena City College swap meet.  The TI-85 was my go-to and favorite calculator through high school (1991 – 1995). 

Today, I am going to compare common programming commands between two of my favorite Texas Instrument calculators, the TI-85 and the current TI-84 CE Plus.  The manuals for each calculator were consulted to answer questions.

Arguments in vector brackets [ ] means the argument is optional.

Command	TI-85 (1992 – 1997) (probably also applies to the TI-86) Software Version 10.0	TI-84 CE Plus (2016-) (most of the this applies to TI-84 Plus 2004-present) Software Version 5.2.2
Variable Names	Up to 8 characters, must begin with a number, no spaces. All variables are global.	Single letters A through Z, n, θ All variables are global.
Complex Number display, Rectangular	(X, Y)	X + Yi
Complex Number display, Polar	(R ∠ θ)	R e^θi
Graphing Modes	Function, Polar, Parametric, Differential Equation	Function, Polar, Parametric, Recurring Sequences
Number of Colors	0 (monochrome display)	15: blue, red, black, magenta, green, orange, brown, navy, light blue, yellow, white, light gray, medium gray, gray, dark gray (backlit display) **CE and C versions only
Input	Input by itself displays the graph screen Input [“prompt string”], varname	Input by itself displays the graph screen Input  [“prompt string”], variable
Prompt:  asking for and storing multiple values	Prompt var1, var2, var3 ,…	Prompt var1, var2, var3, …
Disp	Disp by itself displays the home screen Disp var/string, [var/string …]	Disp by itself displays the home screen Disp var/string, [var/string…]
Pause	Pause [var/string]	Pause [var/string], [time in seconds]
Wait	N/A	Wait time in seconds up to 100
Display the graph screen	DispG displays the graph screen	DispGraph displays the graph screen
Display the function table	N/A	DispTable
Output	Outpt(line, col, var/string) 8 lines, 21 columns	Output(row, col, var/string) 10 rows, 26 columns
InpSt	InpSt stores entered text or equations as strings	N/A.  Use Input
If – Then – Else structure	If condition Then do if true [Else do if false] End	If condition Then do if true [Else do if false] End
For structure	For(var, begin, end, [step]) commands End	For(var, begin, end, [step]) commands End
While structure	While condition do while condition is true End	While condition do while condition is true End
Repeat – Until structure	Repeat condition do while condition is false End	Repeat condition do while condition is false End
Menu	Menu(nn, string, label…) Where nn is from 1 to 15	Menu(“title”, “text”, label…) Up to 9 options
Labels (Lbl/Goto)	Label names can have up to 8 characters.  All labels are local.	A-Z, 0 -99, θ.  All labels are local.
Increment (by 1) and Skip (if greater to value)	IS>(variable, value)	IS>(variable, value)
Decrement (by 1) and Skip (if less than value)	DS<(variable, value)	DS<(variable, value)
Stop program execution	Stop	Stop
Return from a subroutine	Return	Return
Execute a subroutine	Type the name of the program	Call program by pressing [prgm], choosing it from the Program submenu during editing
Clear the graph screen	ClDrw (clear all drawings)	ClrDraw (clear all drawings)
Display text on a graph screen	N/A	TextColor(color) sets the color. Text([-1], row, col, string) 0-164 row pixel, 0-264 column pixel -1 is for large text
Draw a temporary function	DrawF f(x)	DrawF f(x), [color]
Draw a temporary inverse function (f^-1(x) = y, x and y are swapped)	DrInv f(x)	DrawInv f(x), [color]
Shading	Shade (lower, upper, left, right)	Shade (lower, upper, [left, right, pattern, pattern resolution, color])
Draw a line	Line(x1, y1, x2, y2)	Line(x1, y1, x2, y2, [0/1, color, line style]) 0/1: 0 to erase, 1 to draw
Draw a circle	Circle(x, y, radius)	Circle(x, y, radius, [color, line style])
Draw a Point Only the TI-84 Plus CE has similar commands for pixels	PtOn(x,y) PtOff(x,y) PtChg(x,y)	Pt-On(x,y, [mark, color]) Pt-Off(x,y,[mark]) Pt-Change(x,y,[color])
Convert a value to a string	N/A	eval(expression) → Str# No complex results
Convert a string to a value	N/A	expr(string)
Convert a string to a graph variable	St>Eq(string, graph variable)	String>Equ(string, graph variable)
Length of a string	lngth string	length(string) (call from the catalog)
Extract part of a string	sub(string, begin point, length)	sub(string, begin point, length) (call from the catalog)
Execute Linear Regression analysis (other regressions are similar)	LinR xlist, ylist	LinReg(ax+b) xlist, ylist, [freqlist, Y= variable]
Turn a stat plot on	N/A (stat plots are not available on the TI-85)	PlotsOn [1,2,3]
Turn a stat plot off	N/A (stat plots are not available on the TI-85)	PlotsOff [1,2,3]
Turn graph functions on	FnOn [1 – 99]	FnOn [1-9, 0]
Turn graph functions off	FnOff [1 – 99]	FnOff [1-9, 0]

Notes

As we can see, the programming language of the TI-85/86 family is similar to the TI-84 Plus family, translating the programs should not be difficult.  I believe that stat plots are available on the TI-86, but not the TI-85.

Keep in mind if you have complex numbers, that the complex mode on the TI-84 Plus (a+bi or re^(θi) has to be turned on.  Furthermore, logarithmic, power, exponential, and trigonometric functions for complex numbers return error on the TI-84 Plus (substitute expressions must be used).

(use radians mode)

With z = X + Yi = R*e^(θ*i), X = real(z), Y = imag(z), R = abs(z), θ = arg(z)

z^n = R^n * (cos(n*θ) + sin(n*θ)*i), n is a real number

ln (z) = ln R + θ*i

e^(z) = e^X * cos Y + e^X * sin Y * i

sin(z) = sin X * cosh Y + cos X * sinh Y * i

cos(z) = cos X * cosh Y – sin X * sinh Y * i

sin¯¹ (z) = asin(z) = -i * ln (zi ± √ (1 – z^2)

z1 ^ z2 = e^(z2 * ln z1)

Eddie

This blog is property of Edward Shore, 2017