## 90 Reputation

17 years, 285 days

## Simplifying expression with boolean vari...

Hi,

If I have boolean variable x1

And assuming multiplication means "AND" for boolean expressions;

Then

x1 = x1^2 = x1^3 = ...=x1^k, k >= 1

Since "x1 and x1 and x1 ... and x1" = x1;

it is true if x1 is true and false if x1 is false.

How can a boolean expression with variables taken

to various powers be simplified?

I can't take credit for this; but Dave Rusin showed

## Similar matrices...

This isn't specifically Maple-related; but mathematics-related; related to Linear Algebra and Modern Algebra. While reviewing Linear Algebra; I ran across the concept of "Similar Matrices"; which are defined as: if A,B are nxn matrices and there exists invertible nxn matrix P such that P^(-1)*A*P = B then A is similar to B The payoff was: if A, B are similar then they "have the same eigenvalues" (the characteristic equation is same for both A and B). (Here we are talking about the group of invertible nxn matrices, with operation matrix multiplication) --

## Using the latex command to generate LaTe...

Maple
The command "latex(expression)" attempts to generate LaTeX commands that will recreate the expression in LaTeX. For example; latex(%) will try to generate LaTeX commands to recreate the last output from Maple. Let's say I had just entered the Maple command to display an integral; for example: Int(Int(Int(rho^2*sin(phi),rho=sec(phi)..5*sec(phi)),phi=Pi/6..Pi/3),theta=0..2*Pi); If I would like to put that same integral in a LaTeX document; I could enter the following command: latex(%); Which, in Maple 9, returned: \int _{0}^{2\,\pi }\!\int _{1/6\,\pi }^{1/3\,\pi }\!\int _{\sec

## Wieferich primes...

Maple
Hi, I ran into this in my Modern Algebra class; and decided it might be of interest. We were given the problem to: "Find the least prime p s.t. 2^(p-1) congruent to 1 (mod p^2)" EVERY prime p > 2 has the property, 2^(p-1) congruent to 1 (mod p), by Fermat's Theorem (since 2 does not divide such prime p). But, mod p^2 is another story. This was given in a class where everything is done by hand calculation, based on theorems. I couldn't come up with any way to determine it other than brute force. Here is a tiny Maple snippet which finds it:

## Finding a Minimal form for a boolean exp...

I have some background in computer science; which may help explain my interest in Maple. :) In my Computer Science studies; one thing we were required to do was to minimize boolean expressions. I found this to be extremely tedious; something that you really want the computer to do for you. At least; that is how I saw it. So, I always thought that I would write a program to do; what we were doing manually. The result is the following application: Minimize Boolean Expression Worksheet
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