## 19675 Reputation

15 years, 139 days

## A simple question about sets...

Maple 2018

When we specify a set (a sequence of objects enclosed in curly braces), Maple removes duplicates, since the elements of the set must be unique, that is, they cannot be repeated. See below for 2 examples. With the first example  {a<=b  and  b>=a}, everything is in order, since they are one and the same. But Maple treats the same equality, written in two ways  {a=b, b=a} , as different objects. It seems to me that this is not very convenient:

```restart;
{a<=b, b>=a}; # OK
{a=b, b=a}; # not OK
is((a=b)=(b=a)); # not OK
```

## How to prove the identity binomial(2*n,...

Maple 2018

Can Maple prove this simple identity  binomial(2*n, n)/2 = binomial(2*n-1, n-1) ,where n is integer and positive. Doing it manually is very easy. My attempt was unsuccessful:

```is(binomial(2*n, n)/2=binomial(2*n-1, n-1)) assuming n::posint;
```

FAIL

## Challenge for Maple fans...

Maple

Here is a problem that I recently had to solve and I really liked it. I recommend it to all Maple fans:

"The contour of the Christmas tree on the occasion of the New Year 2022 is a triangle, which is divided into 7 small triangles, the bases of which are parallel. The areas of triangles and the star are measured in snowflakes, the values of which are presented on the balls (of course, the number of snowflakes must be integer). It is necessary to determine the areas of triangles, on the balls of which there are no numbers".

At first glance it seems that the area of the star is not related to the problem, but it is not. This will become clear only after the problem is solved.

## Why can't Maple solve a simple equation...

Maple 2018

This question came to me when I answered in this thread  https://www.mapleprimes.com/questions/231603-Solve-Onevariable-Equation

The equation there is quite cumbersome, I extracted a shorter subexpression from it (I converted all floats to exact constants), but the  solve  command hangs when trying to solve it. fsolve  handles the equation easily. We can see that the equation  Eq  is quite simple and easy to solve even by hand. I ask this question in a separate topic, because this seems to be a serious bug in the  solve  command.

```restart;
Eq:=1-1/(1+203808*exp(-342569/506*t)*(1/131537))^(131537/203808)=44983/56599;
solve(Eq);```

Edit. I noticed that the  isolate  command solves the problem, but of course the question remains open with  solve .

## How to simplify the trigonometric expres...

Maple 2018

How to simplify this trigonometric expression with Maple? I only know the way with  identify command, which is difficult to call mathematically correct:

```restart;
Expr:=arctan((1-tan(20*Pi/180))/(1-tan(25*Pi/180)));
evalf[15](Expr);
identify(%);```

 1 2 3 4 5 6 7 Page 1 of 8
﻿