Kitonum

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13 years, 149 days

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These are questions asked by Kitonum

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 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(%);

                           

        

 

The problem: to simplify the expression

for any negative  x  and  y .

Below we see that Maple copes with the task brilliantly (example 1). For example, it presents  sqrt(x*y)  as  sqrt(-x)*sqrt(-y)  and so on. But the same technique, applied only to the numerator of this expression does not give the desired presentation in the form of a square (example 2 and example 3).

restart;
# Example 1
A:=(x+y-2*sqrt(x*y))/(sqrt(-x)+sqrt(-y));
simplify(A) assuming negative;
factor(%,{sqrt(-x),sqrt(-y)});

                                         

restart;
# Example 2
B:=x+y-2*sqrt(x*y);
simplify(B) assuming negative;
factor(%,{sqrt(-x),sqrt(-y)});

                                           

 

restart;
# Example 3
B:=x+y-2*sqrt(x*y);
R:=simplify(B) assuming positive;
combine(R) assuming positive;
factor(R,{sqrt(x),sqrt(y)});

                                                   

Two questions:

1. Does anyone know the reasons for this behavior.

2. Does anyone know an easy way to simplify in examples 2 and 3 (without  substitutions  like  x=+-u^2  and  y=+-v^2 and so on,  of course)

 

Download sqrt.mw

 

after running the command  DocumentTools:-Tabulate  as you can see it in the example below in Maple 2018.2:

DocumentTools:-Tabulate(Matrix(2, [a, b, c, d]), width=20);

Output:
                                  

 

 

An hour or two ago, I answered a question in which it was a question of plotting a complex-valued function of 2 real variables. But the question itself and also my answer to it disappeared somewhere. Therefore, I send my answer here below.

There are two options for plotting:
1. Graphs of real and imaginary parts (as 2 surfaces in 3D).
2. Graph of the absolute value of this function (one surface in 3d) .

restart;
f:=(1+cosh(2*x))*exp(-4*I*t):
plot3d([Re,Im](f), x=0..1, t=0..1, color=[red,blue]);
plot3d(sqrt(add([Re,Im](f)^~2)), x=0..1, t=0..1, color=green);

 

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