why simplify does not work on this example?

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Question:why simplify does not work on this example?

Posted: nm 10401 Product: Maple 2024

June 02 2024

These are good example(s) why I think Maple's simplify needs to be improved.

Example 1

Given an expression which is zero for nonnegative x, one would expect simplify to simplify it to zero when told that x is positive.

But nothing I tried with simplify worked. combine figured it out.

But why? Is this not the job of simplify?

The expression is

e:=x-1/4*(-2+2*(4*x^2+1)^(1/2))^(1/2)*(2+2*(4*x^2+1)^(1/2))^(1/2);

Here is worksheet

>	interface(version);

restart;

>	e:=x-1/4(-2+2(4x^2+1)^(1/2))^(1/2)(2+2(4x^2+1)^(1/2))^(1/2);

>	coulditbe(e=0);

>	#we see it is zero for x>=0 plot(e,x=-3..3)

>	simplify(e) assuming x>=0;

>	simplify(e,size) assuming x>=0;

>	expand(e) assuming x>=0;

>	simplify(e,sqrt) assuming x>=0;

>	simplify(e,symbolic) assuming x>=0;

>	combine(e) assuming x>=0;

Compare some other software on this same problem

It should be as simple as the above in Maple.

A user should not have to try 100 different commands in Maple to find which works.

simplify should have done it in first place. What Am I overlooking here?

Maple 2024

Download why_simplify_do_not_work_example.mw

EXAMPLE 2

In this example the expression is zero for x<0. Here nothing worked for me. This is challenge for Maple experts here to find the command to simplify this to zero.

I know it is zero for x<0.

e := -1/2*(-2*x*sqrt(4*x^2 + 1) + (16*x^3*sinh(3/2*arcsinh(2*x)) - 8*x^2*cosh(3/2*arcsinh(2*x))*sqrt(4*x^2 + 1) + 4*sinh(3/2*arcsinh(2*x))*x - cosh(3/2*arcsinh(2*x))*sqrt(4*x^2 + 1))*sqrt(-2 + 2*sqrt(4*x^2 + 1)))/sqrt(4*x^2 + 1)

>	interface(version);

>	Physics:-Version();

>	e:=-1/2(-2xsqrt(4x^2 + 1) + (16x^3sinh(3/2arcsinh(2x)) - 8x^2cosh(3/2arcsinh(2x))sqrt(4x^2 + 1) + 4sinh(3/2arcsinh(2x))x - cosh(3/2arcsinh(2x))sqrt(4x^2 + 1))sqrt(-2 + 2sqrt(4x^2 + 1)))/sqrt(4x^2 + 1);

-(1/2)*(-2*x*(4*x^2+1)^(1/2)+(16*x^3*sinh((3/2)*arcsinh(2*x))-8*x^2*cosh((3/2)*arcsinh(2*x))*(4*x^2+1)^(1/2)+4*sinh((3/2)*arcsinh(2*x))*x-cosh((3/2)*arcsinh(2*x))*(4*x^2+1)^(1/2))*(-2+2*(4*x^2+1)^(1/2))^(1/2))/(4*x^2+1)^(1/2)

>	plot(e,x=-10..3);