Why can't Maple simplify this further?

In summary, the conversation discusses the issue of Maple not simplifying the formula (√π - √π) to 0. It is suggested that this may be because Maple treats the variable pi as an undefined variable instead of the constant mathematical value. It is also mentioned that Maple may be following the convention of using the principal square root, which is always positive. The conversation also includes suggestions to try using Pi instead of pi in the equation to see if that solves the issue.
  • #1
ztdep
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I am evaluating this formula, it's real value is 0. but maple can't further simplify it?

2022-09-15_8-04-45.png
 
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  • #2
Probably because (√π - √π ) isn't necessarily zero. It depends which of the two square roots you take. If you force it to take the positive square roots, then it will be zero.
 
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  • #3
How can (√π - √π) not be zero? We are not solving a quadratic equation here, so ##\sqrt{\pi} > 0##.
 
  • #4
DrClaude said:
How can (√π - √π) not be zero?

If you select a branch at random each time you write a [itex]\sqrt{}[/itex].

It may be that Maple thinks that each [itex]\pi[/itex] is a separate variable, whose values are not necessarily equal.
 
  • #5
phyzguy said:
Probably because (√π - √π ) isn't necessarily zero. It depends which of the two square roots you take.

DrClaude said:
How can (√π - √π) not be zero? We are not solving a quadratic equation here, so ##\sqrt π>0##.
To elaborate on @DrClaude's comment, the square root of a positive real number is by convention the principal square root of that number. i.e., the positive square root.

Although the equation ##x^2 - 4 = 0## has two solutions -- x = 2 or x = -2, it is an error to say that ##\sqrt 4 = \pm 2##.
 
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  • #6
ztdep said:
I am evaluating this formula, it's real value is 0. but maple can't further simplify it?
Try entering Pi instead of pi.
For Maple, the first one is the famous mathematical constant, the second one is an undefined variable.
 
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  • #7
Mark44 said:
To elaborate on @DrClaude's comment, the square root of a positive real number is by convention the principal square root of that number. i.e., the positive square root.

Although the equation ##x^2 - 4 = 0## has two solutions -- x = 2 or x = -2, it is an error to say that ##\sqrt 4 = \pm 2##.
Conventions are one thing, but what's coded up in the Maple code is another. What's your explanation for why it didn't replace (√π - √π ) in equation 4 of the OP with 0?
 
  • #8
phyzguy said:
Conventions are one thing, but what's coded up in the Maple code is another.
##\sqrt \pi## in Maple must be a positive number. I'd be very surprised if something as basic as that was coded wrongly.
 
  • #9
Maybe try to actually run it through Maple with reference to post #6.
It is a triviality, nothing else. And it certainly does not have anything to do with branches of square roots.
 
  • #10
phyzguy said:
Conventions are one thing, but what's coded up in the Maple code is another. What's your explanation for why it didn't replace (√π - √π ) in equation 4 of the OP with 0?
No idea, but I'm also puzzled why Maple added two expressions whose denominators were both ##\sqrt \pi x^2## to get a single expression with a denominator of ##\sqrt \pi x^2 \sqrt \pi##.

However, I think @S.G. Janssens has hit the nail on the head with his advice to use Pi rather than pi. The Maple documentation backs up this advice - https://www.maplesoft.com/support/help/maple/view.aspx?path=initialconstants.
 
  • #11

FAQ: Why can't Maple simplify this further?

1. Why doesn't Maple simplify my expression automatically?

Maple is a powerful software tool that can perform various mathematical operations. However, it cannot read the user's mind and determine the desired form of the expression. Hence, it requires the user to specify the simplification steps or commands to be performed.

2. Why does Maple sometimes give a more complex expression as the result?

Maple follows a set of mathematical rules and algorithms to simplify an expression. It may sometimes simplify an expression differently than what the user expects. This could be due to the complexity of the expression or the limitations of the software in certain cases.

3. Can I force Maple to simplify an expression in a specific way?

Yes, Maple allows users to specify the simplification steps or commands to be performed. This can be done by using various built-in functions or by writing custom procedures. Users can also specify the desired form of the expression using different options or flags.

4. How can I check if Maple has simplified the expression correctly?

Maple provides a built-in function called "is" that can be used to check the equivalence of two mathematical expressions. Users can compare the original expression with the simplified one to verify if Maple has simplified the expression correctly.

5. Is there a limit to how much Maple can simplify an expression?

Yes, there is a limit to how much Maple can simplify an expression. This is due to the complexity of the expression or the limitations of the software in certain cases. However, users can specify the maximum number of simplification steps or commands to be performed in order to control the extent of simplification.

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