- #1

ztdep

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I am evaluating this formula, it's real value is 0. but maple can't further simplify it?

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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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- 0

I am evaluating this formula, it's real value is 0. but maple can't further simplify it?

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- #2

phyzguy

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- #3

DrClaude

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How can (√π - √π) not be zero? We are not solving a quadratic equation here, so ##\sqrt{\pi} > 0##.

- #4

pasmith

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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

Mark44

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phyzguy said:Probably because (√π - √π ) isn'tnecessarilyzero. It depends which of the two square roots you take.

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.DrClaude said:How can (√π - √π) not be zero? We are not solving a quadratic equation here, so ##\sqrt π>0##.

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##.

- #6

S.G. Janssens

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Try enteringztdep said:I am evaluating this formula, it's real value is 0. but maple can't further simplify it?

`Pi`

instead of `pi`

. For Maple, the first one is the famous mathematical constant, the second one is an undefined variable.

- #7

phyzguy

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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?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##.

- #8

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##\sqrt \pi## in Maple must be a positive number. I'd be very surprised if something as basic as that was coded wrongly.phyzguy said:Conventions are one thing, but what's coded up in the Maple code is another.

- #9

S.G. Janssens

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It is a triviality, nothing else. And it certainly does not have anything to do with branches of square roots.

- #10

Mark44

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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##.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?

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

phyzguy

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I agree that's worth a try. @ztdep , can you try replacing pi^(1/2) with Pi^(1/2) in your definition of v and see if that fixes it?Mark44 said: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.

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.

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.

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.

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.

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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