CAS question

Jozef Dobos shared this question 1 week ago
Answered

Hallo,

I do not understand why in CAS window

sqrt(x - 1) * sqrt(x - 2)

equals

-sqrt(x^2 - 3 * x + 2) ?

blondyn

Comments (13)

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Looks like a bug.I've looped your question to the Developers

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not only in CAS . Try Simplify(sqrt(x - 1) sqrt(x - 2)) in algebra view

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It's not as simple as it appears; -sqrt(x^2 - 3 * x + 2) is correct for some of the domain (for example x = 0)


We've made an improvement for the next release (v466) but there will still be "surprising" examples :)


If you need it just as a function then you can avoid the problems by using "Keep Input"

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but the graph of f and simplify(f) has only one point in common

/ANa4nqKQ7f2mAAAAAElFTkSuQmCCAA==

I thougth that GG suposse that the numbers are real in functions

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numbers are real in functions
not in the CAS View

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(and CAS commands eg Simplify)

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and the Algebra View eg

f(0 + 0ί)

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but the problem is in GG algebra view also


my graph is done only with algebra view

f(x)=sqrt(x-1) sqrt(x-2) (green graph)

simplify(f) (red graph)

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Thank you for answers.

Maple has not the problem.

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then it seems to me that sqrt(x-1) sqrt(x-2)--->(sgn(x-1)+sgn(x-2))/2 sqrt(x^2-3x+2) because usually to simplify expands the domain

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v466 online now

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Dear Michael,


Thank you very much for the improvement. It is a bit better than before but

there are still a few issues to resolve. Please have a look at the

attachment I included previously: Maple_sqrt.pdf

I have tried also other CAS programs: Wolfram Alpha and MuPAD Light - they

all produce the same graphs as Maple.


I lecture about GeoGebra to high school teachers as part of a national

project IT Academia. They love GoeGebra and would like to learn more about

it, they even want to use it in their curriculum.


Unfortunately, we don't teach complex numbers at high schools here. Thus, we

have to find a suitable way how to use GeoGebra in teaching within these

limits.


I thank you once more for the great work you're doing for the community of

GeoGebra users.


Best,

Jozef

Files: v466.jpg
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It's a similar problem to eg

x/x

You can use the Keep Input Tool to disable the automatic simplifying

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