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Interpreting a result obtain with Reduce that includes pure function

Posted 11 years ago
Hello,

I used Reduce on a set of inequalities and I got the message
Reduce::ratnz: Reduce was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result 
plus a result that included the following condition
c < Root[19. T^3 - 30. T^2 #1 + 8. #1^3 &, 3]
Does it mean that "c" must be lower than the third root of the equation
19.T^3-30.x T^2+8.x^3==0
where x is the unknown? Is 19. an abbreviation for an irrational number close to 19?

Thank you in advance for your help
POSTED BY: simone m
2 Replies
Posted 11 years ago
Thank you! The graph was interesting to look at emoticon

S
POSTED BY: simone m
Posted 11 years ago
>Does it mean that "c" must be lower than the third root of the equation

Yes,  Root is aften returned in results by Solve and Reduce
tutorial/AlgebraicNumbers

To get a sense of how the root behaves relative to T:
Plot[Root[19. T^3 - 30. T^2 #1 + 8. #1^3 &, 3], {T, -5, 5}]


But since this is just a third-degree polynomial you can get the roots explicitly by telling Reduce to expand cubics (similar option exists for quartics)
Reduce[19 T^3 - 30 T^2 x + 8 x^3 == 0, x, Cubics->True]

>Is 19. an abbreviation for an irrational number close to 19?

It represents a machine-precision number tutorial/NumericalPrecision
POSTED BY: Simon Schmidt
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