[fricas-devel] How do I get FriCAS to tell me that x^2 must be positive if x is not 0?

[Kyle Andrews]

I am interested in writing a naive procedure for testing whether a square symmetric matrix is positive definite. I'm getting to the Polynomial(Integer) at the end, but haven't found any documentation showing how to test whether a Polynomial(Integer) must be positive (or 0). I know I could write this function by examining eigenvalues but would like to explore the facilities for doing it the other way.

Thanks for any hints or suggestions.

[oldk1331]

Hi, you can use "sign" to know if a polynomial is nonnegative.

Post by Kyle Andrews
I am interested in writing a naive procedure for testing whether a square
symmetric matrix is positive definite. I'm getting to the
Polynomial(Integer) at the end, but haven't found any documentation showing
how to test whether a Polynomial(Integer) must be positive (or 0). I know I
could write this function by examining eigenvalues but would like to
explore the facilities for doing it the other way.
Thanks for any hints or suggestions.
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[Kyle Andrews]

Thanks!

Post by oldk1331
Hi, you can use "sign" to know if a polynomial is nonnegative.

Post by Kyle Andrews
I am interested in writing a naive procedure for testing whether a square
symmetric matrix is positive definite. I'm getting to the
Polynomial(Integer) at the end, but haven't found any documentation showing
how to test whether a Polynomial(Integer) must be positive (or 0). I know I
could write this function by examining eigenvalues but would like to
explore the facilities for doing it the other way.
Thanks for any hints or suggestions.
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"FriCAS - computer algebra system" group.
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