problem with symbolic factorization with two symbols
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rustem
am 21 Okt. 2023
Bearbeitet: Torsten
am 21 Okt. 2023
The output is not a factorized one. I want this form : (s+s1)*(s+s2)*(s+s3). What is the problem?
syms s K
factor(s^3 + 10*s^2 + (21+K)*s + 4*K, [s, K],'FactorMode','full')
The output is
4*K + 21*s + K*s + 10*s^2 + s^3
1 Kommentar
Dyuman Joshi
am 21 Okt. 2023
It is factorized according to the inputs given.
From the documentation - F = factor(x,vars) returns an array of factors F, where vars specifies the variables of interest. All factors not containing a variable in vars are separated into the first entry F(1). The other entries are irreducible factors of x that contain one or more variables from vars.
Note the last sentence.
What is the expected output from the vectorization?
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John D'Errico
am 21 Okt. 2023
Bearbeitet: John D'Errico
am 21 Okt. 2023
That you want to see a simple set of factors is not relevant. You essentially need to obtain the roots of this cubic polynomial in s, where K is a parameter, which would give you that factorization.
syms s K
sroots = solve(s^3 + 10*s^2 + (21+K)*s + 4*K,s,'maxdegree',3)
As you can see, they are fairly messy, and depending on the value of K, they may well be complex even if K is real. This is expected for any cubic polynomial, that we may find exactly two conjugate complex roots.
The factors now are just
prod(s-sroots)
We can expand that to show the result recovers your original polynomial.
simplify(expand(ans))
Finally, why did not factor understand what you wanted to see? You gave it two variables s and K. How should factor possibly know that you wanted it to do what I just did, essentially, that s is the variable of interest, and K a symbolic parameter in the problem? Software cannot read your mind, at least, not yet.
7 Kommentare
Walter Roberson
am 21 Okt. 2023
Factorization of expressions with real components (or components of unknown reality) traditionally only proceeds to the point where any further factoring would require use of imaginary components.
syms x
factor(x^2 + 1)
factor(x^2 - 1)
P1 = expand((x-2) * (x+7) * (x-7))
factor(P1)
P2 = expand((x-2) * (x+7i) * (x-7i))
factor(P2)
P3 = expand((x-2i) * (x+7) * (x-7))
factor(P3)
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