Selecting positive or negative terms of a symbolic vector

I have a symbolic vector say [a^2*b^3, 0, -a*b^2, b^2, -a^4*b]. I would like to obtain two vectors from this. One of them only selecting the entries that have a positive coefficient, in this case I would like to obtain [a^2*b^3, b^2]. The other containing the entries with negative coefficient: [-a*b^2, -a^4*b].

I tried extracting the coefficients and then using if statement to create a vector with the positive entries and similar for the negative.

Is there a more efficient way to do this?

Answer 1

[Star Strider]

This works:

syms a b c 
V =  [a^2*b^3, 0, -a*b^2, b^2, -a^4*b];
Vs = sign(V);
Vgz = V(Vs>0)
Vlz = V(Vs<0)

Vgz =
[ a^2*b^3, b^2]

Vlz =
[ -a*b^2, -a^4*b]

[Farid Salazar Wong]

Thanks for your answer. However, I get this message:

Error using symengine (line 58) Unable to prove '0 < sign(a^2*b^3)' literally. To test the statement mathematically, use isAlways.

Error in sym/subsindex (line 659) X = find(mupadmex('symobj::logical',A.s,9)) - 1;

Error in sym>privformat (line 1473) x = subsindex(x)+1;

Error in sym/subsref (line 685) [inds{k},refs{k}] = privformat(inds{k});

[Star Strider]

Interesting. It worked for me without error in R2015a.

I can’t reproduce the behaviour you saw, so experiment with adding an assume call:

syms a b c 
assume([a b c] > 0)
V =  [a^2*b^3, 0, -a*b^2, b^2, -a^4*b];
Vs = sign(V);
Vgz = V(Vs>0)
Vlz = V(Vs<0)

It didn’t change the result I got, but it might be necessary for your version.

[Farid Salazar Wong]

It worked now. Thanks a lot!

[Star Strider]

My pleasure!

(Please Accept my Answer if it solved your problem.)