How to know which elements of a symbolic vector are real?

I have this sym vector:

c = -(179249^(1/2)*(634751*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 1)^4 - 45299238750*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 1)^2 + 974025000000000)^(1/2))/26887350

(179249^(1/2)*(634751*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 1)^4 - 45299238750*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 1)^2 + 974025000000000)^(1/2))/26887350

-(179249^(1/2)*(634751*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 2)^4 - 45299238750*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 2)^2 + 974025000000000)^(1/2))/26887350

(179249^(1/2)*(634751*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 2)^4 - 45299238750*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 2)^2 + 974025000000000)^(1/2))/26887350

-(179249^(1/2)*(634751*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 3)^4 - 45299238750*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 3)^2 + 974025000000000)^(1/2))/26887350

(179249^(1/2)*(634751*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 3)^4 - 45299238750*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 3)^2 + 974025000000000)^(1/2))/26887350

-(179249^(1/2)*(634751*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 4)^4 - 45299238750*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 4)^2 + 974025000000000)^(1/2))/26887350

(179249^(1/2)*(634751*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 4)^4 - 45299238750*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 4)^2 + 974025000000000)^(1/2))/26887350

-(179249^(1/2)*(634751*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 5)^4 - 45299238750*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 5)^2 + 974025000000000)^(1/2))/26887350

(179249^(1/2)*(634751*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 5)^4 - 45299238750*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 5)^2 + 974025000000000)^(1/2))/26887350

-(179249^(1/2)*(634751*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 6)^4 - 45299238750*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 6)^2 + 974025000000000)^(1/2))/26887350

(179249^(1/2)*(634751*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 6)^4 - 45299238750*root(z^6 - (58169238750*z^4)/634751 + (130018668750000*z^2)/48827 - 1184625000000000000/48827, z, 6)^2 + 974025000000000)^(1/2))/26887350

Is it any easy (coded) way I can know which elements are real and which aren't?

Answer 1

[Gautam]

Hello Renzo,

To determine which elements of a symbolic vector are real, you can use the isAlways function in conjunction with the isreal condition. This approach checks whether each element of the symbolic vector is always real under all assumptions.

isreal: https://www.mathworks.com/help/matlab/ref/double.isreal.html

isAlways: https://www.mathworks.com/help/symbolic/sym.isalways.html

Answer 2

[Walter Roberson]

 c(imag(c)==0)