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

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Renzo Segovia
Renzo Segovia 2020-11-4
回答： Walter Roberson 2025-2-11
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?

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回答（2 个）

Gautam
Gautam 2025-2-11
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
Walter Roberson
Walter Roberson 2025-2-11 
 c(imag(c)==0)

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