asking for a simple locally soluble algorithm for a quartic

[American Citizen <website.reader3@gmail.com>]

Does anyone have a simple GP-Pari script which outputs 0 for false and 1 
for true when the input is a quartic in vector format: [a,b,c,d,e] where 
the quartic is a*x^4 + b*x^3 + c^x^2 + d^x +e and we are trying to find 
the everywhere_local_solubility of the quartic?

Example GP Pari function:

everywhere_locally_soluble(Q) = [0,1] where 0 means false and 1 means true.

I tried to follow the algorithms in Chapter 3 of Cremona's book on 
elliptic curve algorithms, but hit difficulty on trying to write down in 
the GP Pari script the discriminant of a quartic, which forced me to go 
to Wolfram Mathematica to find this expression, which is horribly 
complex and incredibly easy to mistype the values from the image 
graphics file. It is fascinating (in a perverse way) to find that image 
files are posted for long equations, thus forcing a person to manually 
transcribe them, and most people have difficulty doing this without 
transcription error.

I still am stuck in these algorithms in Chapter 3 and trying to 
successfully transcribe them into GP-Pari script.

I appreciate the assist.

THANK YOU.

Randall