Post Reply 
Polynomial Homogeneous Test (CAS)
08-06-2016, 01:22 AM
Post: #1
Polynomial Homogeneous Test (CAS)
A polynomial is homogeneous if all of the nonzero terms has the same degree. Tests a polynomial of four variables x, y, z, and t and their combinations (x*y, x*z, x*y*z, etc). If the polynomial in question is homogeneous, the program returns a 1 (for true), otherwise 0 is returned (for false).

HP Prime Program ishomogeneous
Code:
#cas
ishomogeneous(poly):=
BEGIN
// 2016-08-03 EWS
// x,y,z,t
LOCAL tms,cnt,pt,lst,wp,dg,dgr;
tms:=part(poly);
lst:={};

FOR pt FROM 1 TO tms DO
wp:=part(poly,pt);
dg:=degree(wp,x)+degree(wp,y)+
degree(wp,z)+degree(wp,t);
lst:=concat(lst,{dg});

// test
IF pt≥2 THEN
IF lst(pt)≠lst(pt-1) THEN
RETURN 0;
KILL;
END;
END;

END;
return 1;
END;
#end


Examples:
ishomogeneous(x^2 + 3) returns 0
ishomogeneous(x^2 + 3*y^2) returns 1 (all terms are of degree 2)
ishomogeneous(x^2*z – 3*y^2*t + x^3) returns 1 (all terms are of degree 3)
ishomogeneous(x^2*z – 3*y^2) returns 0

Source:

Avner Ash and Robert Gross. “Elliptic Tales. Curves, Counting, and Number Theory” Princeton University Press, New Jersey 2016.
Visit this user's website Find all posts by this user
Quote this message in a reply
Post Reply 


Messages In This Thread
Polynomial Homogeneous Test (CAS) - Eddie W. Shore - 08-06-2016 01:22 AM



User(s) browsing this thread: 1 Guest(s)