In the expression x2y2+xy2+x3y+5x4y4 I would like to keep only the term where the variables have even power x2y2+5x4y4
Is there a way to do it?
I look into this post.
But once I get the operands, I don't see how to analyze the variable exponent.
Is that what you need?
var('x y');
p=(5*x^2*y^2+x*y^2+x^3*y+x^4*y^4).polynomial(QQ)
sum([v[0]*v[1] for v in p if forall(v[1].exponents()[0],lambda x:is_even(x))[0]])
#x^4*y^4 + 5*x^2*y^2@archrzesz Exactly what I want, thank you. Is there a way to keep the coefficient of each monomial? For example, return 5x4y4.
I've edited my answer according to the Nicolas request. Notice that my answer works for many variables. Just change var and p.
@achrzesz Very flexible approach. Thank you.
The following also works, although it might not be as flexible as the answer by @achrzesz, which handles things nicely.
x, y = var('x, y')
f(x,y)=x^2*y^2-4*x^2*y+2*y^2+4*x*y^4-3*x^4*y^6
g(x,y)=(f(x,y)+f(-x,y))/2
h(x,y)=(g(x,y)+g(x,-y))/2
hHere is an answer using the list command and some list comprehensions.
var('x y')
R.<x,y>=PolynomialRing(RR)
q=x^2*y^2+x+x^2*y+y^2
terms=list(q)
ans=[t[0]*t[1] for t in terms if (t[1].degree(x) % 2)==0 and (t[1].degree(y) % 2==0)]
sum(ans)This will also keep the coefficients.
Asked: 12 years ago
Seen: 581 times
Last updated: Oct 23 '12
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