Nicolas Essis-Breton's profile - activity

@achrzesz Very flexible approach. Thank you.

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

Here 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.

@archrzesz Exactly what I want, thank you. Is there a way to keep the coefficient of each monomial? For example, return $5 x^4 y^4$.

In the expression $$ x^2 y^2+x y^2+x^3y + 5 x^4 y^4 $$ I would like to keep only the term where the variables have even power $$ x^2y^2+5 x^4 y^4 $$

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.

@Shashank Thanks Shashank.

If result.sage is calling add function from addition.sage, you need to load that file in result.sage.

You can also load the file without giving the path, if you type the following two lines in the beginning of the notebook

import sys
sys.path.append('path-to-module')

Let's say I want to write two modules 'addition.sage' and 'result.sage'.
I would like to import 'addition.sage' in 'result.sage'. How can I do this?
I've try the following, but it doesn't seem to work.

'addition.sage' file:
from sage.all import *
add(x,y)=x+y

'result.sage' file:
from addition import add
print add(1,2)

my sage session:
sage: load('myPath/result.sage')

This gives me the error 'ImportError: No module named addition'.
Although, my PYTHONPATH contains the directory where my two modules are located.

@DSM Thanks DSM, your answer is enlightening

You're getting the TypeError because you're double-assigning x: in your second line, you make it a list of variables, but in the third you redefine it as a symbolic variable. The f(x)=sum(x[i],i,0,n) line is translated as

sage: preparse("f(x) = sum(x[i], i, 0, n")
'__tmp__=var("x"); f = symbolic_expression(sum(x[i], i, Integer(0), n).function(x)'

Unfortunately we can't simply rename x to xx: the "f(x,y) = x+y" syntax requires explicit specification of the variables, and you can't pass it a list. So for a fixed n (which is the only case I really know how to handle offhand) I would probably do this instead:

sage: n = 2
sage: xx = [var('x_%d' % i) for i in range(n)]
sage: 
sage: f = sum(xx).function(*xx)
sage: f
(x_0, x_1) |--> x_0 + x_1

[Here I took advantage of the * operator in *xx, which turns f(*[a,b,c]) into f(a,b,c).]

Oh, I've just noticed that I used [0..n-1] as the indices and I think you're using [0..n], but that's easy to change.

How can I define a function of the form $$f(x_1,x_2,...,x_n)=\sum_{i=0}^n x_i$$ I tried the following
sage: n = 2
sage: x = [ var('x_%d' % i) for i in range(n) ]
sage: f(x)=sum(x[i],i,0,n)
The last line gives me the error
"TypeError: 'sage.symbolic.expression.Expression' object does not support indexing".