MarioM's profile - activity

Hello everyone, I have the following groups

F3.<a1,b1,a2,b2,a3,b3> = FreeGroup()
H3 = F3.quotient([a1*b1/a1/b1*a2*b2/a2/b2*a3*b3/a3/b3])

Then I inject the variables to $H3$

H3.inject_variables()

Now when every element that I write have parent $H3$, but when I write the word a1*b1/a1/b1*a2*b2/a2/b2*a3*b3/a3/b3 this does not return the identity of $H3$, although if I put

a1*b1/a1/b1*a2*b2/a2/b2*a3*b3/a3/b3 == H3.one()

this is true. Does anyone know why this happen and how can I get sage to reduce this word to identity of $H3$?

Thank you Samuel, that should work.

When you use partitions a "border strip" is a partition which diagram has no two cell in the same column(horizontal) or not in the same row(vertical). In Sage with partitions you can do remove_horizontal_border_strip which returns the partitions obtained from self by removing an horizontal border strip of length k. For example Partition([5,3,1]).remove_horizontal_border_strip(1).list() [[5, 3], [5, 2, 1], [4, 3, 1]]

Hello, I'm interested to know if there is a way to define the analoge of remove_horizontal_border_strip(k) which returns the partitions obtained from self by removing an horizontal border strip of length k.

For example:

Partition([5,3,1]).remove_horizontal_border_strip(1).list()
 [[5, 3], [5, 2, 1], [4, 3, 1]]

but for vertical border strip.

Thank you!

Thank you i will see the documentation

I define

x = [var('x_%d' % k) for k in range(p)]
y = [var('y_%d' % k) for k in range(p)]
z =x + y
PRz = PolynomialRing(QQ,z)

with $p$ arbitrary, then I need new variables, to comare polynomials, define as:

t = [z[k] + 1/z[k] for k in range(p)]

Is there a way to substitute the list of variables $z$ with the list of varialbes $t$? The only way that I could do it was as

polynomial.subs(y_0 = t[0]/2, y_1 = t[1]/2, y_2 = t[2]/2, y_3 = t[3]/2)

But I want it for a general number of variables.

Thanks

I want a generalization of this kind

[(r1, ..., rk) for r1 in range(n+1) ... for rk in range(n+1) if r1 + ... + rk = n]

For a general number of $r$'s and any $n$

I have the following code:

 for k in range(9):
    if k != 3:
        print(k)
    else:
        print(20)
        # i want to skip the next iteration

So I want to get: 0,1,2,20,5,6,7,8, here I skip the fourth iteration. I already try to use the command next(), but it doesn't give what I want

Problem: Given a finite free resolution C of $\mathbb{Z}$ over $\mathbb{Z}G$ I would like to consider the free resolution $C \otimes C$. Then of course in this new resolution I'm going to have direct sums of tensor products. In sage I'm working with CombinatorialFreeModule, there is a way to defining a direct sum over CombinatorialFreeModule_Tensor?

Thanks in advance.

If I have a symbolic expression, is there a way to obtain, something like the syllables of this expression in the way as in elements of a FreeGroup?

i want to calculate residues on the unit disk, but in the factorization of the functions i work with i have roots or poles in and out the unit disk but i'm interested only in the ones inside the unit disk.

f(t)=\frac{1}{t^{-1}(t-z_1)(t-z_2)}, |z_1|<1<|z_2|,

There is a way that sage identify the poles i want and work with those?