Thrash's profile - activity

Ideals of $\mathbb Z[x]$ I think the following code should output True instead of False because we have $1 = (1-2x)+2x \

Ideals of $\mathbb Z[x]$ I think the following code should output True instead of False because we have $1 = (1-2x)+2x \

Ideals of $\mathbb Z[x]$ I think the following code should output True instead of False because we have $1 = (1-2x)+2x \

Ideals of $\mathbb Z[x]$ I think the following code should output True instead of False: R.<x> = ZZ[] I = R.ideal

Is there any way Sage can handle $\sum_{k=0}^\infty 4^{(-1)^k} x^k$ directly/automatically?

Power series with alternating exponent Mathematically, we have $4^{(-1)^k} = \frac18 (17+15(-1)^k)$ for all integers $k

Is there any way Sage can handle $\sum_{k=0}^\infty 4^{(-1)^k} x^k$ directly?

Is there any way Sage can handle $\sum_{k=0}^\infty 4^{(-1)^k}*x^k$ directly?

Is there any way Sage can handle $\sum_{k=0}^\infty 4^{((-1)^k}*x^k$ directly?

Is there any way Sage can handle $\sum_(k=0)^\infty 4^((-1)^k)*x^k$ directly?

Is there any way Sage can handle $sum_(k=0)^\infty 4^((-1)^k)*x^k$ directly?

Power series with alternating exponent Mathematically, we have $4^{(-1)^k} = \frac18 (17+15(-1)^k)$ for all integers $k

Power series with alternating exponent Mathematically, we have $4^{(-1)^k} = \frac18 (17+15(-1)^k)$ for all integers $k

Thank you both!

I would like to compute $\sum_{k=0}^\infty (1+(-1)^k) x^k$. In Mathematica, one can do

In[1]:= Sum[(1+(-1)^k)*x^k,{k,0,Infinity}]                                     

          -2
Out[1]= -------
              2
        -1 + x

How does it work in Sage? I tried

sage: var('k')
k
sage: sum((1+(-1)^k)*x^k, k, 0, oo)
sum(((-1)^k + 1)*x^k, k, 0, +Infinity)

which doesn't give me any new information.

Compute power series I would like to compute $\sum_{k=0}^\infty (1+(-1)^k) x^k$. In Mathematica, one can do In[1]:= Sum

The combinatorial species of rooted trees can be defined recursively via $A = X\cdot E(A)$, where $X$ denotes the singleton species and $E$ the set species. How can I make the following code work? The last command yields an error.

sage: X = species.SingletonSpecies()
sage: E = species.SetSpecies()
sage: A = CombinatorialSpecies()
sage: A.define(X*E(A))
sage: A.generating_series()

Recursive combinatorial species The combinatorial species of rooted trees can be defined recursively via $A = X\cdot E(A

Recursive combinatorial species The combinatorial species of rooted trees can be defined recursively via $A = X\cdot E(A

Recursive combinatorial species The combinatorial species of rooted trees can be defined recursively via $A = X\cdot E(A

You are right in principle, and that would be the proper (elegant) mathematical way, but knowing the result in the case

You are right in principle, and that would be the proper (elegant) mathematical way, but knowing the result in the case

Accelerating for-loop I have a loop like n = 3 M = MatrixSpace(Integers(n),n) L = [] for m in M: if condition:

Accelerating for-loop I have a loop like n = 3 M = MatrixSpace(Integers(n),n) L = [] for m in M: if condition:

Accelerating for-loop I have a loop like n = 3 M = MatrixSpace(Integers(n),n) L = [] for m in M: if condition:

Accelerating for-loop I have a loop like n = 3 M = MatrixSpace(Integers(n),n) L = [] for m in M: if condition:

Thanks, I've already played with that, too. In this case this should be equivalent to the fact that if we define all the

Thanks, I've already played with that, too. In this case this should be equivalent to the fact that if we define all the

Thanks, I've already played with that, too. In this case this should be equivalent to the fact that if we define all the