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2020-05-02 00:44:02 +0100 asked a question Best practice to save results of a function as a database

I have a function defined inductively that taxes my computer quite a lot. It will help a lot if I can save its results somewhere, preventing it from unnecessary calculations.

To simplify, assume that it's a function $f: \mathbb{N} \to \mathbb{N}$, where $f(0)=1$ and $f(i)$ depends on the value of $f$ at lower $i$'s. Imagine that I want to calculate $f(n)$ where $n \sim 10^{1000}$.

Of course, I can do it by

for i in range(1000):
    f(i).save("./f_value_{}".format(i))

But I feel like this can be improved. Any idea?

2020-04-30 14:00:39 +0100 commented answer Running VIM inside Sage Shell

same issue here

2020-04-18 12:54:17 +0100 received badge  Nice Question (source)
2020-04-17 19:34:07 +0100 commented question SageMath Gap Kernel Compatibility

I have similar issues on sage -i gap_packages too! Error: * No rule to make target 'all-toolchain'. Stop. I'm also on Arch linux, installed via pacman. @skafiskafniak have you figured out a solution?

2020-04-17 16:28:34 +0100 commented answer How do I install a GAP package in Sage?

I got an error by running sage -i gap_packages :make: *** No rule to make target 'all-toolchain'. Stop.

2020-04-17 16:23:04 +0100 asked a question Problem with GAP

Is GAP still compatible with sage? I followed the tutorial on this page, but it immediately broke at the first step:

sage: Q = QuantumGroup(['A',2])

Error message:

FeatureNotPresentError: GAP package QuaGroup is not available.

TestPackagevbailability("QuaGroup") evaluated to fail in GAP.

To install GAP package QuaGroup you can try to run 'sage -i gap_packages'.

Running sage -i gap_packages in my terminal (I'm on archlinux), I got

make: * No rule to make target 'all-toolchain'. Stop.

2020-04-16 19:47:33 +0100 received badge  Student (source)
2020-04-16 19:47:17 +0100 asked a question Polynomial ring indexed over an abelian group (magma).

Hi, I wonder if currently there's a cleaner way to do $x^v \cdot x^w = x^{v+w}$ in Sage, where $v, w$ are some vectors in a vector space?

Once a basis ${v_1, \cdots v_n}$ for the vector space is chosen, this can be done by identifying $x_i$ with $x^{v_i}$, and use the multivariate ring $R[x_1, \cdots, x_n]$. However, I would like to do this in an intrinsic manner, i.e. not choosing a basis.

More generally, I think for any element $m$ in any magma $M$, we should be able to define an algebra $R[x^m|m\in M]$ over any given ring $R$. Notice that this is not the same as FreeAbelianMonoid generated over $M$, as in this case $x^m x^{n}$ is not the same as $x^{mn}$.

Question

Is $R[x^m|m\in M$$ currently doable? If not, I might work on writing it.

Application

A reason why I think it would be helpful: it can help calculating generalized characters of representations of quantum groups.