mathjain's profile - activity

Given a number Field K and its ring of integers $O_K$, I want to enumerate prime ideals and calculate some quantities in $O_K$ modulo the prime ideals. This computation depends on the size of the ideal.

What I did earlier was taking a prime number, creating its ideal, factorizing it and using the factors as prime ideals. But this way I think I am doing very large computations because the norm would be very high.

I want to enumerate prime ideals below a certain norm in SAGE. What can I do?

I wanted to know what procedure does SAGE use for computing class numbers. I typed

sage : K = NumberField(x^2 + x + 1)

sage : K.class_number?

After that I got the documentation and further I opened this file ~/SageMath/local/lib/python2.7/site-packages/sage/rings/number_field/number_field.py

In that I looked for the place where I can find the class number snippet. It turns out that sage returns the order of class group, so I looked for class group snippet.

proof = proof_flag(proof)

    try:
        return self.__class_group[proof, names]
    except KeyError:
        pass
    except AttributeError:
        self.__class_group = {}
    k = self.pari_bnf(proof)
    cycle_structure = tuple( ZZ(c) for c in k.bnf_get_cyc() )

    # Gens is a list of ideals (the generators)
    gens = tuple( self.ideal(hnf) for hnf in k.bnf_get_gen() )

    G = ClassGroup(cycle_structure, names, self, gens, proof=proof)
    self.__class_group[proof, names] = G
    return G

But I couldn't understand where is the implementation of algorithm. Can anyone help me from here to reach where I can get the algorithm?

I am trying to build the multiplicative group of a finite field.

I define a finite field, its multiplicative group, and a conversion map from the finite field to its multiplicative group as follows:

sage: F.<a> = GF(7^2)
sage: G = AbelianGroupWithValues([a], n=1,
....:     gens_orders=[48], values_group=F)
sage: phi = G.convert_map_from(F)

Up to here, everything is fine.

Now there is an error when trying to use phi:

sage: phi(a)
Traceback (most recent call last)
...
TypeError: 'sage.rings.finite_rings.element_givaro.FiniteField_givaroElement' object is not iterable

What does this mean?

I am facing a problem while doing following on terminal in Sage

sage: Fin_field = GF(49) sage: Mult_grp = AbelianGroupWithValues([Fin_field.gen()], n =1 , gens_order = [48], values_group=Fin_field) sage: phi = Fin_field.coerce_map_from(Mult_grp) Upto here, everything is fine. Now there is an error in the next line - sage: phi(Fin_field.gen())

TypeError: 'sage.rings.finite_rings.element_givaro.FiniteField_givaroElement' object is not iterable

What does this mean?

I have created a group in the category - finite enumerated commutative subgroup. But it doesn't have an option of quotient group ( it has but shows Not Implemented Error)

I wanted to know why implementing a quotient group is not possible if quotient ring is done already? Actually, I was thinking to implement it myself, but I thought it will be good to ask here first if people have tried that. Also, does anyone know how I can track the current progress being done in sage.

How to apply it to one's installation? Thanks!

I am currently working with sage offline version (downloaded version). What difference does it make if I use CoCalc. Does offline version supports all features?

I have a finite field with me. I want to work with a multiplicative group of it. I only found that it is possible to do this with Z modulo n in Sage. But my fields are finite extensions of such a field.

If someone has a way to deal with, please help!

Yeah this surely works for the case when R is defined as Integers(something). Is there any method to get it for a general finite field for instance, a residue field?

I tried computing this -

sage : K = CyclotomicField(37^5)

But after almost a minute, the process just popped up "Killed" and automatically exited sage session.

Why does that happen and what is the meaning?

Is there any alternative way to do this?

https://ask.sagemath.org/question/272...

There is a similar question in this link. But I want to know whether I can do this (without knowing the unit group). So, I have collected a list of elements (from another code), which will be generators of the subgroup I want to generate. What should I do?

I wanted to know by what algorithm sage finds a defining polynomial of an unramified extension of p-adic numbers?

I wanted to know by what algorithm sage finds a defining polynomial of an unramified extension of p-adic numbers?