On 4 June 2013 07:47, Jori Mantysalo <[email protected]> wrote:
> Is there any plans to make Sage more useful to beginners? To give two
> examples from different levels:
>
> 1*(2+
>
I don't get the same error, and don't get any response at all until I
close the parenthesis. What's wrong with "Syntax error"? Would you
have preferred "That doesn't make sense?!)
> This gives "SyntaxError: invalid syntax" and explanation is "... exec
> compile(u'open("___code___.py","w").write("# -*- coding: utf-8 ..." --- what
> is beginner supposed to do with this?
>
> R.<x>=QQ[]; [x^5+a*x+b for a in range(1,50) for b in range(1,50) if
> len(factor(x^5+a*x+b))==1 and PermutationGroup(NumberField(x^5+a*x+b,
> 'z').galois_group(type="pari").group()).is_isomorphic(AlternatingGroup(5))]
>
> This works (as of Sage 5.6) but...
>
> - There is no function to check if polynomial is irreducible or not.
> len(factor(f)) is workaround --- and for x^5 does not work. Try to change
> range(1,50) to range(-25,25).
>
???
sage: R.<x>=QQ[]
sage: f=x^5+x+1
sage: f.is_irreducible()
False
sage: f=x^5+x+3
sage: f.is_irreducible()
True
sage: f.galois_group().is_isomorphic(SymmetricGroup(5))
True
> - User needs some "generator" to get Galois group.
Not if you do what I did above.
>
> - Galois group is not right type for is_isomorphic()-function, so user must
> convert it.
>
ditto.
Of course if was really trying to find a lot of A5 polynomials I would
put in some other much quicker checks, starting (after irreducibility)
with a check that the discriminant is not a square.
> Underlying software is great! And as last example shows, with Sage user can
> find polynomial with given Galois group. It is even fast to write code
> snippets like this --- if you happen to know all bits needed.
>
> But Sage is not going to be widely used at least here. It is too hard to
> use.
So is any complicated software when you start.
>
> --
> Jori Mäntysalo
>
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