[sage-support] Re: Comment in python code [[cloud.sagemath.com]]
This is not a bug. Rather it is a consequence of the syntax require by python. To quote from the python documentationhttp://docs.python.org/release/2.5.1/ref/indentation.html : Leading whitespace (spaces and tabs) at the beginning of a logical line is used to compute the indentation level of the line, which in turn is used to determine the grouping of statements. The reason why you are getting an error here is that in python code, including comment, in for-loops must be indented. The rationale for this is that it makes the code easier to read. I tend to agree because I used to indent my code before I started using python. I even indent in tex files:) Andrew On Sunday, 3 November 2013 11:29:20 UTC+1, projetmbc wrote: Hello. I think that is not good to have an error with the following code. for i in range(10): # Here is a basic comment... print i, --, i**2 The error due to the comment is the following one. Error in lines 1-1 Traceback (most recent call last): File /mnt/home/pjXx5pJx/.sagemathcloud/sage_server.py, line 633, in execute exec compile(block+'\n', '', 'single') in namespace, locals File string, line 1 for i in range(Integer(10)): ^ SyntaxError: unexpected EOF while parsing Just add a space before # and everything is ok... Too weird... This should be fixed. Best regards. C. -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
[sage-support] Re: Problems with multivariate Laurent polynomial subtitution
As I posted in sage-dev the problem actually is with the coefficients and I found a somewhat heavy handed solution: sage: R.u,v=LaurentPolynomialRing(ZZ,2) sage: p=2*u**-1*v**-1+u*v sage: sum( R(c)*u**-exp[0]*v**-exp[1] for (exp,c) in p.dict().iteritems() ) 2*u*v + u^-1*v^-1 Andrew -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
[sage-support] Problems with multivariate Laurent polynomial subtitution
Hello All,
I have some polynomials in two varaibles, say u and v, and I want to apply
the map which u to u^-1 and v to v^-1. Sadly, I run to problems insude sage:
With one variable it is OK:
sage: R.u=LaurentPolynomialRing(ZZ)
sage: p=u**-1
sage: p.substitute(u=u^-1)
u
but when I go to two variables then it breaks:
sage: R.u,v=LaurentPolynomialRing(ZZ,2)
sage: p=u**-1
sage: p.substitute(u=u^-2)
---
TypeError Traceback (most recent call last)
ipython-input-32-d9f8f61b1503 in module()
1 p.substitute(u=u**-Integer(2))
/usr/local/src/sage/sage-5.11/local/lib/python2.7/site-packages/sage/structure/element.so
in sage.structure.element.Element.substitute
(sage/structure/element.c:6349)()
/usr/local/src/sage/sage-5.11/local/lib/python2.7/site-packages/sage/rings/polynomial/laurent_polynomial.so
in sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_mpair.subs
(sage/rings/polynomial/laurent_polynomial.c:10778)()
/usr/local/src/sage/sage-5.11/local/lib/python2.7/site-packages/sage/structure/element.so
in sage.structure.element.RingElement.__imul__
(sage/structure/element.c:14780)()
/usr/local/src/sage/sage-5.11/local/lib/python2.7/site-packages/sage/structure/coerce.so
in sage.structure.coerce.CoercionModel_cache_maps.bin_op
(sage/structure/coerce.c:8169)()
TypeError: unsupported operand parent(s) for '*': 'Multivariate Laurent
Polynomial Ring in u, v over Rational Field' and 'Multivariate Laurent
Polynomial Ring in u, v over Integer Ring'
If p=u then this is fine, so it is the u^-1 that is causing the problem.
Of course what I really want to do is p.substitute({u:u**-1, v:v**-1})
where o is computed on the fly but if I can even do this then I am stuck.
Does ayone know if I am doing something wrong here or if there is a way
around this?
Cheers,
Andrew
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[sage-support] Re: Constructing subsapces of vector spaces
Thanks Nils. I this is similar to, but more elegant than, what I tried earlier. I went back to the solution above, however, I thought that there was probably a lot of overhead in creating the space ZZ^3 and the homomorphism. Indeed, %timeit V.hom([(ZZ^3)(v) for v in [[1,2,3],[2,1,4],[3,3,7]]]).kernel() 125 loops, best of 3: 2.15 ms per loop sage: %timeit V.submodule_with_basis([V.linear_combination_of_basis(b.list()) for b in mat.kernel().basis()]) 625 loops, best of 3: 1.39 ms per loop so it does seem to be slower, although one example is hardly definitive. Andrew -- You received this message because you are subscribed to the Google Groups sage-support group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
[sage-support] Re: Constructing subsapces of vector spaces
Hi John, Thanks for the reply, but you have my problem upside down as I don't need to restrict from the ambient space to the subspace but rather to extend from the subspace to the ambient space. For example, I could have: sage: V Free module of degree 4 and rank 3 over Integer Ring User basis matrix: [0 1 2 3] [2 3 1 4] [1 3 2 1] sage: mat=matrix([[1,2,3],[2,1,4],[3,3,7]]); mat.kernel() Free module of degree 3 and rank 1 over Integer Ring Echelon basis matrix: [ 1 1 -1] The problem that is V is isomorphic to Z^3, but it is represented as a subspace of Z^4, whereas the kernel is a subspace of Z^3. As I mentioned, sage: V.submodule_with_basis([V.linear_combination_of_basis(b.list()) for b in mat.kernel().basis()]) Free module of degree 4 and rank 1 over Integer Ring User basis matrix: [1 1 1 6] does give the kernel as a subspace of V. I was just wondering if there was a better way of doing this. Cheers, Andrew -- You received this message because you are subscribed to the Google Groups sage-support group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
[sage-support] Constructing subsapces of vector spaces
Hi All, I have been playing with some code where I want to find a submodule of a module V which is annihilated by a bunch of maps. What I want to do something like the following: V= some free submodule of rank v inside a space of rank d\ge v. mat=[[0 for col in range(w)] for row in range(v)] # fairly sparse matrix which describes the map f on bases of V and W ...compute non-zero entries of the matrix ``mat`` V = V.intersection( matrix(mat).kernel() ) where v=dim V, w=dim W where f is a map from V to W. Of course, this doesn't quite work because matrix(mat).kernel() returns a submodule of ZZ^v with respect to its standard basis whereas the space V has a very different basis in general. To get around this I found myself writing kernel=V.submodule_with_basis([V.linear_combination_of_basis(b.list()) for b in matrix(pmat).kernel().basis()]) V=V.intersection(kernel) This strikes me as being a very convoluted way of writing something is presumably quite common: writing the standard basis elements as linear combinations of another basis. My question is: is there a better way to do this? For a little while, I tried defining W=FreeModule(ZZ,w) and then constructing the map f explicitly as a homomorphism from V to W. Doing it this way does make f.kernel() into a submodule of V, but this approach just seems to create a lot of extra overhead with very little benefit as I essentially still had to construct the matrix ``mat`` above and used it to define ``f`` with respect to the bases of ``V`` and ``W``. In fact, all this really did was shift my problem above of writing the basis of the kernel in terms of the basis of V to the problem of writing the images of f in terms of the standard basis of W. (Even though I imagine that this second approach is much slower I really should have checked by doing some profiling before rewriting as above, but I didn't...) Any thoughts? Cheers, Andrew -- You received this message because you are subscribed to the Google Groups sage-support group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
[sage-support] Re: Monoid algebra
I think that this does want you want and it's just the absence of documentation that is letting you down. Try: sage: M = FreeMonoid(3,['a','b','c']) sage: a,b,c=M.gens() # or use M.inject_variables() sage: A=M.algebra(QQ) sage: A(a)*A(b)+ A(c) B[c] + B[a*b] Andrew -- You received this message because you are subscribed to the Google Groups sage-support group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
[sage-support] Re: swtich Gap to Sage
I think that this does the same as your code, although it seems to me that
this is not want you really want because the pairs (A,B) of subgroups that
you return will not in general have the property that G=A x B. I have not
played at all with groups in sage before so this may be far from optimal:
def direct_summands(G):
r
Return the direct summands of the abelian group ``G``.
EXAMPLES::
sage: direct_summands( CyclicPermutationGroup(4) )
[(Permutation Group with generators [()], Permutation Group with
generators [(1,2,3,4)]),
(Permutation Group with generators [(1,3)(2,4)], Permutation Group
with generators [(1,3)(2,4)])]
if not (G in Groups and G.is_finite() and G.is_abelian() ):
raise ValueError, '%s must be a finite abelian group' % G
# will create a dictionary of the subgroups in G up to isomorphism
indexed by size
subgroups_by_size={}
for H in G.subgroups(): # loop over *all* subgroups of G
h=H.cardinality()
if h in subgroups_by_size:
if not all(H.is_isomorphic(K) for K in subgroups[h]):
subgroups_by_size[h].append(H)
else:
subgroups_by_size[h]=[H]
# n is the number of divisors of |G|
g=G.cardinality()
divisors = [(d, g/d) for d in g.divisors() if 2*d=g]
return [(A,B) for (d,e) in divisors if d in subgroups_by_size and e in
subgroups_by_size
for A in subgroups_by_size[d] for B in
subgroups_by_size[e] ]
Put this into a file, say, summands,py, and then type
sage: attach summands,py
inside sage.
As a general rule, you can find out what to do using tab-completion. For
example, if you type
sage: G=CyclicPermutationGroup(4)
sage: G.tab
then you will get a list of the methods that apply to the group G.
Andrew
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[sage-support] Localising at a prime ideal
Hi All, Is there any way in sage to construct the localisation (or localization if you prefer) of a ring at a prime ideal? For example, I would like to do the following: sage: R=ZZ.extension(cyclotomic_polynomial(6),'xi') sage: xi=R.gen(1) sage: I=R.ideal(7,xi+4) sage: RI = R.localise(I) Andrew -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Calculating with primitive roots of unity in sage
Thanks for the replies! Over other fields it's no good just extending by a root of the n'th cyclotomic polynomial, since that need not be irreducible! The example you gave was particularly unfortunate since over GF(5) the 5th cyclotomic poly has only 1 root with multiplicity 4. So it's quite right to say that the resulting algebra is not a field. (The question about Sage not being able to tell that the result is finite is unfortunate, and should be logged as a feature to be implemented., but is not particularly relevant to the current discussion). I clearly shouldn't post these things late at night! In the context that I am working with a primitive pth root of unity in characteristic p is an important special case, but this corresponds to xi=1 so I can simply work with GF(p). For fields of characteristic p0, I need to work in GF(p^a) for some a so I guess that my question really is: does anyone know how to construct the smallest extension of GF(p) which contains a primitive eth root of unity when gcd(e,p)=1? Andrew -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
