I may be wrong but as I try to understand it they have a more abstract
class of ideals(independent of rings) and more methods are defined on
this abstract formulation of ideals. Is it possible to change few of the
present implementation so that we can have such kind of in dependency
for abstract things. As I said I may be completely wrong but I am trying
to understand this.
On Fri, Apr 26, 2013 at 2:04 AM, Tom Bachmann <[email protected]
<mailto:[email protected]>> wrote:
On 25.04.2013 21:31, Amit Jamadagni wrote:
Thanks for the replies. I have a doubt is the generator
restricted to
polynomials or can we use it even symbolically. Like they use :
I = ideal (a^2*b-c^2, a*b^2-d^3, c^5-d) .
You cannot do it like this. Ideals are always relative to a
surrounding ring. You can do
>>> R = QQ[a, b, c, d]
>>> I = R.ideal(a^2*b-c^2, a*b^2-d^3, c^5-d)
And is it possible to
implement methods as they have done , in Sympy ??
Yes, very much so. All algorithms I know use polynomial
factorization and groebner bases. The only thing I'm not sure about
is if you need factorization in extension fields, which may not be
implemented.
In any case, these things are *very* non-trivial. Have a look at "a
singular introduction to commutative algebra".
An awesome project would be to implement primary decomposition. Not
sure how feasible this is.
On Fri, Apr 26, 2013 at 1:49 AM, Aaron Meurer
<[email protected] <mailto:[email protected]>
<mailto:[email protected] <mailto:[email protected]>>> wrote:
I think that SymPy also uses generators, like QQ[x].ideal(x
+ 1) is
the ideal generated by x + 1. Note that Ideal is just an
abstract
base class.
Aaron Meurer
On Apr 25, 2013, at 2:15 PM, Amit Jamadagni
<[email protected] <mailto:[email protected]>
<mailto:bitsjamadagni@gmail.__com
<mailto:[email protected]>>> wrote:
I was again referring to this page where the ideals
have been
implemented
http://docs.sympy.org/0.7.2/__modules/polys/agca.html#sympy.__polys.agca.ideals.Ideal.is___prime
<http://docs.sympy.org/0.7.2/modules/polys/agca.html#sympy.polys.agca.ideals.Ideal.is_prime>
and was comparing with this implementation
http://www.math.uiuc.edu/__Macaulay2/doc/Macaulay2-1.5/__share/doc/Macaulay2/__Macaulay2Doc/html/_ideals.html
<http://www.math.uiuc.edu/Macaulay2/doc/Macaulay2-1.5/share/doc/Macaulay2/Macaulay2Doc/html/_ideals.html>
The second one uses generator as the input but in sympy
there is a
difference approach as I tried to understand it.Can we
have such
an implementation and carry on to the same to
matrices. Any
comments on this would be helpful.
On Mon, Apr 22, 2013 at 12:06 AM, Amit Jamadagni
<[email protected] <mailto:[email protected]>
<mailto:bitsjamadagni@gmail.__com
<mailto:[email protected]>>> wrote:
Yes I have sort of started writing GSoC proposal. I
am still
not clear since I have other ideas in mind which
seem more
concrete but are diffused(referring to the second
proposal).I
have these 3 topics in mind
1.Covariant and Contravariant vectors
2.Advancement in Spherical Harmonics
3.q - Calculus
These seem completely diffused so I thought of
making some
progress in group theory(referring to this
proposal). Coming
to my background I am currently pursuing my Masters in
Mathematics and have been dealt with courses like
Algebra and
have been doing some paper reading under the
guidance of
professor in the same area (the bounds of rubiks
cube using
group theory). At the same time I have been reading the
Handbook of Computational group theory.I have done some
patches in quantum module(relating to spin module).So
basically stuck between two proposals the second
one is almost
getting ready but my apprehensions remain as the
topics are
diffused as stated earlier.Thanks.
On Sun, Apr 21, 2013 at 11:55 PM, David Joyner
<[email protected] <mailto:[email protected]>
<mailto:[email protected] <mailto:[email protected]>>> wrote:
On Sun, Apr 21, 2013 at 2:17 PM, Amit Jamadagni
<[email protected] <mailto:[email protected]>
<mailto:bitsjamadagni@gmail.__com
<mailto:[email protected]>>>
wrote:
So these would suffice to a project work or
if it does
not I am willing to work on it.Thanks.
I don't know. Did you write up your project on
the GSOC
page? You still haven't told me what your goal is
in doing it. What exactly do you plan on doing,
in detail?
What experience do
you have (what books have you read related to the
project...) that make us believe
you can do it?
On Sun, Apr 21, 2013 at 11:40 PM, David Joyner
<[email protected] <mailto:[email protected]>
<mailto:[email protected] <mailto:[email protected]>>> wrote:
That is the idea.
On Sun, Apr 21, 2013 at 2:01 PM, Amit
Jamadagni
<[email protected] <mailto:[email protected]>
<mailto:bitsjamadagni@gmail.__com
<mailto:[email protected]>>> wrote:
I guess you were to referring to
something
like this
http://www.sagemath.org/doc/__reference/polynomial_rings/__sage/rings/polynomial/__polynomial_quotient_ring.html
<http://www.sagemath.org/doc/reference/polynomial_rings/sage/rings/polynomial/polynomial_quotient_ring.html>
On Sun, Apr 21, 2013 at 11:19 PM,
David Joyner
<[email protected] <mailto:[email protected]>
<mailto:[email protected] <mailto:[email protected]>>> wrote:
On Sun, Apr 21, 2013 at 1:45
PM, Amit
Jamadagni
<[email protected] <mailto:[email protected]>
<mailto:bitsjamadagni@gmail.__com
<mailto:[email protected]>>> wrote:
In addition to all that is
it possible
to think more abstractly
and a little
beyond polynomials??
I mentioned integer quotient
rings. Were
you also including polynomial
quotient
rings (in one variable)?
On Sun, Apr 21, 2013 at
10:49 PM,
David Joyner
<[email protected] <mailto:[email protected]>
<mailto:[email protected] <mailto:[email protected]>>> wrote:
On Sun, Apr 21, 2013 at
1:10 PM,
Amit Jamadagni
<[email protected] <mailto:[email protected]>
<mailto:bitsjamadagni@gmail.__com
<mailto:[email protected]>>>
wrote:
Yes in the case of
polynomials
we are looking at
Euclidean
domains but as I
understand
the fist part (The
Abstract
Domains) and was
comparing
with this
http://tnt.math.se.tmu.ac.jp/__nzmath/manual/modules/ring.__html.Is
<http://tnt.math.se.tmu.ac.jp/nzmath/manual/modules/ring.html.Is>
this going right in
the right
way or completely
wrong??
What do you mean by
"right way"?
Is your intention to
include a
ring module in SymPy
and then have
the class of SymPy
polynomials
rings and integer
quotient rings
inherit properties from
that
class? What is your
ultimate goal?
Thanks.
On Sun, Apr 21,
2013 at 10:25
PM, David Joyner
<[email protected] <mailto:[email protected]>
<mailto:[email protected] <mailto:[email protected]>>>
wrote:
On Sun, Apr 21,
2013 at
12:51 PM, Amit
Jamadagni
<[email protected] <mailto:[email protected]>
<mailto:bitsjamadagni@gmail.__com
<mailto:[email protected]>>>
wrote:
I have
referred to this
http://docs.sympy.org/0.7.2/__modules/polys/internals.html?__highlight=ring#sympy.polys.__domains.Ring.invert
<http://docs.sympy.org/0.7.2/modules/polys/internals.html?highlight=ring#sympy.polys.domains.Ring.invert>
and there
seems we can
have some more
properties
for in the
abstract
domains like
Residue
class for
which would
be a
subclass of
Commutative
RIng and
which would
be a
subclass of
Ring.Any
comments on
this would
be
helpful.Thanks.
The only
algorithm I know
if to compute
inversions
in polynomials
rings is
the extended
Euclidean
algorithm, so
the rings
would have to
be Euclidean
domains for
that to work.
Are these Euclidean
domains you are
looking at?
On Sun, Apr
21, 2013
at 9:14 PM,
David
Joyner
<[email protected] <mailto:[email protected]>
<mailto:[email protected] <mailto:[email protected]>>>
wrote:
Again,
sounds fine
with me
but there
are a
lot of rings
(implicitly)
already
in SymPy.
Are you
going to
add
inheritance
for
each of these?
What
functionality
are you
adding?
On Sun,
Apr 21,
2013 at
11:05 AM,
Amit
Jamadagni
<[email protected] <mailto:[email protected]>
<mailto:bitsjamadagni@gmail.__com
<mailto:[email protected]>>>
wrote:
Can the
abstract
things like
rings be also
included ?? I
have browsed
through the
code and
everything is
abstract would
it
be a useful
to
add.Thanks.
On
Sun, Apr
21,
2013 at
3:36 PM, Amit
Jamadagni
<[email protected] <mailto:[email protected]>
<mailto:bitsjamadagni@gmail.__com
<mailto:[email protected]>>>
wrote:
Thanks for
the reply
and I
didnt go
through
the
license
policy of
PARI
,sorry for
that.
On Sun,
Apr 21,
2013 at
3:20 PM,
David
Joyner
<[email protected] <mailto:[email protected]>
<mailto:[email protected] <mailto:[email protected]>>>
wrote:
On
Sun,
Apr
21,
2013
at
4:54
AM,
Amit
Jamadagni
<[email protected] <mailto:[email protected]>
<mailto:bitsjamadagni@gmail.__com
<mailto:[email protected]>>>
wrote:
Can we
have
this
three
modules
from
nzmath
in
Sympy
I
have
gone
through
the manual
and the
topics
which
seem
feasible
are
1.Finite
fields
2.Groups
3.Rings
4.Matrix
related
Algebra
5.Polynomials
over
Rings
nzmath
is
BSD-licensed.
I
think
integrating
their
code
into
SymPy,
at
least for
finite
fields
and
matrices
and
groups, is
a good
idea,
but I
don't
know the
maintainers'
policy
on
this.
Make
sure
that
the
original
author's
copyright
is
preserved.
6.If
time
permits
extending
it
to
implementation
of
Galois
group
of
polynomials.
(I
have
scanned
through
PARI
and this
seems
it
can be
done).
PARI's
license is
GPL,
so you
can't
use
any
PARI
code
in SymPy.
Any comments
on
this
would
be
helpful.Thanks.
On
Fri,
Apr 19,
2013
at
1:59
AM, Amit
Jamadagni
<[email protected] <mailto:[email protected]>
<mailto:bitsjamadagni@gmail.__com
<mailto:[email protected]>>>
wrote:
So
would
be
feasible
to
have
a proposal
with
discrete
topics.I
am
trying
hard
to
work
out
something
on
quantum
module
but
if
that
does
not
happen
the
above
question
would
come
into
picture.Thanks.
On
Fri,
Apr
19,
2013
at
1:27
AM,
David
Joyner
<[email protected] <mailto:[email protected]>
<mailto:[email protected] <mailto:[email protected]>>>
wrote:
I haven't
looked
at
that
project
but
I think
I see
what
you
mean.
The
two
ideas
sounds
a bit
too
disjointed
to
fit
smoothly
into
one
GSOC
proposal,
but
I could
be
wrong.
Maybe
you
could
write
a second
GSOC
proposal
with
the
discrete
topics
(finite
fields,
matrix
theory
over
finite
fields,
etc)
and
then
worry
later
about
which
one
you
want
to
do?
On
Thu,
Apr
18,
2013
at
2:40
PM,
Amit
Jamadagni
<[email protected] <mailto:[email protected]>
<mailto:bitsjamadagni@gmail.__com
<mailto:[email protected]>>>
wrote:
I already
have
discussed
the
idea
of
spherical
harmonics
in
detail
on
this
link.
https://groups.google.com/__forum/?fromgroups=#!topic/__sympy/be0WuW9gs7I
<https://groups.google.com/forum/?fromgroups=#!topic/sympy/be0WuW9gs7I>
It
basically
states
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