or so ago and this
was only merged at the end of October.
Since https://github.com/sagemath/sage/pull/36529 is already merged is it
too late to add a comment on the ticket?
Andrew
On Wednesday 13 December 2023 at 12:30:03 pm UTC+11 John H Palmieri wrote:
> Could this be related to ht
, at
least on the two macs that I have available, is
sage: view(crystals.LSPaths(
RootSystem(['A',4]).weight_space().basis()[1] ) )
If people agree that this is a bug then I am happy to post a fix.
Andrew
On Monday 11 December 2023 at 16:35:59 UTC+11 Andrew wrote:
> I am trying to v
, at
least on the two macs that I have available, is
sage: view(crystals.LSPaths(
RootSystem(['A',4]).weight_space().basis()[1] ) )
If people agree that this is a bug then I am happy to post a fix.
Andrew
On Monday 11 December 2023 at 4:35:59 pm UTC+11 Andrew wrote:
> I am trying to v
iew(B, tightpage=True)
When it does work, a nice tikz generated pdf file pops up. Am I missing
some steps? Can anyone tell me what I am doing wrong?
Andrew
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I am trying to view some crystal graphs from inside sage. Sometimes this
works properly, and other times, I am met with a pop error message that
says:
The document “sage.pdf” could not be opened. The file doesn’t exist.
I am using:
SageMath version 10.3.beta1
Release Date: 2023-12-10
Using
Thanks. That makes sense (even if it tweaks my sense of consistency) but it
might more sense as MPI is built in via Python as well... but we do have
conda on the cluster and it puts them in control more or less of their
process.
Thanks
On Thursday, August 10, 2023 at 2:22:33 PM UTC-4 Nathan
I've done some research, googled around, searched though ask sage, looked
at some of the thematic tutorials and have finally come to this google
group (ask sage, in all fairness, never approved this post, deleted me and
it, and no idea why and it was from my corporate email address? But ask a
and
the second failing example is below..
Andrew
Here are the points that this fails on:
x2=
2/9*cos(37/14-(3506*t)/31)+5/26*cos(71/27-(3217*t)/32)+4/21*cos(34/19-(1753*t)/31)+4/19*cos(117/47-(1709*t)/34)+13/43*cos(82/27-(2419*t)/55)+847/57*cos(59/44-(289*t)/46)+9/14*cos((377*t)/30+53/27)+57/31
As I discovered on CoCalc running Sage 9.1, it appears that any attempt to
use nauty/genbg to build bipartite/hyper-/di- graphs with more than 32
total vertices fails silently.
Please compare the results of:
-
L=list(hypergraphs.nauty(13, 13, uniform=2, regular=2,max_intersection=1))
As I discovered on CoCalc running Sage 9.1, it appears that any attempt to
use nauty/genbg to build bipartite/hyper-/di- graphs with more than 32
total vertices fails silently.
Please compare the results of:
-
L=list(hypergraphs.nauty(13, 13, uniform=2, regular=2,max_intersection=1))
There are some conversion scripts around for converting python 2 code to
python 3. They are not perfect but are typically a good first approximation
to what you want. See, for example:
- https://docs.python.org/2/library/2to3.html
- https://www.pythonconverter.com/
On Saturday, 8
Sorry, I didn't look at your examples carefully enough. I agree that these
should have the same parent.
Andrew
On Saturday, 4 May 2019 16:18:40 UTC+10, Daniel Krenn wrote:
>
> On 04.05.19 06:04, Andrew wrote:
> > The `Permutation` function is more general. For example, the folllow
the degree of the permutations you can always use:
sage: S5=SymmetricGroup(5)
sage: S5([1,4,3,2,5])
(2,4)
sage: _.parent()
Symmetric group of order 5! as a permutation group
Andrew
On Friday, 3 May 2019 22:11:29 UTC+10, Daniel Krenn wrote:
>
> sage: Permutation([5,4,3,2,1]).parent()
> St
OK, it seems that it is the nesting of LaurentPolynomial rings that causes
the problems. it is slightly cumbersome in my real application but work I
can solve my problem by creating my creating my coefficient rings only
once, without nesting them.
Andrew
On Friday, 22 June 2018 13:01:00 UTC+2
Under the hood these are the sort of calculations that my code is doing:
{{{
sage: Rq. = LaurentPolynomialRing(ZZ,'q')
sage: Ruq. = PolynomialRing(Rq,'u')
sage: mat = matrix([[q-q,u-q],[1,1]])
Under the hood these are the sort of calculations that my code is doing:
sage: Rq. =
If by mapping to R you mean applying
sage: R( f )
then, no, this doesn't work. I'll see if I can post an example to make this
more concrete.
Andrew
On Thursday, 21 June 2018 15:51:31 UTC+2, slelievre wrote:
>
> Have you tried defining
>
> sage: R. = LaurentPolyn
()
---
ArithmeticError Traceback (most recent call last)
...
ArithmeticError: unable to reduce because gcd algorithm not implemented on
input
Andrew
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Is there an update to date description somewhere of how to set up a
(secure) sage notebook sever, with jupyter notebooks, that has multiple
user accounts. The best description that I have found is
https://wiki.sagemath.org/SageServer
Andrew
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I doubt that this has anything to do with sage and, instead, apple broke
something in their update and you need to re-enable your local webserver.
As a first step try
sudo apachectl configtest
and see what error messages this gives. Hopefully this will tell you what
to fix. Failing that, try
Open up a terminal window and type:
sage -i database_odlyzko_zeta
On Tuesday, 21 February 2017 09:14:58 UTC+11, Fernando Montans wrote:
>
>
>
> I want to use zeta_zeros() on a macbook running OS X 10.12 with Sage 7.5.1
> already installed and working quite fine.
>
>
> According to the
On Monday, 28 November 2016 12:44:32 UTC+11, William wrote:
>
> Hi,
>
> It would be great if somebody could create some sort of index of such
> packages, which we could link to (or include) on sagemath.org.
>
Vincent's link https://wiki.sagemath.org/SageMathExternalPackages seems to
be a
Sorry, you're right. I hadn't tried this with cython classes.
Andrew
On Sunday, 9 October 2016 12:43:10 UTC+11, Emmanuel Charpentier wrote:
>
> Sorry, that doesn't work with Sage's compiled classes :
>
> @add_method_to_class(sage.symbolic.expression.Expression)
> def demoivre
ed/want to do this I use the following decorator:
Andrew
def add_method_to_class(klass):
r"""
Add a new method to a pre-existing (sage) class.
"""
def add_func(func):
setattr(klass,func.func_name,func)
return func
return add_func
The decorator takes the cl
not like it either. I'll have a look and see if it is manageable. The
real issue is writing the content from scratch.
Andrew
On Thursday, 25 August 2016 02:07:29 UTC+10, leif wrote:
>
> Dima Pasechnik wrote:
> > Hi Simon,
> > the question is delicate; I know that in UK
Nathan does give the link to the original post, but he is quoting out of
context. Here is the full post:
On Sunday, 21 August 2016 07:15:56 UTC+10, William wrote:
> So there is no confusion, my top priority right now is to **make a lot
> of money** by building a profitable company on open
this
functionality and thought that this should be possible using sage notebooks.
I'm sure that the answer to this question is yes but my trusty friend
google and I haven't found anything about this.
Andrew
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I was doing some school work and after making a few revisions to my code i
came to realize that i had typed over some of my work. I was wondering how
to turn off this feature.
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share memory that would probably be good, but it is
not essential. As this seems to require extra effort I'll try first to see
how it goes without sharing.
Andrew
On Wednesday, 11 May 2016 14:56:27 UTC+10, vdelecroix wrote:
>
> On 10/05/16 23:32, Andrew wrote:
> > On Wednesday, 11
mat[t][s]=mat[s][t]
The `_inner_product_st` method computes certain structure constants in a
module. This method is time consuming and slightly recursive with "basic"
cases being cached. Parallelising this loop seemed like the right place to
me but, to be honest, I have no idea what I am doi
tutorial
http://doc.sagemath.org/html/en/thematic_tutorials/numerical_sage/parallel_computation.html
which suggests that it is still being used.
Andrew
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Have you tried:
sage: RR.=PolynomialRing(RR)
sage: p= -51813033263*X^2+(-1291618080*sqrt(23)*sqrt(91)-7932964704*sqrt(91
)*sqrt(2)-16045600662*sqrt(23)-13979137536*sqrt(2))*X+1551583008*sqrt(23)*
sqrt(91)*sqrt(2)-296053>
sage: p.roots()
[(-1968/51813033263*sqrt(91)*(328155*sqrt(23) +
There are a number of ways in which sage assumes you only have a single
version of python installed. The main reason for introducing the python3
package was so developers interested in porting sage to python 3 could
easily try building sage with python 3 instead of python 2.
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It is wrong, but not as wrong as you make it out to be. Your function is f
= abs(h), where h = 2*cos(5/8*sqrt(x)+1/2)/sqrt(x). Rather that integrating
f, it seems to have integrated h.
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, although that is in a much rougher state
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To post
, ... to be invertible. Unfortunately,
sage: FractionField(R4)
returns a not implemented error.I can probably get around this by
adjoining inverses, but I am hoping that there is a better to do this. Any
suggestions?
Cheers,
Andrew
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are using `git` are you in the master branch or another one?
Andrew
On Tuesday, 17 June 2014 03:58:56 UTC+2, Peter Samuelson wrote:
I'd like to use PartitionTuples, but I ran into problems (e.g. I couldn't
create a PartitionTuple). I then ran the code
TestSuite( PartitionTuples() ).run
On Saturday, 7 June 2014 00:13:50 UTC+10, Dinakar Muthiah wrote:
Ideally, I would like to define a subclass of Partition called MyPartition
and include all my custom methods. I think this is a standard way to extend
libraries, but for some reason this doesn't work at all. Is there a
Oops, cut and past the wrong bits at the end - and google's syntax
highlighting was going haywire:
sage: MyPartition([3,2])
[3, 2]
sage: MyPartition([3,2]).cells()
[(0, 0), (0, 1), (0, 2), (1, 0), (1, 1)]
sage: MyPartition([3,2]).fred()
'fred'
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:
sage: mu=Partition([4,3,1])
sage: mu.i_part(0)
[4, 3, 1]
sage: mu.i_part(1)
[3, 2]
sage: mu.i_part(2)
[3, 2, 1, 1]
sage: mu.i_part(3)
[3, 2, 2, 1]
sage: mu.i_part(-3)
[5, 4]
Andrew
On Friday, 6 June 2014 07:50:22 UTC+10, Dinakar Muthiah wrote:
I literally wrote the following at the top of my
Actually you should only need the RH to prove that this method is reasonably
fast. I don't think sage has Li^{-1} implemented, which is really what you need
in order to implement this (Li ~ pi, so Li^{-1} ~ pi^{-1} = nth_prime function).
There has been some effort to include the open source
example matrices below the normal form would be
[[0,1,1],[1,0,1],[1,1,1]].
For 0-1 matrices, however, I wouldn't be surprised if the sets of row and
column sums determine the orbit uniquely.
Andrew
On Friday, 28 February 2014 06:25:24 UTC+11, Keivan Monfared wrote:
In a problem that I am
)} # subset of NN with
neighbours contained in N
print [(x,y) for (x,y) in CartesianProduct(NN,NN) if x!=y]
Andrew
On Thursday, 9 January 2014 08:27:25 UTC+1, Neda wrote:
Hello, I want to compute this:
G= graphs.CompleteGraph(4)
G.delete_edge({1,2})
L = [u for u in G.vertices()]
for x
)
\Edge[lw=0.1cm,style={post, bend right,color=cv1v2,},](v1)(v2)
%
\end{tikzpicture}
Andrew
On Wednesday, 8 January 2014 19:10:01 UTC+1, jori.ma...@uta.fi wrote:
Is there an easy way to make tikz picture from sage poset? How about
prettyprinting poset that can also be seen as lattice?
To give
exotic graphs?
Andrew
On Tuesday, 17 December 2013 11:22:12 UTC+1, Nathann Cohen wrote:
Yooo !!
Edge coloring multigraphs raises exception
Ahahaha. That's possible.
sage:
P=graphs.PetersenGraph();ep=P.edges(labels=0);P2=Graph(ep+ep,multiedges=1)
sage
Dear geo909 (I can't believe what some people call their children!)
Try:
sage: [1,1,2,1,3] in LyndonWords()
True
sage: [2,1,3,2] in LyndonWords()
False
Andrew
On Wednesday, 11 December 2013 16:22:42 UTC+1, geo909 wrote:
Hi all,
From wikipedia:
*In mathematics, in the areas
Sorry, I didn't see the later posts.
It turns out that __contains__ in LyndonWords() use a try-except statement
to call LyndonWord(). If you're creating a Word() anyway then the
Word(*).is_lyndon() test you found will be more efficient.
Andrew
On Thursday, 12 December 2013 10:17:06 UTC+1
You could try:
sage: f(x)=x^2-sin(x)
sage: f.find_root(-1,1)
0.8767262153950626
sage: f.find_root(-1,0.5)
1.7263300161400947e-18
Andrew
On Thursday, 5 December 2013 09:22:09 UTC+1, Daniel Krenn wrote:
How do I solve the symbolic equation x^2 == 16*sin(x) symbolically? I
don't even get 0
On Thursday, 5 December 2013 10:35:00 UTC+1, Daniel Krenn wrote:
Am 2013-12-05 09:30, schrieb Andrew:
Thanks, but as I wrote, I want a symbolic solution.
In particular, I wonder how I get the solution 0.
Sorry, I'm confused. Since you mentioned finding 0 as a particular
(numeric
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
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
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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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Suppose I want to generate partitions that are in an arithmetic progression
with a particular step size...seems straightforward enough, so I just set
max_slope and min_slope to that step size. Is this interpretation correct?
Ps=Partitions(11,max_slope=-1, min_slope=-1)
print Ps.cardinality()
]]]).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
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if there was
a better way of doing this.
Cheers,
Andrew
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slower I really should have checked by doing some
profiling before rewriting as above, but I didn't...)
Any thoughts?
Cheers,
Andrew
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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
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Andrew
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)
Andrew
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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
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outside the def statement. So is there a problem
loading files generically inside a function definition? Is there some
other way around this?
Thanks,
Andrew
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Hi Everyone,
I have been trying to set up a sage chroot environment. I have
documented the steps I have taken here
http://www.techidiots.net/notes/sage-notebook-chroot-ubuntu
I have the chroot environment created, and sage compiled inside of
it.
If I run sage as my server user without dchroot
I have the following code
P.x0,x1,y0,y1,y2,y3 = PolynomialRing(QQ,order='degrevlex')
I = Ideal(x0^4-y0,x0^3*x1-y1,x0*x1^3-y2,x1^4-y3)
print I
R.y0,y1,y2,y3 = PolynomialRing(QQ,order='degrevlex')
I1=Ideal(1)
J=I.intersection(I1)
print J
but gives error
File
On Tue, Dec 7, 2010 at 4:29 PM, luisfe lftab...@yahoo.es wrote:
On Dec 7, 5:03 pm, andrew ewart aewartma...@googlemail.com wrote:
I have the following code
P.x0,x1,y0,y1,y2,y3 = PolynomialRing(QQ,order='degrevlex')
I = Ideal(x0^4-y0,x0^3*x1-y1,x0*x1^3-y2,x1^4-y3)
print I
R.y0,y1,y2
On Tue, Dec 7, 2010 at 4:58 PM, Simon King simon.k...@uni-jena.de wrote:
On 7 Dez., 17:48, andrew ewart aewartma...@googlemail.com wrote:
I thought I1=R=1
As I said, nobody could guess that you believe that 1 is in R.
also the intersection should be in R, not just in P, so how
lambda is a special word in python, it indicates a type of one-line
function definition. Using any other word should work.
See:
http://groups.google.com/group/sage-support/browse_thread/thread/728f27989ff87203/4b08aaaed8309cbc?q=sage+support+lambda
for a similar discussion.
For more on lambda
On 12/2/10 8:01 AM, Jason Grout wrote:
On 12/2/10 8:24 AM, Andrew Dawes wrote:
lambda is a special word in python, it indicates a type of one-line
function definition. Using any other word should work.
See:
http://groups.google.com/group/sage-support/browse_thread/thread/728f27989ff87203
I want to be able to right a little code that would take any
projective variety and break it down into its irreducible variety
components
any suggestions.
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I want to write code that does the following
Given ideals I,J in CC[x1,...,xn]
check if Radical(I+J)=Radical(I)+Radical(J)
also maybe throw in an example of yes and no just to see it working
Radical(I)={f:there is an m such that f^m is in I} (f is a polynomial
of CC[x1,...,xn]
also
looking at the code in ticket 7458 (link:http://trac.sagemath.org/
sage_trac/attachment/ticket/7458/sylvester.patch)
ive tried to calculate the sylvester matrix of a given f and g (polys
of (x,a)) and its deteminant (with respect to a) with the following
code
R.x,a = PolynomialRing(ZZ)
f = x^5 +
no i dont think so
i saved it as file.sage
then ran it as sage file.sage
so how do i apply this particular patch to my version of sage and then
run it as part of sage
On Nov 5, 7:18 pm, Mike Hansen mhan...@gmail.com wrote:
On Fri, Nov 5, 2010 at 12:14 PM, andrew ewart
aewartma
is to define a
global numerical pi, e.g. npi = RDF(pi) and then use npi
everywhere.
Yes, that works, as does using any float in place of pi. I can do
from numpy import pi as npi
and it works as expected. In this case, npi is a float.
-Andrew
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I want to translate the following code from magma to SAGE
KKep := CyclotomicField(21);
ze := ep^3;
RRx,y,z := PolynomialRing(KK,3);
PP := Proj(RR);
F := z*x^3+x*y^3+y*z^3;
H := 1/2*Determinant(1/3*Matrix(3,3,
[Derivative(Derivative(F,RR.i),RR.j) : i in [1..3], j in [1..3]]));
Flex :=
this behavior
despite those bugs being marked fixed. The difference here is the pi
in the exp(). I am running Sage Version 4.5.2 on Mac OS 10.6.4.
Please let me know if I'm doing something wrong or if this should be
filed as a bug.
Best,
Andrew Dawes
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wrote:
On Oct 23, 9:39 pm, andrew ewart aewartma...@googlemail.com wrote:
if alpha is a root of x^2+a_1*x+a_0 and beta is a root of x^2+b_1*x
+b_0 (both polynomials r in QQ), then how do i construct code such
that it can tell me the minimum polynomials of the following roots
alpha+beta
If i have an element alpha=3^(1/3)+(7^(1/2)*2^(1/4))
and an ideal I=a^3-3, b^2-7,c^4-2, alpha-(a+b*c)
how do i show the minimum polynomial of alpha lies in the ideal I
then use it to construct the minumum polynomial of alpha
So far I have:
P.a,b,c = PolynomialRing(QQ)
if alpha is a root of x^2+a_1*x+a_0 and beta is a root of x^2+b_1*x
+b_0 (both polynomials r in QQ), then how do i construct code such
that it can tell me the minimum polynomials of the following roots
alpha+beta
and
alpha*beta
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What is the best way of writing out code to calculate the symmetry
group of the Klein Quartic
(The klein quatric is the set of the solutions to f=0, where f is the
polynomial x^3*y+y^3*z+z^3+x in QQ[x,y,z])
I know of 2 symmetry types
one is the rotation of terms of order 3 ( (x,y,z), (z,x,y),
If I is Ideal(x+y+z-3,x^2+y^2+z^2-5,x^3+y^3+z^3-7) and X=V(I), where
V(I) is the variety of I
and I have the following code
Code:
P.x,y,z = PolynomialRing(CC,order='lex')
I = Ideal(x+y+z-3,x^2+y^2+z^2-5,x^3+y^3+z^3-7)
ans=I.groebner_basis()
print ans
and i get an output
[x + y + z -
If I is Ideal(x+y+z-3,x^2+y^2+z^2-5,x^3+y^3+z^3-7) and X=V(I), where
V(I) is the variety of I
and I have the following code
Code:
P.x,y,z = PolynomialRing(CC,order='lex')
I = Ideal(x+y+z-3,x^2+y^2+z^2-5,x^3+y^3+z^3-7)
ans=I.groebner_basis()
print ans
and i get an output
[x + y + z -
i think its just reffering to vector space dimension
I have no idea what the Krull dimension of this space is
Also if i try lex in QQ the grobner basis i get out is
[x + y + z - 3, y^2 + y*z - 3*y + z^2 - 3*z + 2, z^3 - 3*z^2 + 2*z +
2/3]
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hmm sage doesnt seem to recognise the Im() command
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i tried to take this into consideration
giving the following code
P.x,y,z = PolynomialRing(QQ,order='neglex')
I = Ideal(x^5 + y^4 +z^3, x^3 + y^2 + z^2 -1)
print I
gb=I.groebner_basis()
rgb=Ideal(gb).interreduced_basis()
bgr=Ideal(rgb)
ir=Ideal(f.Im() for f in bgr)
print 'with revlex order'
print
whats the best way to code the following
I want a print out of a grobner basis for an ideal I generated by the
polynomials
x^5 + y^4 +z^3, x^3 + y^2 + z^2 -1
this is respect to the reverse lexicographic and lexicographic order
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no it should be chekcing the term with the highest power of x and then
make it monic
that includes possibilitys like x*y as this is not monic wrt x
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if i have a function f(x,y)
i want to write a function is_irri(f) that would say if f is
irreduible or not
how do i go about this
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For
is there a good way of testing if a polynomial f(x,y) is irreducible
or not as there is a lack of a is_irreducible command
also is there a way for sage not to print the line
? not implemented
after checking randomly generated f fits various criterion
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is there a good way of testing if a polynomial f(x,y) is irreducible
or not as there is a lack of a is_irreducible command
also is there a way for sage not to print the line
? not implemented
after checking randomly generated f fits various criterion
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supose i have an input list (which is a list of unknown size) and
where each term is a polynomial of form f(x,y)
i want to define a function moniclist(list)
such that the output makes each term of list monic wrt x
eg
if list=[2*x, x^2*y^2+x+1, 4*x^2+y^2+3]
output would be[x, x^2+x+1, x^2+y^2+3]
supose i have an input list (which is a list of unknown size) and
where each term is a polynomial of form f(x,y)
i want to define a function moniclist(list)
such that the output makes each term of list monic wrt x
eg
if list=[2*x, x^2*y^2+x+1, 4*x^2+y^2+3]
output would be[x, x^2+x+1, x^2+y^2+3]
suppose i have a funciton
def_f1(f)
f=2
return f
how do i then make the output f the input of a antother function
def_eg1(f)
g=f^2
return g
as at the moment its telling me that f isnt defined
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To
code
S=GF(5)
R.z1, z2=PolynomialRing(S, 2, z)
T.x=PolynomialRing(S)
def poly_ran():
ef=R(1)
eye=0
if eye10:
f=R.random_element()
g=f.factor(proof=false)
if g[0][0]*g.unit==f:
ef=ef*f
eye=eye+1
else:
eye=eye
else:
ef is the resultant of poly_ran
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when i try that i get these errors
Traceback (most recent call last):
File quickfact2.py, line 21, in module
ef=poly_ran()
File quickfact2.py, line 13, in poly_ran
if g[_sage_const_0 ][_sage_const_0 ]*g.unit==f:
File element.pyx, line 1436, in
ah found why got that missed brqacket on end of g.unit()
now by using g.factor
how do i express the factors of a polynomial in a list
eg
g=x^2+x
g.factor= x(x+1)
so want something that does
list(g)
giving output
[x,x+1]
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To
How do u stick a matrix on the bottom of antoher martix, in particular
the identity matrix
so if had M (l,k) how do I stick Id(k) on the bottom to produce a new
matrix
N=M and N is dimension (l+k,k)
Id
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if a have a matrix M of dimension (m,n)
how do i first check for j columns deep (from left), j=n
for when the ith row will be all zeros
eg
M=([1,0,1],[0,0,1],[1,1,1])
check j=1 gives output of 1
j=2 gives output of 1 and j=3 gives output of 3
also how do i take out a matrix N of dimension (k,l)
want i want to compute is a vector for each power of ad^j that lists all the
coefficients wrt t and y which will have length at most (degree+1)*degx
of course if it is shorter i want to stick 0's on the end until i get to
this length
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so for ad^0 i should get out
[1,0,0,0,0,...,0]
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