On Tue, Feb 26, 2019 at 5:42 PM Pierre Guillot <pierre.guil...@gmail.com> wrote:
>
> Hi again,
>
> Mostly, this does the job :
>
> def sparse_magma_matrix(mat):
> s= "SparseMatrix(" + str(mat.nrows()) + ", " + str(mat.ncols()) + ", ["
> entries= ", ".join([ "<"+str(i+1)+", " + str(j+1)+", "+str(mat[i,j])+">"
> for i,j in mat.dict() ])
> return s + entries + "])"
>
> One should probably worry about the coefficient ring -- as such, it only
> works if Magma can guess what it is by itself.
>
> For anyone reading this, concretely, i have then tried:
>
> f= open("foo.m", "w")
> f.write("M:= " + sparse_magma_matrix(mat) + ";")
> f.close()
>
> Then within Magma, I have created the polynomial ring -- which, it turned
> out, had to be the appropriate fraction field, otherwise the determinant
> function does not work -- so in my case :
>
> R<a0, a1, a2, a3, a4, a5>:= FunctionField(GF(5), 6) ;
>
> and then:
>
> load "foo.m";
>
> (don't forget the ; at the end!!!)
>
> Then i tried
>
> Determinant(M);
>
> and, amazingly, Magma gives an answer instantly. Absolutely incredible :-)
Can Sage do this determinant on its own?
Just wondering (yes, Sage is lacking in sparse matrices over
multivariate polynomial rings support).
>
>
>
>
>
>
>
>
>
>
> On Tuesday, February 26, 2019 at 6:21:44 PM UTC+1, John Cremona wrote:
>>
>>
>>
>> On Tue, 26 Feb 2019 at 17:01, Vincent Delecroix <20100.d...@gmail.com> wrote:
>>>
>>> I don't think this has ever been implemented in Sage. You
>>> have to figure out how to create a sparse matrix in magma
>>> and write Sage code to produce it. You can get inspiration
>>> from the current code of _magma_init_
>>>
>>> def _magma_init_(self):
>>> P = magma(self.parent())
>>> v = [x._magma_init_(magma) for x in self.list()]
>>> return '%s![%s]'%(P.name(), ','.join(v))
>>>
>>> Vincent
>>
>>
>> This would be a very useful addition (for some people). Magma constructs
>> sparse matrices using SparseMatrix() with several interfaces including
>>
>> (m::RngIntElt, n::RngIntElt, Q::SeqEnum[Tup]) -> MtrxSprs
>>
>> The m by n sparse matrix, whose entries are given by the tuples in Q
>> of the form <i, j, x> (specifying that x is at entry (i, j)).
>>
>> Example:
>>
>> > M:=SparseMatrix(3,3,[<1,1,1>,<2,2,1>,<3,3,1>]);
>> > IdentitySparseMatrix(Integers(), 3) eq M;
>> true
>>
>>
>>
>>>
>>>
>>> Le 26/02/2019 à 17:55, Pierre Guillot a écrit :
>>> > Thanks! I think to know where the issue is :
>>> >
>>> > M= random_matrix(ZZ, 10, sparse= True, density= 0.1)
>>> > M._magma_init_(magma)
>>> >
>>> > '_sage_[11]![0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-14,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,8,0,0,0,0]'
>>> >
>>> >
>>> > This does not look like a sparse matrix to me : it's been converted to a
>>> > "dense" matrix before magma code was produced...
>>> >
>>> > no wonder if my 50,000 x 50,000 matrix takes forever to load...
>>> >
>>> > If anyone has an easy fix, it would be great. Otherwise, i'll have to
>>> > learn
>>> > the syntax for sparse matrices in magma, and figure out how magma reads
>>> > from a file...
>>> >
>>> >
>>> >
>>> >
>>> >
>>> >
>>>
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