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I am looking for quadratic forms with a given point - so I want short integer vectors which are perpendicular to

v=[XX,XY,XZ,XT,YY,YZ,YT,ZZ,ZT,TT]

for (in this case) [X,Y,Z,T]=[4423,7583,8765,3459]

This sounds like a problem with LLL written all over it, so I do

L=[[Y,-X,0,0,0,0,0,0,0,0],[0,Z,-Y,0,0,0,0,0,0,0],[0,0,T,-Z,0,0,0,0,0,0],[0,0,0,YY,-XT,0,0,0,0,0],[0,0,0,0,Z,-Y,0,0,0,0],[0,0,0,0,0,T,-Z,0,0,0],[0,0,0,0,0,0,ZZ,-YT,0,0],[0,0,0,0,0,0,0,T,-Z,0],[0,0,0,0,0,0,0,0,T,-Z]]

M=matrix(L)

M.lll()

but this gives an error message AttributeError: 'sage.matrix.matrix_integer_dense.Matrix_integer_dense' object has no attribute 'lll'

I am looking for quadratic forms with a given point - so I want short integer vectors which are perpendicular to

v=[X*X,X*Y,X*Z,X*T,Y*Y,Y*Z,Y*T,Z*Z,Z*T,T*T]

for (in this case) [X,Y,Z,T]=[4423,7583,8765,3459]

This sounds like a problem with LLL written all over it, so I do

  L=[[Y,-X,0,0,0,0,0,0,0,0],[0,Z,-Y,0,0,0,0,0,0,0],[0,0,T,-Z,0,0,0,0,0,0],[0,0,0,Y*Y,-X*T,0,0,0,0,0],[0,0,0,0,Z,-Y,0,0,0,0],    [0,0,0,0,0,T,-Z,0,0,0],[0,0,0,0,0,0,Z*Z,-Y*T,0,0],[0,0,0,0,0,0,0,T,-Z,0],[0,0,0,0,0,0,0,0,T,-Z]]
 
M=matrix(L)  M=matrix(L)
  
M.lll()  M.lll()

but this gives an error message AttributeError: 'sage.matrix.matrix_integer_dense.Matrix_integer_dense' object has no attribute 'lll'

I am looking for quadratic forms with a given point - so I want short integer vectors which are perpendicular to

v=[X*X,X*Y,X*Z,X*T,Y*Y,Y*Z,Y*T,Z*Z,Z*T,T*T]

for (in this case) [X,Y,Z,T]=[4423,7583,8765,3459]

This sounds like a problem with LLL written all over it, so I do

  L=[[Y,-X,0,0,0,0,0,0,0,0],[0,Z,-Y,0,0,0,0,0,0,0],[0,0,T,-Z,0,0,0,0,0,0],[0,0,0,Y*Y,-X*T,0,0,0,0,0],[0,0,0,0,Z,-Y,0,0,0,0], 
  [0,0,0,0,0,T,-Z,0,0,0],[0,0,0,0,0,0,Z*Z,-Y*T,0,0],[0,0,0,0,0,0,0,T,-Z,0],[0,0,0,0,0,0,0,0,T,-Z]]

  M=matrix(L)

  M.lll()

but this gives an error message AttributeError: 'sage.matrix.matrix_integer_dense.Matrix_integer_dense' object has no attribute 'lll'