Subversion Repositories wimsdev

!if $wims_read_parm!=slib_header

 !goto proc

!endif

slib_title=Generates a random orthogonal matrix

slib_parms=3\

2,matrix size m\

4, N coefficient range\

2,product of n reflexions

Q,coefficient ring: Q for the time being ,R,C,G (Gauss ring)

slib_author=Bernadette PERRIN-RIOU

slib_out=the generated matrix

slib_comment= product of n reflexions associated to n independant linear vectors  (so its determinant is (-1)^n), the vector  coefficients are bounded by N

slib_example= 4,3,3

slib_require=pari

!exit

:proc

!distribute items $wims_read_parm into slib_size,slib_range,slib_n, slib_ring

!default slib_ring=Q

!bound slib_size between integer 2 and 20 default 2

!bound slib_n between integer 1 and $slib_size default 2

!bound slib_range between integer 1 and 1000000 

!default  slib_range=4

!if $slib_ring=Q

!readproc slib/matrix/givenrank $slib_n,$slib_size,$slib_n,$slib_range

!!slib_matrix=!translate internal ; to $\

$ in $slib_out

slib_matrix=$slib_out

slib_out=!exec pari {slib_A=matid($slib_size);slib_n=$slib_n; \\

slib_M= Mat([$slib_matrix]);\\

for(slib_j=1 , slib_n,slib_vv=slib_M[slib_j,]; slib_A=slib_A*(matid($slib_size)-2/norml2(slib_vv)*slib_vv~*slib_vv));\\

print(slib_A)}

slib_out= !trim $slib_out

slib_out=!line -1 of $slib_out

!endif