FUNCTION : qseries[findlincombomodp] - tries to express a q-series as a
linear combination mod p of
a given list of q-series.
CALLING SEQUENCE : findlincombomodp(f,L,SL,p,q,topshift)
PARAMETERS : L - list of q-series
SL - list of names
p - prime
q - variable
topshift - integer greater than -20
GLOBAL VARIABLES : ct, gooo
SYNOPSIS :
findlincombomodp(f,L,SL,p,q,topshift) returns a set of potential
set of linear combinations mod p from L for the given q-series f.
The value of topshift is usually taken to be zero. However if
it appears that spurious relations are being generated then a higher
value of topshift should be taken.
SL is a list of names used in printing the linear combinbations.
NOTE: The global var ct is tranpose of matrix of coeffs.
The global var gooo is its Nullspace mod p. These used for debugging
purposes. This function is a mod p version of findlincombo
EXAMPLES :
> E4:=1+240*add(n^3*q^n/(1-q^n),n=1..300):
> E6:=1-504*add(n^5*q^n/(1-q^n),n=1..300):
> P:=series(1/etaq(q,1,300),q,300):
> ETA1:=etaq(q,1,300):
> F1:=sift(E4^16*E6*P,q,13,6,299):
> BB13:=[seq(ETA1^11*E6*E4^(3*j+1),j=0..5)]:
> SBB13:=[seq(_ETA1^11*_E6*_E4^(3*j+1),j=0..5)]:
> findlincombomodp(F1,BB13,SBB13,13,q,-8);
nx = , 6
# of terms , 19
11
-6 _ETA1 _E6 _E4
DISCUSSION :
We see that F1 is a linear combination of functions in BB13 mod 13.
SEE ALSO : findhom, findhomcombo, findhomcombomodp, findlincombo