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