ReadNumberOfClassTwoAssociativeAlgebrasByRankAndDimension( <r>, <d> )
Reads the porc function determining the number of isomorphism classes of
associative algebras of rank <r> and dimension <d>.
ValueOfPorcPolynomial( <porc>, <val> )
Evaluates a porc function <porc> at a given integer <val>.
InformationOnPorcPolynomial( <porc> )
Gives some information on a porc function <porc> in a nice form.
gap> #Number of Isomorphism Classes of Rank 4 Algebras of Dimension 6 gap> f := ReadNumberOfClassTwoAssociativeAlgebrasByRankAndDimension(4,6); q^13+q^12+3*q^11+4*q^10+8*q^9+10*q^8-q^7*(q-0,2)+21*q^7-3*q^6*(q-0,2)+32*q^6-8*q^5\ *(q-0,2)+58*q^5-16*q^4*(q-0,2)+1/2*q^4*(q-0,3)+q^4*(q-1,3)+181/2*q^4-33*q^3*(q-0,2\ )+3*q^3*(q-1,3)+2*q^3*(q-1,4)-q^2*(q-0,2)*(q-1,3)+156*q^3-55*q^2*(q-0,2)+q^2*(q-0,\ 3)+9*q^2*(q-1,3)+4*q^2*(q-1,4)-2*q*(q-0,2)*(q-1,3)+229*q^2-77*q*(q-0,2)-1/2*q*(q-0\ ,3)+13*q*(q-1,3)+6*q*(q-1,4)-(q-0,2)*(q-1,3)+583/2*q-59*(q-0,2)-1/2*(q-0,3)+6*(q-1\ ,3)+4*(q-1,4)+415/2 gap> gap> #Number of Isomorphism Classes for some fields with gap> #Characteristic 2 gap> List([2,4,8,16,32,64], x -> ValueOfPorcPolynomial(f, x)); [ 37269, 103902049, 649829917665, 4842847499250697, 38159292795030970209, 307179941016763478391529 ] gap> gap> #Characteristic 3 gap> List([3,9,27,81], x -> ValueOfPorcPolynomial(f, x)); [ 3205858, 2936030157546, 4220214584822595826, 6543852495425121166747674 ] gap> gap> #Information on f in a nice form gap> InformationOnPorcPolynomial(f); _____________________________________________________________________________ | | SUMMARY | | Degree in 'q': 13 | | Gcd's with... 2 3 4 | First occurence 7 4 3 | (power of 'q') | | Total modulus of PORC function: 12. More information? (true/false) true _____________________________________________________________________________ | | INFO on 'q' | | Degree in 'q': 13 | Polynomial is dense in 'q'. | (All powers (including q^0) are present.) _____________________________________________________________________________ | | INFO on gcds with 2 | | (q-0,2) appears for all powers of 'q' less than or equal to 7. _____________________________________________________________________________ | | INFO on gcds with 3 | | (q-0,3) first appears at power 4 of 'q'. | Then it is present for the following power(s) of 'q' only: | 4, 2, 1, 0. | (q-1,3) appears for all powers of 'q' less than or equal to 4. _____________________________________________________________________________ | | INFO on gcds with 4 | | (q-1,4) appears for all powers of 'q' less than or equal to 3. No further gcd's are included.