with(Groebner):
eq1 := a+b*c;
eq2 := a*b*c+a;
eq1a := Homogenize(eq1, h);
eq2a := Homogenize(eq2, h);
eliminate([eq1a,eq2a], h);

after eliminate not equal to eq1 and eq2

if DegreeLexicographic is T2:=lexdeg([a,b,c],[x,y,z]);

DegreeReverseLexicographic = T2:=lexdeg([c,b,a],[z,y,x])  ?

with(PolynomialIdeals):

quotientlist := Quotient(GB, varj[j]);
finallist2 := [];
for z from 1 to nops(quotientlist) do
if
finallist2 := [op(finallist2), op(z,quotientlist)];
od:

there are only 3 monomials in quotientlist, but nops return 6

how to compute the ideal mapping from ideal A to ideal B

how to calculate hlibert series as in maple with Gröbner Bases

would like to know the algorithm and try in another programming language such as F#

i find the algorithm in book Singular introduction to commutative algebra

page 320 and 322 

1. is it equal to the hilbert series function in maple?

eq1a := Homogenize(eq1, h);
eq2a := Homogenize(eq2, h);
eq3a := Homogenize(eq3, h);
T3:=lexdeg([a,b,c,h]);
GB := Basis([eq1a,eq2a,eq3a], T3); #a

MonomialHilbertPoincare(LeadingMonomial(GB[1],T3), LeadingMonomial(GB[2],T3), LeadingMonomial(GB[3],T3));

F:=[LeadingMonomial(GB[1],T3), LeadingMonomial(GB[2],T3), LeadingMonomial(GB[3],T3)];
InterReduce(F, ???);

 2. what is the maple function for degree reverse lex ordering ?