#
# file:         reduced-poly-ring.gap
# created:      pasha jan 6 2005
# modified:     pasha jan 13 2005
# modification: minor formatting
#



# returns reduced polynomial algebra K[x]/(x^n)
# (factorization by ideal in PolynomialRing doesn't work (at least straightforwardly)
# as PolynomialRing is not an algebra object)
ReducedPolyRingAux := function (K, n)
	local T,i,j;
	T := EmptySCTable (n, Zero(K), "symmetric");
	# the basis element x^i, 0<=i<=n-1, is at place (i+1)
	for i in [0..n-1] do
		for j in [0..n-1] do
			if i+j < n then
				# this corresponds to x^i x^j = x^{i+j} if i+j<n and 0 otherwise
				SetEntrySCTable (T, i+1, j+1, [1, i+j+1]);
			fi;
		od;
	od;
	return (AlgebraByStructureConstants (K, T));
end; 


# K[x_1, ..., x_n]/(x_1^p, ..., x_n^p}, realized as tensor product
ReducedPolyRing := function (K, n)
	local p;
	p := Characteristic(K);
	if p = 0 then
		Error ("the ground field supposed to be of positive characteristic");
	fi;
	return (TensorPower (ReducedPolyRingAux (K, p), n));
end;


# end of reduced-poly-ring.gap