#
# MAPLE file: 	bb4mult
# runs under:	Maple V Release 3
# author:	J"org Peters, jorg@cs.purdue.edu
# date:   	Aug 1995
#
# multiply two bivariate polynomials in tensor BB-form
#
#-----------------------------------------------------------------

bb4mult := proc(b1, d1u, d1v, b2, d2u, d2v)

# bi: array(0..di)
# di: degrees
#-----------------------------------------------------------------

local i,j,u1,u2,v1,v2, mu,mv, du,dv,out:
    if nargs <> 6 then 
      ERROR(`[bb4mult] wrong number of arguments`): fi:

    du := d1u + d2u:
    dv := d1v + d2v:

    for i from 0 to du do
	for j from 0 to dv do
	    out[i,du-i][j,dv-j] := 0;
	od:
    od:
    for u1 from 0 to d1u do
	for u2 from 0 to d2u do
	    mu := binomial(d1u,u1)*binomial(d2u,u2)/binomial(d1u+d2u,u1+u2);
	    for v1 from 0 to d1v do
		for v2 from 0 to d2v do
		    mv := binomial(d1v,v1)*binomial(d2v,v2)/
			binomial(d1v+d2v,v1+v2);
		    out[u1+u2,du-(u1+u2)][v1+v2, dv-(v1+v2)] := 
			out[u1+u2,du-(u1+u2)][v1+v2, dv-(v1+v2)] + mu*mv*
			b1[u1,d1u-u1][v1,d1v-v1]*b2[u2,d2u-u2][v2,d2v-v2];
    od:od:od:od:
    out;
end:
#-----------------------------------------------------------------

test := 0:
if test = 1 then
    dg := 1:
    b1[0,1][0,1] := 1:
    b1[1,0][0,1] := 1:
    b1[0,1][1,0] := 1:
    b1[1,0][1,0] := 1:
    b2[0,1][0,1] := 1:
    b2[1,0][0,1] := 2:
    b2[0,1][1,0] := 3:
    b2[1,0][1,0] := 4:
    bb := bb4mult(b1,dg,dg,b2,dg,dg):    
    print(bb);
fi: