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D.12.7.5 matbil

Procedure from library rootsmr.lib (see rootsmr_lib).

Usage:
matbil(h,b,i); h poly, b,i ideal

Return:
matrix: the matrix of the bilinear form (f,g) |-> trace(m_fhg), m_fhg = multiplication with fhg on r/i

Assume:
i is a Groebner basis and b is an ordered monomial basis of r/i, r = basering

Example:
 
LIB "rootsmr.lib";
ring r = 0,(x,y),dp;
ideal i = x4-y2x,y2-13;
i = std(i);
ideal b = qbase(i);
poly f = x3-xy+y-13+x4-y2x;
matrix m = matbil(f,b,i);
print(m);
==> 0,     13182, 0,     -13182,0,    0,    0,    1014, 
==> 13182, 0,     -13182,0,     0,    0,    1014, 0,    
==> 0,     -13182,0,     0,     0,    1014, 0,    -1014,
==> -13182,0,     0,     0,     1014, 0,    -1014,0,    
==> 0,     0,     0,     1014,  0,    -1014,0,    0,    
==> 0,     0,     1014,  0,     -1014,0,    0,    0,    
==> 0,     1014,  0,     -1014, 0,    0,    -338, 104,  
==> 1014,  0,     -1014, 0,     0,    0,    104,  -26   
See also: matmult; tracemult.