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D.12.6.5 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
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See also:
matmult;
tracemult.
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