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D.12.6.7 tracemult
Procedure from library rootsmr.lib (see rootsmr_lib).
- Usage:
- tracemult(f,B,I);f poly, B,I ideal
- Return:
- number: the trace of the multiplication by f (m_f) on r/I, written in
the monomial basis B of r/I, r = basering (faster than matmult + trace)
- Assume:
- I is given by a Groebner basis and B is an ordered monomial basis of r/I
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 = matmult(f,b,i);
print(m);
==> 0, 1, 0, -1,0, 0, 1, 0,
==> 13, 0, -13,0, 0, 0, 0, 1,
==> 0, 0, 0, 1, 0, -1,0, 0,
==> 0, 0, 13, 0, -13,0, 0, 0,
==> 0, -13,0, 0, 0, 1, 0, -1,
==> -169,0, 0, 0, 13, 0, -13,0,
==> 0, 0, 0, 0, 0, 0, -13,1,
==> 0, 0, 0, 0, 0, 0, 13, -13
tracemult(f,b,i); //the trace of m
==> -26
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See also:
matmult;
trace.
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