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Symbolic Numerical Polynomial Solving
Solving polynomial systems using Gröbner bases and
triangular sets:
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Input: |
Zero-dimensional system
f1 ,...,
fk in
K[x1 ,..., xn]
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Output: |
Complex roots of
f1 = ... = fk = 0
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The algorithm proceeds in 3 steps:
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Step 1: |
Compute a reduced lexicographical Gröbner basis of the
ideal I.
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Step 2: |
Compute a triangular
system T1 ,...,
Ts .
V(I) is the union
of the V(Ti ).
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Step 3: |
Use a numerical solver (e.g. Laguerre's method) to find all zeros of
Ti , i=1,..., s .
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