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D.8.2.2 solve
Procedure from library solve.lib (see solve_lib).
- Usage:
- solve(G [, m, n [, l]] [,"oldring"] [,"nodisplay"] ); G = ideal,
m, n, l = integers (control parameters of the method), outR ring,
m: precision of output in digits ( 4 <= m) and of the generated ring
of complex numbers;
n: control of multiplicity
n = 0, return all different roots
n != 0, find all roots (with multiplicity)
l: precision of internal computation in decimal digits ( l >=8 )
only if the basering is not complex or complex with smaller
precision,
[default: (m,n,l) = (8,0,30), or if only (m,n) are set explicitly
with n!=0, then (m,n,l) = (m,n,60) ]
- Assume:
- the ideal is 0-dimensional;
basering has characteristic 0 and is either complex or without
parameters;
- Return:
- (1) If called without the additional parameter
"oldring" :
ring R with the same number of variables but with complex
coefficients (and precision m). R comes with a list
SOL of numbers, in which complex roots of G are stored:
* If n = 0, SOL is the list of all different solutions, each
of them being represented by a list of numbers.
* If n != 0, SOL is a list of two list: SOL[i][1] is the list
of all different solutions with the multiplicity SOL[i][2].
SOL is ordered w.r.t. multiplicity (the smallest first).
(2) If called with the additional parameter "oldring" , the
procedure looks for an appropriate ring (at top level) in which
the solutions can be stored (interactive).
The user may then select an appropriate ring and choose a name for
the output list in this ring. The list is exported directly to the
selected ring and the return value is a string "result exported to"
+ name of the selected ring.
- Note:
- If the problem is not 0-dim. the procedure stops with ERROR. If the
ideal G is not a lexicographic Groebner basis, the lexicographic
Groebner basis is computed internally (Hilbert driven).
The computed solutions are displayed, unless solve is called
with the additional parameter "nodisplay" .
Example:
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