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LRSDegeneracyOrder --
the LRS degeneracy order of a polynomial
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LRSDegeneracyOrder(f: RINGELEM): INT
LRSDegeneracyOrders(f: RINGELEM): LIST of INT |
If
f is a univariate polynomial with rational coefficients
LRSDegeneracyOrder
returns the least LRS-degeneracy order of
f, or 0 to mean that
f
is not LRS-degenerate. Recall
f is
k-LRS-degenerate iff it has
two distinct roots whose ratio is a primitive
k-th root of unity.
The function
LRSDegeneracyOrders returns a list of all
k;
this function may take a long time.
Note: some polynomials are LRS-degenerate for several orders, for instance
cyclotomic(3,x)*cyclotomic(5,x).
In Cipu, Diouf, Mignotte the property was called just "degenerate".
/**/ use R ::= QQ[x];
/**/ LRSDegeneracyOrder(x^6+3*x^5+6*x^4+6*x^3+9*x^2+9*x+3);
18
/**/ LRSDegeneracyOrder(x^2+x+2);
0
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