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KASH3 Reference Manual
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### Keyword

Orders of Number Fields

### Description

KASH3 makes it easy to compute in arbitrary orders of number fields. Given the minimal polynomial 'f' of an algebraic integer 'rho' one obtains the equation order 'Z[rho]' easily as 'Z[x]/(rho)'. In order to compute a maximal order 'O' of the number field 'F=Q(rho)', one has to compute an integral bases of 'F'. Maximal orders are not given by polynomials but a transformation matrix, which transforms a power basis '(1,rho,...,rho^4)' to a basis '(w_1,...,w_5)' of the maximal order. The 'MaximalOrder' function computes an integral basis '(w_1,...,w_5)'. Using the 'Element' function one can enter algebraic numbers with respect to this basis.

### Examples

f := X^5 + 4*X^4 - 56*X^2 -16*X + 192; o := EquationOrder(f); O := MaximalOrder(o); # maximal order of 'o' w1 := Element(O,[1,0,0,0,0]); w2 := Element(O,[0,1,0,0,0]); w3 := Element(O,[0,0,1,0,0]); w4 := Element(O,[0,0,0,1,0]); w5 := Element(O,[0,0,0,0,1]);
Built: Mon Nov 14 21:12:39 UTC 2005 on mack
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