The minimal polynomial of an algebraic number is the monic polynomial of smallest degree with integer coefficents which has the algebraic number as a root.
The pmin command finds the minimum polynomial of an algebraic number.
pmin(α,x) returns the minimal polynomial for α as a symbolic expression with the variable x.
pmin(sqrt(2)+sqrt(3)) |
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pmin(sqrt(2)+sqrt(3),x) |
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Note that (√2+√3)2=5+2√6 and so ((√2+√3)2−5)2=24, which can be rewritten as (√2+√3)4−10 (√2+√3)2+1=0.
pmin(sqrt(2)+i*sqrt(3)) |
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pmin(sqrt(2)+i*sqrt(3),z) |
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pmin(sqrt(2)+2*i) |
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pmin(sqrt(2)+2*i,z) |
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