The blossoming principle

Matija Steblaj

1 Polynomial maps between affine spaces

Definition 1
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A coordinate system on a given affine space \((P,V,+)\) consists of an origin point in \(P\) and a vector space basis for \(V\).

Definition 2
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A polynomial map between two affine spaces with chosen coordinate systems ...

Theorem 3
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Polynomial map definition is independent of chosen affine space basis.

Definition 4
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Polynomial map (for any basis)

Theorem 5
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Affine maps are polynomial of degree 1.

2 Blossoming principle

Definition 6
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Multiaffine map

Definition 7
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Symmetric map

Theorem 8
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Blossoming principle