Sentence examples for basis for an ideal from inspiring English sources
The computational cost of calculating a Gröbner basis is extensive and some problems are almost never solved in a realistic timescale, even if theoretically it is always possible to obtain a Gröbner basis for an ideal.
A Gröbner basis for an ideal
The researchers used the Harvard Healthy Eating Plate model as their basis of an ideal nutrition model.
The Pulay force is systematically controlled and is not required to be calculated, which makes the optimized local basis set an ideal tool for ab initio molecular dynamics and structure optimization.
Believing the story provided an "ideal basis" for an animated feature film and keen on creating a film that took place underwater, Clements wrote and presented a two-page treatment of "Mermaid" to Disney CEO Jeffrey Katzenberg at a "gong show" idea suggestion meeting.
One type of generator or basis that permits elimination theory for an ideal to be applied is the Gröbner basis with lexicographic order.
The following theorem gives a linear basis for the ideal I d ( S ) provided that S ⊂ k ⟨ X ⟩ is a GS basis.
If S ⊂ k ⟨ X ⟩ is a Gröbner Shirshov basis then, given u ∈ X ∗ I r r ( S ), by Lemma 2 there exists u ^ ∈ k I r r ( S ) with u ^ ¯ < u (if u ^ ≠ 0 ) such that u - u ^ ∈ I d ( S ) and the set { u - u ^ | u ∈ X ∗ I r r ( S ) } is a linear basis for the ideal I d ( S ) of k ⟨ X ⟩.
Another key benefit of the CSI approach lies in its ability to infer upstream interactions on a node-by-node basis, making it an ideal theoretical method for leveraging Y1H screens.
Lester traces the conceptual origins of the drawing back to the ancient Greek sculptors and builders who sought to record the proportions of the perfect human body, and from there to Vitruvius himself, who used similar calculations as the basis for his ideal architectural proportions.
