# Difference between revisions of "Main Page/Applications"

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Andraschko (talk | contribs) (Added simple syntax highlighting) |
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Computing reduced [[Package sagbi|SAGBI bases]]: | Computing reduced [[Package sagbi|SAGBI bases]]: | ||

− | <span style="color:blue">Use</span> QQ[x,y], <span style="color:red">DegLex</span>; | + | <span style="color:blue">Use</span> P ::= QQ[x,y,z], <span style="color:red">DegLex</span>; |

− | SB. | + | S := SB.Subalgebra(P,[y-x^2,z-x^3]); |

− | <span style="color:#777777">-- reduced DegLex-SAGBI basis of | + | SB.SAGBI(S); <span style="color:#777777">-- reduced DegLex-SAGBI basis of S</span> |

Solving polynomial equations over <math>\mathbb{Z}/2\mathbb{Z}</math> using a SAT solver: | Solving polynomial equations over <math>\mathbb{Z}/2\mathbb{Z}</math> using a SAT solver: |

## Latest revision as of 14:29, 29 October 2020

### Application Examples

Computing reduced Gröbner bases:

Use P ::= QQ[x,y,z], DegRevLex; I := ideal(P,[y-x^2,z-x^3]); GBasis(I); -- reduced DegRevLex Gröbner basis of I

Computing reduced SAGBI bases:

Use P ::= QQ[x,y,z], DegLex; S := SB.Subalgebra(P,[y-x^2,z-x^3]); SB.SAGBI(S); -- reduced DegLex-SAGBI basis of S

Solving polynomial equations over **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{Z}/2\mathbb{Z}}**
using a SAT solver:

Use ZZ/(2)[x,y,z]; f1 := x*y + x*z + y*z + z; f2 := y + 1; f3 := x*y + z; SAT.Solve([f1,f2,f3]); -- [0, 1, 0]