Difference between revisions of "Main Page/Applications"
From ApCoCoAWiki
Andraschko (talk | contribs) m (forgot </div>) |
Andraschko (talk | contribs) (simplified sagbi example) |
||
| (One intermediate revision by the same user not shown) | |||
| Line 2: | Line 2: | ||
<h3>Application Examples</h3> | <h3>Application Examples</h3> | ||
Computing reduced Gröbner bases: | Computing reduced Gröbner bases: | ||
| − | Use P ::= QQ[x,y,z], DegRevLex; | + | <span style="color:blue">Use</span> P ::= QQ[x,y,z], <span style="color:red">DegRevLex</span>; |
I := ideal(P,[y-x^2,z-x^3]); | I := ideal(P,[y-x^2,z-x^3]); | ||
| − | GBasis(I); -- reduced DegRevLex Gröbner basis of I | + | GBasis(I); <span style="color:#777777">-- reduced DegRevLex Gröbner basis of I</span> |
Computing reduced [[Package sagbi|SAGBI bases]]: | Computing reduced [[Package sagbi|SAGBI bases]]: | ||
| − | Use QQ[x,y], DegLex; | + | <span style="color:blue">Use</span> P ::= QQ[x,y,z], <span style="color:red">DegLex</span>; |
| − | + | S := SB.Subalgebra(P,[y-x^2,z-x^3]); | |
| + | 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: | ||
| − | Use ZZ/(2)[x,y,z]; | + | <span style="color:blue">Use</span> ZZ/(2)[x,y,z]; |
f1 := x*y + x*z + y*z + z; | f1 := x*y + x*z + y*z + z; | ||
f2 := y + 1; | f2 := y + 1; | ||
f3 := x*y + z; | f3 := x*y + z; | ||
| − | + | SAT.Solve([f1,f2,f3]); <span style="color:#777777">-- [0, 1, 0]</span> | |
</div> | </div> | ||
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 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]
