Difference between revisions of "Main Page/Applications"

Revision as of 11:49, 29 October 2020

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 QQ[x,y], DegLex;
SB.SAGBI([x^2*y, x^2 -y^2, x^2*y^2 -y^4, x^2*y^4]);
-- reduced DegLex-SAGBI basis of Q[x^2y, x^2-y^2, x^2y^2-y^4, x^2y^4]

Solving polynomial equations over $\mathbb {Z} /2\mathbb {Z}$ 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]

@@ Line 2: / Line 2: @@
 <h3>Application Examples</h3>
 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]);
-  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]]:
-  Use QQ[x,y], DegLex;
+  <span style="color:blue">Use</span> QQ[x,y], <span style="color:red">DegLex</span>;
-  [[Package sagbi/SB.SAGBI|SB.SAGBI]]([x^2*y,  x^2 -y^2,  x^2*y^2 -y^4,  x^2*y^4]);
+  SB.SAGBI([x^2*y, x^2 -y^2, x^2*y^2 -y^4, x^2*y^4]);
+ <span style="color:#777777">-- reduced DegLex-SAGBI basis of Q[x^2y, x^2-y^2, x^2y^2-y^4, x^2y^4]</span>
 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;
   f2 := y + 1;
   f3 := x*y + z;
-  [[Package sat/SAT.Solve|SAT.Solve]]([f1,f2,f3]);
+  SAT.Solve([f1,f2,f3]); <span style="color:#777777">-- [0, 1, 0]</span>
 </div>