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<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
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  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;
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  <span style="color:blue">Use</span> P ::= QQ[x,y,z], <span style="color:red">DegLex</span>;
  [[Package sagbi/SB.SAGBI|SB.SAGBI]]([x^2*yx^2 -y^2, x^2*y^2 -y^4,  x^2*y^4]);
+
  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];
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  <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;
  [[Package sat/SAT.Solve|SAT.Solve]]([f1,f2,f3]);
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  SAT.Solve([f1,f2,f3]); <span style="color:#777777">-- [0, 1, 0]</span>
 +
</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 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]