Difference between revisions of "Main Page/Applications"

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(Added simple syntax highlighting)
(simplified sagbi example)
 
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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>;
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  <span style="color:blue">Use</span> P ::= QQ[x,y,z], <span style="color:red">DegLex</span>;
  SB.SAGBI([x^2*y, x^2 -y^2, x^2*y^2 -y^4, x^2*y^4]);
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  S := SB.Subalgebra(P,[y-x^2,z-x^3]);
  <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>
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  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]