CoCoA:Gin, Gin5

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Gin, Gin5

generic initial ideal

Description

These functions return the [probabilistic] gin (generic initial ideal)

of the ideal I. It is obtained by computing the leading term ideal of

g(I), where g is a random change of coordinates.

While Gin uses integer coefficients in [-Range, Range], with

default value [-100, 100] (repeated until 4 consecutive random changes

of coordinates give the same result), the function Gin5 uses the special TwinFloat implementation in CoCoAServer to allow a much wider range of coefficients (and then performs the computation only twice). The latter is faster, but needs you to start the server!

Example

```  Use R ::= Q[x,y,z], DegRevLex;
Gin(Ideal(y^2-xz, x^2z-yz^2));
Ideal(x^2, xy^2, y^4)
-------------------------------
Use R ::= Q[x,y,z], Lex;
Gin(Ideal(y^2-xz, x^2z-yz^2), 10);  -- coeffs in [-10, 10]
Ideal(x^2, xy^2, xyz^2, xz^4, y^6)
-------------------------------
Use R ::= Q[x,y,z], DegRevLex;      -- default range [10000, 10000]
Gin5(Ideal(y^2-xz, x^2z-yz^2));
Ideal(x^2, xy^2, y^4)
-------------------------------
Use R ::= Q[x,y,z], Lex;
Gin5(Ideal(y^2-xz, x^2z-yz^2), 2); -- coeffs in [-2,2], dangerously small:
-- ==&gt; answer might be wrong
```

Syntax

```Gin(I: IDEAL): IDEAL
Gin(I: IDEAL, Range: INT): IDEAL
Gin5(I: IDEAL): IDEAL
Gin5(I: IDEAL, Range: INT): IDEAL
```
```   <type>ideal</type>
<type>cocoaserver</type>
```