make automated tests

[edgarcosta]

Here are some examples:

Hyperelliptic and geometrically simple:
[x^7,1]
[x^7-2*x^3-x,0]
[x^7-2*x^3+x,0]
[2*x^6+3*x^5+5*x^4+6*x^3+4*x^2+x,x^4+x^3+x]
[-2*x^6-4*x^5+3*x^4+7*x^3-2*x^2-2*x+3,x^4+x^3+x]
[x^8+x^7-2*x^6-4*x^5+4*x^3+2*x^2-x-1,0]

Non-hyperelliptic and geometrically simple:
[x^3*z + x^2*z^2 + x*y^3 - x*z^3 + y^3*z]
[x^3*z + x^2*y^2 + x*y^3 + x*y^2*z + x*y*z^2 - x*z^3 + y^3*z - y^2*z^2]
[x^3*z + x^2*y*z + x*y^3 + 2*x*y^2*z + x*y*z^2 - x*z^3 - y^3*z + y*z^3]
[x^3*z + x^2*y^2 + x^2*y*z - x^2*z^2 + x*y^3 - x*y*z^2 + x*z^3 + y^3*z -
y*z^3]
[x^3*y + x^3*z + x^2*z^2 + x*y^3 + 2*x*y^2*z - x*y*z^2 - x*z^3 - 2*y^3*z
- 2*y^2*z^2 - y*z^3 - z^4]
[x^3*z + x^2*y^2 + 2*x^2*y*z - 2*x^2*z^2 - x*y^3 - 2*x*y^2*z + 2*x*z^3 +
y^3*z - y*z^3]
[x^3*z + y^4 + y^3*z + 2*y^2*z^2 + y*z^3 + z^4]
[x^3*z + x^2*y^2 + x*y^3 + x*y^2*z - 2*x*y*z^2 - x*z^3 + y^4 - y^3*z -
y^2*z^2 + y*z^3]
[x^3*z + x*y^3 - 2*x*z^3 + y^3*z + z^4]
[x^3*z + x^2*y^2 + x*y^3 - 2*x*y^2*z + 2*x*y*z^2 - 2*x*z^3 - y^3*z + y*z^3]
[x^3*z + y^4 + y^3*z - 2*y^2*z^2 - y*z^3 + z^4]
[x^3*z + x^2*y^2 + x^2*y*z - x^2*z^2 - x*y^3 - x*y^2*z + x*z^3 - y^3*z +
2*y*z^3 - z^4]

Non-hyperelliptic and geometrically a power:
[x^4 + 2*x^3*z + x^2*y^2 + x^2*y*z + 3*x^2*z^2 + x*y^2*z + x*y*z^2 +
2*x*z^3 + y^4 + 2*y^3*z + 3*y^2*z^2 + 2*y*z^3 + z^4]
[x^3*z + x*y^3 + y*z^3]
[x^4 + 2*x^3*z + 3*x^2*y^2 + 3*x^2*y*z + 3*x^2*z^2 + 3*x*y^2*z +
3*x*y*z^2 + 2*x*z^3 + y^4 + 2*y^3*z + 3*y^2*z^2 + 2*y*z^3 + z^4]
[x^3*z - x*z^3 + y^4]
[x^3*z + x*z^3 + y^4]

[edgarcosta]

HeuristicDecomposition(Genus2Elliptic2("21a1","32a2")[2]);

from CHIMP