poly factoring in small characteristic

[seelisch]

Ich forwarde drei mails von William Stein. Die erste befasst sich mit einem bug. Gruss, Wolfram Decker

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Subject: bug: poly factoring in small characteristic From: "William Stein" <wstein@…> Date: Wed, March 11, 2009 6:06 pm To: decker@…

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This uses Singular:

sage: R.<x,y> = PolynomialRing?(GF(3),2) sage: h = - (-x2 - x*y + y2 - 1)2 * (x2*y2 + y4 + x2*y + x*y2 + y3 - x2 + x*y + y2 - 1) * (-x4 - x3*y - x*y3 + y4 - x3 + x2*y + x*y2 - x2 - x*y - y2 + x + 1) sage: h.factor(proof=False) (-1) * (-x2 - x*y + y2 - 1) * (x8*y2 - x7*y3 + x6*y4 - x5*y5 + x3*y7 + x2*y8 + x*y9 + y10 + x8*y + x7*y2 - x3*y6 - x2*y7 + y9 - x8 + x3*y5 + x*y7 - y8 - x7 + x4*y3 + x3*y4

• x2*y5 + y7 - x4*y2 + x3*y3 + x2*y4 + x*y5 - y6 - x5 -

x4*y - y5 + x4 - x3*y + x2*y2 + x3 + x*y2 - y3 + x2 - x*y + x + 1) sage: h.factor(proof=False) (-1) * (-x2 - x*y + y2 - 1)2 * (x2*y2 + y4 + x2*y + x*y2 + y3

• x2 + x*y + y2 - 1) * (-x4 - x3*y - x*y3 + y4 - x3 + x2*y +

x*y2 - x2 - x*y - y2 + x + 1)

sage: z = singular(h) sage: z.factorize()

[1]:

_[1]=-1 _[2]=x2*y2+y4+x2*y+x*y2+y3-x2+x*y+y2-1 _[3]=x6-x5*y+x*y5+y6+x5+x*y4-x4+x2*y2+x*y3+y4+x2*y-y2-x-1 _[4]=-x2-x*y+y2-1

[2]:

1,1,1,1

sage: z.factorize()

[1]:

_[1]=-1 _[2]=x2*y2+y4+x2*y+x*y2+y3-x2+x*y+y2-1 _[3]=-x4-x3*y-x*y3+y4-x3+x2*y+x*y2-x2-x*y-y2+x+1 _[4]=-x2-x*y+y2-1

[2]:

1,1,1,2

-- William Stein Associate Professor of Mathematics University of Washington ​http://wstein.org

[seelisch]

to be included in redesign tasks regarding the factory module of SINGULAR