Re: [sage-devel] p-adic factorization/root finding bug.

[David Roe]

Thanks.  Created https://trac.sagemath.org/ticket/24193
David

On Fri, Nov 10, 2017 at 3:08 AM, Simon Brandhorst 
wrote:

> {{{
> sage: f=x^22 + 9*x^21 + 16*x^20 - 92*x^19 - 408*x^18 - 144*x^17 +
> 2080*x^16 + 4096*x^15 + 128*x^14 - 8192*x^13 - 12800*x^12 - 18432*x^11 -
> 51200*x^10 - 131072*x^9 + 8192*x^8 + 1048576*x^7 + 2129920*x^6 - 589824*
> : x^5 - 6684672*x^4 - 6029312*x^3 + 4194304*x^2 + 9437184*x + 4194304
> :
> sage: f.factor()
> (x - 2)^6 * (x + 2)^8 * (x^8 + 5*x^7 + 16*x^6 + 40*x^5 + 88*x^4 + 160*x^3
> + 256*x^2 + 320*x + 256)
> sage: g=f.change_ring(Qp(2,200))
> sage: g.roots()
>
> [(1 + 2 + 2^3 + 2^4 + 2^5 + 2^7 + 2^8 + 2^10 + 2^11 + 2^12 + 2^15 + 2^16 +
> 2^19 + 2^20 + 2^22 + 2^28 + 2^31 + 2^32 + 2^38 + 2^39 + 2^40 + 2^41 + 2^43
> + 2^44 + 2^46 + 2^47 + 2^50 + 2^53 + 2^54 + 2^56 + 2^57 + 2^59 + 2^60 +
> 2^61 + 2^68 + 2^71 + 2^74 + 2^75 + 2^76 + 2^77 + 2^84 + 2^86 + 2^89 + 2^90
> + 2^94 + 2^95 + 2^97 + 2^100 + 2^106 + 2^107 + 2^110 + 2^112 + 2^113 +
> 2^118 + 2^119 + 2^124 + 2^126 + 2^127 + 2^128 + 2^132 + 2^135 + 2^141 +
> 2^143 + 2^145 + 2^146 + 2^147 + 2^148 + 2^149 + 2^150 + 2^151 + 2^152 +
> 2^155 + 2^160 + 2^162 + 2^165 + 2^166 + 2^168 + 2^170 + 2^171 + 2^173 +
> 2^174 + 2^176 + 2^177 + 2^180 + 2^181 + 2^183 + 2^184 + 2^185 + 2^187 +
> 2^189 + 2^190 + 2^191 + 2^192 + 2^193 + 2^194 + 2^195 + 2^196 + 2^197 +
> 2^198 + O(2^200),
>   1),
>  (2^2 + 2^3 + 2^6 + 2^7 + 2^8 + 2^10 + 2^11 + 2^12 + 2^13 + 2^14 + 2^17 +
> 2^18 + 2^20 + 2^23 + 2^24 + 2^28 + 2^29 + 2^33 + 2^34 + 2^36 + 2^39 + 2^40
> + 2^42 + 2^44 + 2^45 + 2^47 + 2^54 + 2^55 + 2^56 + 2^58 + 2^59 + 2^61 +
> 2^63 + 2^69 + 2^70 + 2^71 + 2^78 + 2^81 + 2^82 + 2^84 + 2^87 + 2^88 + 2^89
> + 2^90 + 2^91 + 2^93 + 2^95 + 2^99 + 2^100 + 2^101 + 2^102 + 2^103 + 2^104
> + 2^108 + 2^110 + 2^113 + 2^115 + 2^116 + 2^117 + 2^118 + 2^121 + 2^122 +
> 2^123 + 2^124 + 2^126 + 2^128 + 2^130 + 2^131 + 2^133 + 2^135 + 2^137 +
> 2^139 + 2^140 + 2^141 + 2^142 + 2^144 + 2^145 + 2^146 + 2^148 + 2^151 +
> 2^152 + 2^157 + 2^158 + 2^159 + 2^163 + 2^165 + 2^166 + 2^169 + 2^170 +
> 2^171 + 2^174 + 2^175 + 2^176 + 2^177 + 2^179 + 2^181 + 2^182 + 2^184 +
> 2^188 + 2^192 + 2^193 + 2^194 + 2^195 + 2^196 + 2^198 + O(2^200),
>   1)]
>
>
> }}}
>
>
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[sage-devel] p-adic factorization/root finding bug.

[Simon Brandhorst]

{{{
sage: f=x^22 + 9*x^21 + 16*x^20 - 92*x^19 - 408*x^18 - 144*x^17 + 2080*x^16 
+ 4096*x^15 + 128*x^14 - 8192*x^13 - 12800*x^12 - 18432*x^11 - 51200*x^10 - 
131072*x^9 + 8192*x^8 + 1048576*x^7 + 2129920*x^6 - 589824*
: x^5 - 6684672*x^4 - 6029312*x^3 + 4194304*x^2 + 9437184*x + 4194304
: 
sage: f.factor()
(x - 2)^6 * (x + 2)^8 * (x^8 + 5*x^7 + 16*x^6 + 40*x^5 + 88*x^4 + 160*x^3 + 
256*x^2 + 320*x + 256)
sage: g=f.change_ring(Qp(2,200))
sage: g.roots()

[(1 + 2 + 2^3 + 2^4 + 2^5 + 2^7 + 2^8 + 2^10 + 2^11 + 2^12 + 2^15 + 2^16 + 
2^19 + 2^20 + 2^22 + 2^28 + 2^31 + 2^32 + 2^38 + 2^39 + 2^40 + 2^41 + 2^43 
+ 2^44 + 2^46 + 2^47 + 2^50 + 2^53 + 2^54 + 2^56 + 2^57 + 2^59 + 2^60 + 
2^61 + 2^68 + 2^71 + 2^74 + 2^75 + 2^76 + 2^77 + 2^84 + 2^86 + 2^89 + 2^90 
+ 2^94 + 2^95 + 2^97 + 2^100 + 2^106 + 2^107 + 2^110 + 2^112 + 2^113 + 
2^118 + 2^119 + 2^124 + 2^126 + 2^127 + 2^128 + 2^132 + 2^135 + 2^141 + 
2^143 + 2^145 + 2^146 + 2^147 + 2^148 + 2^149 + 2^150 + 2^151 + 2^152 + 
2^155 + 2^160 + 2^162 + 2^165 + 2^166 + 2^168 + 2^170 + 2^171 + 2^173 + 
2^174 + 2^176 + 2^177 + 2^180 + 2^181 + 2^183 + 2^184 + 2^185 + 2^187 + 
2^189 + 2^190 + 2^191 + 2^192 + 2^193 + 2^194 + 2^195 + 2^196 + 2^197 + 
2^198 + O(2^200),
  1),
 (2^2 + 2^3 + 2^6 + 2^7 + 2^8 + 2^10 + 2^11 + 2^12 + 2^13 + 2^14 + 2^17 + 
2^18 + 2^20 + 2^23 + 2^24 + 2^28 + 2^29 + 2^33 + 2^34 + 2^36 + 2^39 + 2^40 
+ 2^42 + 2^44 + 2^45 + 2^47 + 2^54 + 2^55 + 2^56 + 2^58 + 2^59 + 2^61 + 
2^63 + 2^69 + 2^70 + 2^71 + 2^78 + 2^81 + 2^82 + 2^84 + 2^87 + 2^88 + 2^89 
+ 2^90 + 2^91 + 2^93 + 2^95 + 2^99 + 2^100 + 2^101 + 2^102 + 2^103 + 2^104 
+ 2^108 + 2^110 + 2^113 + 2^115 + 2^116 + 2^117 + 2^118 + 2^121 + 2^122 + 
2^123 + 2^124 + 2^126 + 2^128 + 2^130 + 2^131 + 2^133 + 2^135 + 2^137 + 
2^139 + 2^140 + 2^141 + 2^142 + 2^144 + 2^145 + 2^146 + 2^148 + 2^151 + 
2^152 + 2^157 + 2^158 + 2^159 + 2^163 + 2^165 + 2^166 + 2^169 + 2^170 + 
2^171 + 2^174 + 2^175 + 2^176 + 2^177 + 2^179 + 2^181 + 2^182 + 2^184 + 
2^188 + 2^192 + 2^193 + 2^194 + 2^195 + 2^196 + 2^198 + O(2^200),
  1)]


}}}


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