Re: Re: polynomial congruence
- To: mathgroup at smc.vnet.net
- Subject: [mg26196] Re: [mg26145] Re: [mg26138] polynomial congruence
- From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
- Date: Thu, 30 Nov 2000 22:02:13 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Yes, that was a case of carelessness followed by thoughtlessness. What I meant was (of course): f[x_, y_] := x^2 + y^2 - 25 Table[Solve[{f[x, y] == 0, Modulus == 11}, x], {y, 0, 10}] Out[4]= {{{Modulus -> 11, x -> 5}, {Modulus -> 11, x -> 6}}, {}, {}, {{Modulus -> 11, x -> 4}, {Modulus -> 11, x -> 7}}, {{Modulus -> 11, x -> 3}, {Modulus -> 11, x -> 8}}, {{Modulus -> 11, x -> 0}, {Modulus -> 11, x -> 0}}, {{Modulus -> 11, x -> 0}, {Modulus -> 11, x -> 0}}, {{Modulus -> 11, x -> 3}, {Modulus -> 11, x -> 8}}, {{Modulus -> 11, x -> 4}, {Modulus -> 11, x -> 7}}, {}, {}} I then wanted to get rid of the irritating Modulus->11, and the rest was just as I wrote above. What I meant to do was something like: In[5]:= DeleteCases[%, Rule[Modulus, _], Infinity] Out[5]= {{{x -> 5}, {x -> 6}}, {}, {}, {{x -> 4}, {x -> 7}}, {{x -> 3}, {x -> 8}}, {{x -> 0}, {x -> 0}}, {{x -> 0}, {x -> 0}}, {{x -> 3}, {x -> 8}}, {{x -> 4}, {x -> 7}}, {}, {}} Andrzej on 00.12.1 2:02 AM, Daniel Lichtblau at danl at wolfram.com wrote: > Andrzej Kozlowski wrote: >> >> As long as p is not very large it is easy to do. For example, suppopse you >> want to solve all the congruences >> >> In[1]:= >> f[x_, y_] := x^2 + y^2 - 25 >> >> In[2]:= >> Table[Solve[{f[x, y] == 0, Modulus == 11}[[1]], x], {y, 0, 10}] >> >> Out[3]= >> {{{x -> -5}, {x -> 5}}, {{x -> -2 Sqrt[6]}, >> >> {x -> 2 Sqrt[6]}}, {{x -> -Sqrt[21]}, {x -> Sqrt[21]}}, >> >> {{x -> -4}, {x -> 4}}, {{x -> -3}, {x -> 3}}, >> >> {{x -> 0}, {x -> 0}}, {{x -> -I Sqrt[11]}, >> >> {x -> I Sqrt[11]}}, {{x -> -2 I Sqrt[6]}, >> >> {x -> 2 I Sqrt[6]}}, {{x -> -I Sqrt[39]}, >> >> {x -> I Sqrt[39]}}, {{x -> -2 I Sqrt[14]}, >> >> {x -> 2 I Sqrt[14]}}, >> >> {{x -> -5 I Sqrt[3]}, {x -> 5 I Sqrt[3]}}} >> >> Note that these answers really lie in the algebraic closure of the finite >> filed Z/11. >> >> on 11/28/00 3:56 PM, Constantinos Draziotis at roth at math.auth.gr wrote: >> >>> >>> Hello,i am a new user of mathematica,i will appreciate very much if you >>> can help me with this(it seems simple) problem:i want to solve a >>> polynomial congruence modulo prime number i.e f(x,y)=0modulo(p)(prime >>> number) with y=0,1,2,3...,n (n:integer).i have to find the classes >>> xmodulo(p) >>> >>> thanks for your time >>> >>> Costas >>> > > Your mislocated ...[[1]] messed this up. > > We used to return "radical" solutions for modular equations, but that > was fixed years ago, I think in version 2.2. > > Daniel -- Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/ http://sigma.tuins.ac.jp/