Maybe during break I can write a little tutorial about doing modular arithmetic to include in the docs. Your example, Aaron, is exactly what I was looking for with the arithmetic (though the repr form is rather ugly -- see below). And Hector's work will allow one to answer the other question (about finding a number that has a certain residual profile for a given set of bases) though perhaps the routine I presented could be used in the case where the moduli are not all prime. That could go in a solve_congruence routine in solve (to answer your question, Hector) and that routine could call the gf_csolve when the moduli are prime or else do the other calculation that I gave:
```python >>> def div(a,b,m): ... m=FF(m) ... try: return m(a)/m(b) ... except: ... if m(a): return oo # perhaps this, rather than an error would be more sympy like ... return S.NaN # ditto ... >>> for i in range(5): ... for j in range(i,5): ... print '%i/%i =%s'%(i,j,div(i,j,5)) ... 0/0 =nan 0/1 =0 mod 5 0/2 =0 mod 5 0/3 =0 mod 5 0/4 =0 mod 5 1/1 =1 mod 5 1/2 =3 mod 5 1/3 =2 mod 5 1/4 =4 mod 5 2/2 =1 mod 5 2/3 =4 mod 5 2/4 =3 mod 5 3/3 =1 mod 5 3/4 =2 mod 5 4/4 =1 mod 5 >>> for i in range(6): ... for j in range(i,6): ... print '%i/%i =%s'%(i,j,div(i,j,6)) ... 0/0 =nan 0/1 =0 mod 6 0/2 =nan 0/3 =nan 0/4 =nan 0/5 =0 mod 6 1/1 =1 mod 6 1/2 =oo 1/3 =oo 1/4 =oo 1/5 =5 mod 6 2/2 =oo 2/3 =oo 2/4 =oo 2/5 =4 mod 6 3/3 =oo 3/4 =oo 3/5 =3 mod 6 4/4 =oo 4/5 =2 mod 6 5/5 =1 mod 6 >>> m7=FF(7) >>> [(m7(i)) for i in range(7)] [SymmetricModularIntegerMod7(0), SymmetricModularIntegerMod7(1), SymmetricModula rIntegerMod7(2), SymmetricModularIntegerMod7(3), SymmetricModularIntegerMod7(4), SymmetricModularIntegerMod7(5), SymmetricModularIntegerMod7(6)] >>> [sqrt(m7(i)) for i in range(7)] [0, 1, sqrt(2), sqrt(3), sqrt(3)*I, sqrt(2)*I, I] >>> [str(m7(i)) for i in range(7)] ['0 mod 7', '1 mod 7', '2 mod 7', '3 mod 7', '4 mod 7', '5 mod 7', '6 mod 7'] >>> str(m7(4)+m7(3)) '0 mod 7' >>> str(m7(4)-m7(3)) '1 mod 7' >>> str(m7(4)*m7(3)) '5 mod 7' >>> str(m7(4)/m7(3)) '6 mod 7' >>> str(m7(4)**3) '1 mod 7' >>> str(sqrt(m7(4))) 'sqrt(3)*I' >>> sqrt(m7(4))**2 -3 >>> m7(_)==m7(4) True ``` I wonder if the positive value for the sqrt should be returned. http://ptrow.com/perl/calculator.pl lists the square roots of 4 mod 7 as being 2 and 5 (half of the numbers between 1 and modulus - 1 -- in this case half of 2, 3, 4, 5, or 2 and 5 -- are square roots mod n). sympy returned sqrt(-3) rather than 2 or 5. Also, I wonder if the str form should be the default printed in interactive sessions rather than the repr form. /c -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
