On Wed, Jun 22, 2011 at 12:35 PM, Ken Levasseur <[email protected]> wrote:
> Hello. I'm trying to implement the algorithm for representing primes
> congruent to 1 mod 4 as a sum of squares and I know the logic of the
> algebra is right (identical equations work in Mathematica). However,
> I get a "ZeroDivisionError: Inverse does not exist." error when I
> evaluate the expression
>
> sum_of_squares(73).
>
> where the definition of sum_of_squares is
>
> def sum_of_squares(p):
> if p.mod(4)==1:
> A=startingA(p)
> print A
> B=1
> M=(A**2+B**2)/p
> while M>1:
> [a,b,r]=iterate(A,B,M,p)
> [A,B,M]=[a,b,r]
> return [A,B]
> else:
> print 'no'
>
> The error appears to be when M is computed just before the while
> loop. I know that A is computed correctly because the correct values
> come out randomly when I print A, but then I never get to the loop.
> I evaluate the following before the definition of the function.
>
> p=var('p')
> A=var('A')
> B=var('B')
> r=var('r')
> a=var('a')
> b=var('b')
>
> Anyone know what's going on?
What is startingA ? What is the parent of A?
> The full error message from evaluating sum_of_squares(73) is
>
> ]Traceback (most recent call last):
> File "<stdin>", line 1, in <module>
> File "_sage_input_36.py", line 10, in <module>
> exec compile(u'open("___code___.py","w").write("# -*- coding:
> utf-8 -*-\\n" +
> _support_.preparse_worksheet_cell(base64.b64decode("c3VtX29mX3NxdWFyZXMoNzMp"),globals())
> +"\\n"); execfile(os.path.abspath("___code___.py"))
> File "", line 1, in <module>
>
> File "/private/var/folders/dV/dVqvhWPV2RWo0U+8ZQR1k++++TM/-Tmp-/
> tmpGm6sIU/___code___.py", line 3, in <module>
> exec compile(u'sum_of_squares(_sage_const_73 )
> File "", line 1, in <module>
>
> File "/private/var/folders/dV/dVqvhWPV2RWo0U+8ZQR1k++++TM/-Tmp-/
> tmpXtNmdU/___code___.py", line 8, in sum_of_squares
> M=(A**_sage_const_2 +B**_sage_const_2 )/p
> File "element.pyx", line 1551, in
> sage.structure.element.RingElement.__div__ (sage/structure/element.c:
> 12000)
> File "coerce.pyx", line 713, in
> sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/
> coerce.c:6153)
> File "element.pyx", line 1549, in
> sage.structure.element.RingElement.__div__ (sage/structure/element.c:
> 11981)
> File "integer_mod.pyx", line 2223, in
> sage.rings.finite_rings.integer_mod.IntegerMod_int._div_ (sage/rings/
> finite_rings/integer_mod.c:19173)
> ZeroDivisionError: Inverse does not exist.
>
>
>
>
> Ken Levasseur
> UMass Lowell
>
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