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?
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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