[sage-support] Re: %auto not automatically running code when upload notebook worksheet
> "x is %d" % y is standard Python for having variables in strings.
Thank, that helped a lot. In Python documentation I found the
solution.
> > html('In Scientific Notation: ${%d} \cdot 10^{%d}$'%base%exponent)
>
> > doesn't work either.
>
> I didn't see that inhttp://phil4.com/public/Sci.sws. I'm not sure
> where you saw that.
In fact it is not from that worksheet. I tried to change it. See
below.
> The *ONLY* problem is that it will not automatically run
> thanks to %auto.
I have the solution to that problem though it is not as much of a
solution as rather an idea what the reason could be.
On my system the %auto command works fine if there is no comment in
front of the cell.
Please open a new worksheet and copy the following code into the first
cell.
%auto
%hide
@interact
def _(base=(1..10),exponent=(-6..6)):
html('The Number: $%f$'%(base * 10**exponent))
html('In Scientific Notation: ${%d} \cdot 10^{%d}$'%(base,
exponent))
Works with me, and you will see my enhancement to the code. The two
variable thing.
Best regards
R.
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[sage-support] unanticipated divison by zero
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 "", line 1, in
File "_sage_input_36.py", line 10, in
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
File "/private/var/folders/dV/dVqvhWPV2RWo0U+8ZQR1kTM/-Tmp-/
tmpGm6sIU/___code___.py", line 3, in
exec compile(u'sum_of_squares(_sage_const_73 )
File "", line 1, in
File "/private/var/folders/dV/dVqvhWPV2RWo0U+8ZQR1kTM/-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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Re: [sage-support] unanticipated divison by zero
On Wed, Jun 22, 2011 at 12:35 PM, Ken Levasseur 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 "", line 1, in
> File "_sage_input_36.py", line 10, in
> 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
>
> File "/private/var/folders/dV/dVqvhWPV2RWo0U+8ZQR1kTM/-Tmp-/
> tmpGm6sIU/___code___.py", line 3, in
> exec compile(u'sum_of_squares(_sage_const_73 )
> File "", line 1, in
>
> File "/private/var/folders/dV/dVqvhWPV2RWo0U+8ZQR1kTM/-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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> To post to this group, send email to sage-support@googlegroups.com
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[sage-support] Re: unanticipated divison by zero
On Jun 22, 4:06 pm, Robert Bradshaw wrote: > What is startingA ? What is the parent of A? > The full .sws file is at http://homepage.mac.com/klevasseur/sum_of_squares.sws Ken -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: unanticipated divison by zero
If you take a look at the code, there is something fishy. Add the following statements. def sum_of_squares(p): if p.mod(4)==1: A=startingA(p) print A B=1 temp = A**2+B**2 print type(A**2+B**2) temp 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' For 73 you get 46 Traceback (click to the left of this block for traceback) ... ZeroDivisionError: Inverse does not exist. So A^2+B^2 (legitimate syntax in Sage) is a modular integer. In fact, you can check that its modulus is 73, and so it's no surprise that dividing by 73 \equiv 0 will result in a zero-division error. You'll have to find a way to get the power modulo p without actually making the thing an integer mod p. Hope this helps! - kcrisman On Jun 22, 7:43 pm, Ken Levasseur wrote: > On Jun 22, 4:06 pm, Robert Bradshaw > wrote: > > > What is startingA ? What is the parent of A? > > The full .sws file is athttp://homepage.mac.com/klevasseur/sum_of_squares.sws > > Ken -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: unanticipated divison by zero
Yes, it's exactly what I needed. I wasn't aware of the type distinction between integers and integers mod m. What I needed to use is the lift method: s=pow(2,11,23) [type(s),type(s.lift())] [, ] Thank you! Ken On Jun 22, 8:28 pm, kcrisman wrote: > If you take a look at the code, there is something fishy. Add the > following statements. > > def sum_of_squares(p): > if p.mod(4)==1: > A=startingA(p) > print A > B=1 > temp = A**2+B**2 > print type(A**2+B**2) > temp > 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' > > For 73 you get > > 46 > > Traceback (click to the left of this block for traceback) > ... > ZeroDivisionError: Inverse does not exist. > > So A^2+B^2 (legitimate syntax in Sage) is a modular integer. In fact, > you can check that its modulus is 73, and so it's no surprise that > dividing by 73 \equiv 0 will result in a zero-division error. > You'll have to find a way to get the power modulo p without actually > making the thing an integer mod p. > > Hope this helps! > - kcrisman > > On Jun 22, 7:43 pm, Ken Levasseur wrote: > > > > > On Jun 22, 4:06 pm, Robert Bradshaw > > wrote: > > > > What is startingA ? What is the parent of A? > > > The full .sws file is > > athttp://homepage.mac.com/klevasseur/sum_of_squares.sws > > > Ken -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: %auto not automatically running code when upload notebook worksheet
On Jun 22, 4:26 am, Rolf wrote: > Works with me, and you will see my enhancement to the code. The two > variable thing. Rolf Thanks. Does your version automatically start up when you upload the worksheet? Your version works like mine but doesn't start automatically for me like mine still. cs -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: %auto not automatically running code when upload notebook worksheet
> Thanks. Does your version automatically start up when you upload the > worksheet? Yes, as I said it starts automatically but it must have no descriptive comment above the cell. That is a worksheet with only one naked cell and no description in it. That's why I suggested to start a new worksheet from scratch. Your worksheet (http://phil4.com/public/Sci.sws) doesn't work with me either. Good luck R. -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
