Paul
I was wrong, both yuor questions are rather simple
If you want to use Singular you have to give an argument which
Singular wants
and SAGE provides "somthing completly different", so the conversion is
natural
sage: type(n12)
<class 'sage.calculus.calculus.SymbolicArithmetic'>
sage: type(repr(n12))
<type 'str'>
Andrzej Chrzeszczyk
On 12 Sty, 21:57, achrzesz <[EMAIL PROTECTED]> wrote:
> If you dont want factor you can use
> n12 = numerator((s1-s2).rational_simplify())
>
> On 12 Sty, 16:53, achrzesz <[EMAIL PROTECTED]> wrote:
>
> > Paul
> > Have you noticed that your SAGE code is much faster tha MAPLE's?
> > Your final questions are interesting but not easy to me
> > Andrzej Chrzeszczyk
>
> > On 12 Sty, 16:27, achrzesz <[EMAIL PROTECTED]> wrote:
>
> > > Paul
> > > Im impressed again. Thank you so much
> > > I had only a rough idea and you are realy effective in SAGE (too).
> > > This time I have no additional concrete questions
> > > but I'm strongly interested in your general opinion
> > > conce rning the comparison MAPLE-SAGE (any links?)
> > > Andrzej Chrzeszczyk
>
> > > On 11 Sty, 23:09, Paul Zimmermann <[EMAIL PROTECTED]> wrote:
>
> > > > Dear Andrzej,
>
> > > > > I don't know if elegant Paul Zimmermann's MAPLE solution
> > > > > has counterpart in SAGE (I'm affraid it hasn't) but his remark on
> > > > > the Groebner bases (SINGULAR, MACAULAY2 interf?) may be essentiall.
> > > > > Does the discussion mean that I have to use the closed source
> > > > > software?
> > > > > Still waiting for reply.
>
> > > > I was able to do the job with SAGE, but I have to confess it was not as
> > > > easy
> > > > as in Maple (however I am still more fluent in Maple):
>
> > > > ----------------------------------------------------------------------
> > > > | SAGE Version 2.9.3, Release Date: 2008-01-05 |
> > > > | Type notebook() for the GUI, and license() for information. |
> > > > ----------------------------------------------------------------------
> > > > sage: var('x1,y1,x2,y2,x3,y3,a,b')
> > > > sage: eq1 = y1^2 -(x1^3+a*x1+b)
> > > > sage: eq2 = y2^2 -(x2^3+a*x2+b)
> > > > sage: eq3 = y3^2 -(x3^3+a*x3+b)
> > > > sage: lambda12 = (y1 - y2)/(x1 - x2)
> > > > sage: x4 = (lambda12*lambda12 - x1 - x2)
> > > > sage: nu12 = (y1 - lambda12*x1)
> > > > sage: y4 = (-lambda12*x4 - nu12)
> > > > sage: lambda23 = ((y2 - y3)/(x2 - x3))
> > > > sage: x5 = (lambda23*lambda23 - x2 - x3)
> > > > sage: nu23 = (y2 - lambda23*x2)
> > > > sage: y5 = (-lambda23*x5 - nu23)
> > > > sage: s1 =(x1 - x5)*(x1 - x5)*((y3 - y4)*(y3-y4) -
> > > > (x3+x4)*(x3-x4)*(x3-x4))
> > > > sage: s2 =(x3 - x4)*(x3 - x4)*((y1 - y5)*(y1-y5) -
> > > > (x1+x5)*(x1-x5)*(x1-x5))
> > > > sage: n12 = numerator(factor(s1-s2))
> > > > sage: R = singular.ring(0, '(a,b,x1,x2,x3,y1,y2,y3)')
> > > > sage: I = singular.ideal([repr(eq1), repr(eq2), repr(eq3)])
> > > > sage: I2 = I.groebner()
> > > > sage: singular.reduce(repr(n12), I2)
>
> > > > 0
>
> > > > In particular:
>
> > > > (1) is there a better way to normalize a rational expression that
> > > > calling
> > > > factor? Apparently numerator alone does not do the job.
> > > > (2) can we get rid of the repr() calls?
>
> > > > Paul Zimmermann
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