On Mon, Aug 25, 2008 at 4:47 AM, Burcin Erocal <[EMAIL PROTECTED]> wrote:
>
> On Sun, 24 Aug 2008 15:55:25 -0700 (PDT)
> Jason Merrill <[EMAIL PROTECTED]> wrote:
>
>>
>> In hopes that it may be a useful reference during the current work on
>> symbolics, I wrote a toy Mathematica program for transforming a single
>> higher order ODE into a system of first order ODEs. Most of the free
>> numerical differential equation solvers I've seen want input in the
>> form y'[x] == f(y,x), so the purpose of a program like this is to take
>> more general input and turn it into something suitable for those
>> routines.
> <snip>
>
> Thank you for taking the time to write this. It is very useful indeed.
>
> The interface to pynac (William's modified version of GiNaC) doesn't
> support pattern matching yet, though it is not hard to add this. I'll
> add this functionality and try to reproduce your example in Sage once I
> finish reviewing the initial pynac interface patches (#3872).
Burcin -- I did actually mostly implement pattern matching in Pynac.
Some examples:
sage: var('x,y,z,a,b,c,d,e,f',ns=1); S = parent(x)
(x, y, z, a, b, c, d, e, f)
sage: w0 = S.wild(0); w1 = S.wild(1); w2 = S.wild(2)
sage: ((x+y)^a).match((x+y)^a)
True
sage: ((x+y)^a).match((x+y)^b)
False
sage: (a^2 + b^2 + (x+y)^2).subs(w0^2 == w0^3)
(x + y)^3 + a^3 + b^3
sage: (a^4 + b^4 + (x+y)^4).subs(w0^2 == w0^3)
(x + y)^4 + a^4 + b^4
sage: (a^2 + b^4 + (x+y)^4).subs(w0^2 == w0^3)
(x + y)^4 + a^3 + b^4
sage: ((a+b+c)^2).subs(a+b==x)
(a + b + c)^2
sage: ((a+b+c)^2).subs(a+b+w0==x+w0)
(c + x)^2
sage: (a+2*b).subs(a+b==x)
a + 2*b
sage: (a+2*b).subs(a+b+w0 == x+w0)
a + 2*b
sage: (a+2*b).subs(a+w0*b == x)
x
sage: (a+2*b).subs(a+b+w0*b == x+w0*b)
a + 2*b
sage: (4*x^3-2*x^2+5*x-1).subs(x==a)
4*a^3 - 2*a^2 + 5*a - 1
sage: (4*x^3-2*x^2+5*x-1).subs(x^w0==a^w0)
4*a^3 - 2*a^2 + 5*x - 1
sage: (4*x^3-2*x^2+5*x-1).subs(x^w0==a^(2*w0)).subs(x==a)
4*a^6 - 2*a^4 + 5*a - 1
sage: sin(1+sin(x)).subs(sin(w0)==cos(w0))
cos(cos(x) + 1)
sage: (sin(x)^2 + cos(x)^2).subs(sin(w0)^2+cos(w0)^2==1)
1
sage: (1 + sin(x)^2 + cos(x)^2).subs(sin(w0)^2+cos(w0)^2==1)
sin(x)^2 + cos(x)^2 + 1
sage: (17*x + sin(x)^2 + cos(x)^2).subs(w1 +
sin(w0)^2+cos(w0)^2 == w1 + 1)
17*x + 1
sage: ((x-1)*(sin(x)^2 + cos(x)^2)^2).subs(sin(w0)^2+cos(w0)^2 == 1)
x - 1
>
>
> Cheers,
>
> Burcin
>
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---
