On Aug 25, 12:50 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
> 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>
>
> 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
Awesome. Thanks for making all this happen. I'm really excited about
where Sage is going. I've only been watching for a couple weeks now,
but I think I chose a fun time to find out about it.
Is the syntax for this stuff set in stone? I'm not sure I like the
equality inside the subs call. Equality is reflexive, but
substitution is a one way operation. What about a dictionary, sage: (a
+2*b).subs({a+b:x}), or even just a single equal sign, like keyword
args, sage: (a+2*b).subs(a+b=x). The double equals would work too,
but now is probably a better time for discussion than later.
JM
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