On Fri, May 10, 2013 at 10:00 AM, Matt <[email protected]> wrote:
> I'm new to Sage, coming from a Maple background. I have some fairly
> complicated multivariate polynomial Vandermonde inverses to generate, and my
> method of choice is constructing a generic polynomial, applying whatever
> operations I wish (differentiate, integrate, sample, etc) for constraints,
> then taking the Jacobian of the constraints with respect to polynomial
> coefficients (which are symbolic placeholders at this point), and finally
> inverting that Jacobian and multiplying by the RHS data that fits those
> constraints. This requires the use of a symbolic vector as a placeholder. The
> only way I've found of doing this so far (for a half-tensor 2-D polynomial)
> is:
>
> N = 4
> var('x','y')
> ns = (N+1)*N/2
> p = 0
> count = 0
> for j in range(N) :
> for i in range(N) :
> if ( i + j ) < N :
> p = p + var('a%s'%count) * x^i * y^j
> count = count + 1
>
> And this works just fine, and I can take the Jacobian of constraints as:
>
> A = jacobian( constr , ( [ var('a%s'%i) for i in range(ns) ] ) )
What is "constr". You didn't define it above. I guessed it might be
"p", but that's not right since then A isn't square (which is the case
below).
>
> But, I cannot then assign to the coefficients to retrieve the fitted
> polynomial and perform further operations on it. I've tried this, and it
> fails:
>
> coefs = A^-1 * vector( [ var('m%s'%i) for i in range(ns) ] )
> for i in range(ns) :
> 'a%s'%i = coefs[i]
>
> As I expected, I get "SyntaxError: can't assign to operator." How can I
> assign to a generated variable name? Better still, is there a way to create a
> symbolic vector that isn't assigned values, that I can use as a placeholder?
> Thanks,
>
> -Matt
>
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>
--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
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