08/12/2009, 12:24 AM

I'm attaching SAGE variables, for those who use SAGE. The zip file contains two sobj files, which are SAGE objects. I'm also attaching a text file with the coefficients, one per line, for those who don't have SAGE. (Note: I'm using SAGE 4.0.1, a slightly outdated version.)

First, the file jay_sexp_vec_128terms_1024bits.sobj contains the coefficients in a vector(RealField(1024), 129). These are the coefficients of the Taylor series, not the derivatives directly (i.e., the factorial is already factored in).

The file jay_sexp_pol_128terms_1024bits.sobj is a polynomial over the ring PolynomialRing(ComplexField(1024), 'z'), with 129 terms (128 not including the constant). To use it, simply load it into a variable, e.g., sexp, then use it like a function:

To convert the vector into a polynomial, you could do the following (there's probably an easier way, but the documentation is a bit sparse at times):

The text file jay_sexp_coeffs_128terms_256bits.txt contains the coefficients in a text format, one per line. I truncated it to 256 bits, so that the decimal expansions would be a reasonable length.

First, the file jay_sexp_vec_128terms_1024bits.sobj contains the coefficients in a vector(RealField(1024), 129). These are the coefficients of the Taylor series, not the derivatives directly (i.e., the factorial is already factored in).

The file jay_sexp_pol_128terms_1024bits.sobj is a polynomial over the ring PolynomialRing(ComplexField(1024), 'z'), with 129 terms (128 not including the constant). To use it, simply load it into a variable, e.g., sexp, then use it like a function:

Code:

`sexp = load('jay_sexp_pol_128terms_1024bits.sobj');`

APC = ComplexField(1024);

print sexp(APC(0.2, 0.1));

To convert the vector into a polynomial, you could do the following (there's probably an easier way, but the documentation is a bit sparse at times):

Code:

`svec = load('jay_sexp_vec_128terms_1024bits.sobj');`

APC = ComplexField(1024);

APCPol = PolynomialRing(APC, 'z');

z = APCPol('z');

sexp = sum(s[kk] * z**kk for kk in xrange(len(svec)));

The text file jay_sexp_coeffs_128terms_256bits.txt contains the coefficients in a text format, one per line. I truncated it to 256 bits, so that the decimal expansions would be a reasonable length.

~ Jay Daniel Fox