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#
# legendre.m
#
# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
#
pkg load miscellaneous
global N;
N = 30;
function retval = legendrepath(fn, n, name)
global N;
m = n * N;
c = legendrepoly(n)
x = (-m:m)/m;
v = polyval(c, x);
fprintf(fn, "\\def\\legendre%s{\n", name)
fprintf(fn, "\t ({%.5f*\\dx},{%.5f*\\dy})", x(1), v(1));
for i = (2:length(v))
fprintf(fn, "\n\t-- ({%.5f*\\dx},{%.5f*\\dy})", x(i), v(i));
endfor
fprintf(fn, "\n}\n");
ci = polyint(conv(c, c))
polyval(ci, 1)
normalization = sqrt(polyval(ci, 1) - polyval(ci, -1))
fprintf(fn, "\\def\\normalization%s{%.5f}\n", name, normalization);
endfunction
function retval = legendreprodukt(fn, a, b, name)
global N;
n = max(a, b);
m = n * N;
pa = legendrepoly(a);
pb = legendrepoly(b);
p = conv(pa, pb);
x = (-m:m)/m;
v = polyval(p, x);
fprintf(fn, "\\def\\produkt%s{\n", name)
fprintf(fn, "\t ({%.5f*\\dx},{%.5f*\\dy})", x(1), v(1));
for i = (2:length(v))
fprintf(fn, "\n\t-- ({%.5f*\\dx},{%.5f*\\dy})", x(i), v(i));
endfor
fprintf(fn, "\n}\n");
endfunction
fn = fopen("legendrepaths.tex", "w");
legendrepath(fn, 1, "one");
legendrepath(fn, 2, "two");
legendrepath(fn, 3, "three");
legendrepath(fn, 4, "four");
legendrepath(fn, 5, "five");
legendrepath(fn, 6, "six");
legendrepath(fn, 7, "seven");
legendrepath(fn, 8, "eight");
legendrepath(fn, 9, "nine");
legendrepath(fn, 10, "ten");
legendreprodukt(fn, 4, 7, "ortho");
legendreprodukt(fn, 4, 4, "vier");
legendreprodukt(fn, 7, 7, "sieben");
fclose(fn);
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