The goal is to get Kalman Form

https://docs.google.com/file/d/0Bxs_ao6uuBDUT25BeVhtWjZwRUU/edit?usp=sharing

https://docs.google.com/file/d/0Bxs_ao6uuBDUVXU5dXh6Rl9zUUU/edit?usp=sharing

I am doing the example in page 707 of Partial Differential control theory Volume 2 by J.F.

when using Robertz Daniel's Ore and Involutive packages

with(Involutive):

with(OreModules):

Alg := DefineOreAlgebra(diff=[D,t...

x = a*(3*cos(t) - cos(3*t))
y = a*(3*sin(t) - sin(3*t))

is there a library or function to convert above parametric equations into one equation in terms of x and y?

sys := x = a*(3*cos(t) - cos(3*t));
k := solve(sys, t);
simplify(subs(t=k[1], y = a*(3*sin(t) - sin(3*t))));

any simpler form?

refer to Madan's paper about VG in year 1998

equation (6)

tm := int(expand(1/(rho*sqrt(2*Pi*g))*exp(-((X-theta*g)^2)/(2*g*rho^2))*g^(t/v-1)*exp(-g/v)/v^(t/v)/GAMMA(t/v)),g=0..infinity);
characteristicfun := invfourier(int(tm,x=0..infinity),x,w);

it is not equal to (1/(1-i*theta*v*u+(v/2*rho^2)*u^2))^(t/v) ?

it can not be calculated

http://en.wikipedia.org/wiki/Hodge_theory
H(M) = ker(d_k) / im(d_k-1)

would like to see the example of calculation of H(M) above

eqn := y^2 = x^3 + a*x  + b

where a and b are summation of things, or constant

if use convert(eqn, ratpoly) to get a ratpoly

can it be used to guess gf using guessgf directly?

or

convert ratpoly to differential equation and then calculate eigenfunction and calculate generating function?