# \320\237\320\276\321\206\320\265\320\264\321\203\321\200\320\270 \320\276\320\261\321\207\320\270\321\201\320\273\320\265\320\275\320\275\321\217 \320\277\320\276\321\205\321\226\320\264\320\275\320\270\321\205 \320\262\320\265\320\272\321\202\320\276\321\200-\321\204\321\203\320\275\320\272\321\206\321\226\320\271
restart;
with(linalg):
NiI=
df:=(f,t)-> diff(f,t);
df(cos(t),t);
NiI=
r:=(x,y,z)-> [x,y,z];
dr:=(x,y,z,t)-> [df(x,t),df(y,t),df(z,t)];
dr(cos(t),sin(t),t,t);
NiI=
d2f:=(f,t)-> diff(f,t$2);
d2f(cos(t),t);
NiI=
d2r:=(x,y,z,t)-> [d2f(x,t),d2f(y,t),d2f(z,t)];
d2r(cos(t),sin(t),t,t);
NiI=
d3f:=(f,t)-> diff(f,t$3);
d3f(cos(t),t);
NiI=
d3r:=(x,y,z,t)-> [d3f(x,t),d3f(y,t),d3f(z,t)];
d3r(cos(t),sin(t),t,t);
NiI=
Mod:=(a)->simplify(sqrt(linalg[innerprod](a,a))):
NiI=
Mod([cos(t),sin(t),t]);
Mod(d2r(cos(t),sin(t),t,t));
NiI=
mod_dr:=(x,y,z,t)-> Mod(dr(x,y,z,t)):
mod_d2r:=(x,y,z,t)-> Mod(d2r(x,y,z,t)):
NiI=
mod_dr(cos(t),sin(t),t,t);
mod_d2r(cos(t),sin(t),t,t);
NiI=
dvec_12:=(x,y,z,t)->linalg[crossprod](dr(x,y,z,t),d2r(x,y,z,t));
mod_dvec_12:=(x,y,z,t)->Mod(dvec_12(x,y,z,t));
NiI=
k:=(x,y,z,t)->simplify(mod_dvec_12(x,y,z,t)/mod_dr(x,y,z,t)^3);
NiI=
k(a*cos(t),a*sin(t),b*t,t);
JSFH
JSFH