return sage.calculus.calculus\
.symbolic_expression_from_string(
string,syms={'t':t},accept_sequence=True)def _(function=['[2t,t^2]','[7sin(t),4cos(t)+6]',
'[cos(t)^2*2t,cos(t)^2*t^2]']):
n=10; var('t'); c=['#3636ff','#ff3636'] f=(sefs(function)); print(f)
df=(f[0].diff(),f[1].diff())
d2f=(df[0].diff(),df[1].diff())
def norm(g): return sqrt(sum(el^2 for el in g))
fnormal=(df[1]/norm(df),-df[0]/norm(df))
r=norm(df)^3/(df[1]*d2f[0]-df[0]*d2f[1])
centers=(f[0]+r*fnormal[0],f[1]+r*fnormal[1])
print('f: x(t)=%s; y(t)=%s'%(f[0],f[1])) p=parametric_plot(f,(t,-n,n),color=c[0],thickness=2)
p+=parametric_plot(centers,(t,-n,n),color=c[1],
thickness=3,linestyle='--')
p+=sum(line2d([(f[0](t=i),f[1](t=i)),
(centers[0](t=i),centers[1](t=i))],
thickness=1,rgbcolor=Color('silver').rgb()) for i in sxrange(-n,n,.1))
p.show(xmin=-8,xmax=8,ymin=-2,ymax=14,figsize=5)
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