Hello I would like found a curve B(t) that join the curve v(t) and u(t)
I calculated by hand and I get the poly B(t)=(t+1,-t^2+t+1)
by resolving the equation system
v(1)==B(0)
u(0)==B(1)
v'(1)=B'(0)
u'(0)=B'(1)
I didn't understand why the solution of the equation is emply?!?
my code:
a,b,c,d,e,f,t = var('a,b,c,d,e,f,t')
v(t)=(t,t)
u(t)=(2+t,1-t)
B(t)=(a*t^2+b*t+c,d*t^2+e*t+f)
eq1=v.substitute(t==1)==B.substitute(t==0) # v(1)==B(0)
eq2=u.substitute(t==0)==B.substitute(t==1) # u(0)==B(1)
eq3=diff(v(t),t).substitute(t==1)==diff(B,t).substitute(t==0) # v'(1)=B'(0)
eq4=diff(u(t),t).substitute(t==0)==diff(B,t).substitute(t==1) # u'(0)=B'(1)
solve([eq1,eq2,eq3,eq4],a,b,c,d,e,f,t)
Thanks in advance
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