def laplace_and_matrix():
t, s = symbols('t, s')
if False:
y = laplace(exp(t), t, s)
disp(y)
y = laplace(4+5*exp(-3*t), t, s)
disp(y)
y = laplace(4+5*exp(-3*t), t, s)
disp(y)
disp( laplace(2*t-3*exp(-t), t, s) )
# poly
p = poly( [9, 1], s )
q = poly( [3, 7, 1], s )
f = p/q
disp( f )
# final/init value
# Не всегда применими, см. видеолекции Classical Control Theory by
# Brian Douglas
#
# https://en.wikipedia.org/wiki/Final_value_theorem
final_val = limit( s*f, s, 0 )
disp( final_val )
initial_val = limit( s*f, s, inf )
disp( initial_val )
f = (s+3)/((s+1)*(s+2)*(s+4))
A = pfss(f)
map( lambda v: disp( ilaplace(v, s, t) ), A )
def main():
# laplace
print laplace(exp(-t), t, s)
