grave wraith
i wrote this thing in np and it works for d(k)*2 but not for d(k)*3 for that i get 0
output:
$\displaystyle - \frac{\max\left(0, - k + x\right)}{k^{2}} + \frac{\max\left(0, - k + x, \min\left(k, x\right)\right)}{k^{2}}$
$\displaystyle \frac{- \max\left(0, - k + x\right) + \max\left(0, - k + x, \min\left(k, x\right)\right)}{k^{2}}$
$\displaystyle 0$
code:
import sympy as sp
from typing import Callable
Dist = Callable[[sp.Symbol], sp.Expr]
sp.init_printing()
input, k = sp.symbols('x k', real=True)
d1, d2 = sp.symbols('d1 d2', cls=sp.Function)
def d(y: sp.Symbol) -> Dist:
return lambda x: sp.Piecewise(
(1/y, (0 < x) & (x < y)),
(0, True),
)
def SUM(dist1: Dist, dist2: Dist) -> Dist:
t = sp.symbols('t', real=True)
return lambda x: sp.integrate(dist1(t) * dist2(x-t), (t, -sp.oo, sp.oo)).doit()
dsum = SUM(d(k), d(k))(input)
print(dsum._repr_latex_())
dsum_simplified = sp.simplify(
dsum
.doit())
print(dsum_simplified._repr_latex_())
def MULT(dist1: Dist, n: int) -> Dist:
dist_res = dist1
for _ in range(n-1):
dist_res = SUM(dist_res, dist1)
return dist_res
dmult = MULT(d(k), 3)(input)
dmult = sp.simplify(dmult.doit())
print(dmult._repr_latex_())
grim patrol
