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all partial derivation

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Didictateur 2026-02-15 01:07:00 +01:00
parent 073de786f5
commit 431570ce73
3 changed files with 143 additions and 31 deletions
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1
.gitignore vendored Normal file
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@ -0,0 +1 @@
__pycache__

22
example.py
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@ -1,7 +1,21 @@
from legrandchien import * import legrandchien as lgc
if __name__ == "__main__": if __name__ == "__main__":
k = Const(3) g = lgc.Const(-10)
kk = Const(4) m = lgc.Const(1)
eq = k + kk x = lgc.Var("x")
T = 0.5 * m * x.diff() * x.diff()
V = m * g * x
L = T - V
dL = L.diff()
dico = {
"x" : 0,
"d_x" : 1,
"d_d_x" : 1,
}
print(dL.evaluate(dico))

151
legrandchien.py
View file

@ -20,13 +20,20 @@ class Const:
self.value = value self.value = value
self.type = "Const" self.type = "Const"
def evaluate(self, dico):
return self.value
def copy(self):
return Const(self.value)
def __add__(self, other): def __add__(self, other):
if other.type == "Const": if other.type == "Const":
return Equation( return Equation(
Operation.CONST, Operation.CONST,
None, None,
None, None,
self.value self.copy()
) + Equation( ) + Equation(
Operation.CONST, Operation.CONST,
None, None,
@ -38,7 +45,7 @@ class Const:
Operation.CONST, Operation.CONST,
None, None,
None, None,
self.value self.copy()
) + Equation( ) + Equation(
Operation.VAR, Operation.VAR,
None, None,
@ -50,16 +57,20 @@ class Const:
Operation.CONST, Operation.CONST,
None, None,
None, None,
self.value self.copy()
) + other ) + other
def __radd__(self, other):
if isinstance(other, (int, float)):
return Const(other) + self
def __sub__(self, other): def __sub__(self, other):
if other.type == "Const": if other.type == "Const":
return Equation( return Equation(
Operation.CONST, Operation.CONST,
None, None,
None, None,
self.value self.copy()
) - Equation( ) - Equation(
Operation.CONST, Operation.CONST,
None, None,
@ -71,7 +82,7 @@ class Const:
Operation.CONST, Operation.CONST,
None, None,
None, None,
self.value self.copy()
) - Equation( ) - Equation(
Operation.VAR, Operation.VAR,
None, None,
@ -83,16 +94,20 @@ class Const:
Operation.CONST, Operation.CONST,
None, None,
None, None,
self.value self.copy()
) - other ) - other
def __rsub__(self, other):
if isinstance(other, (int, float)):
return Const(other) - self
def __mul__(self, other): def __mul__(self, other):
if other.type == "Const": if other.type == "Const":
return Equation( return Equation(
Operation.CONST, Operation.CONST,
None, None,
None, None,
self.value self.copy()
) * Equation( ) * Equation(
Operation.CONST, Operation.CONST,
None, None,
@ -104,7 +119,7 @@ class Const:
Operation.CONST, Operation.CONST,
None, None,
None, None,
self.value self.copy()
) * Equation( ) * Equation(
Operation.VAR, Operation.VAR,
None, None,
@ -116,16 +131,20 @@ class Const:
Operation.CONST, Operation.CONST,
None, None,
None, None,
self.value self.copy()
) * other ) * other
def __rmul__(self, other):
if isinstance(other, (int, float)):
return Const(other) * self
def __truediv__(self, other): def __truediv__(self, other):
if other.type == "Const": if other.type == "Const":
return Equation( return Equation(
Operation.CONST, Operation.CONST,
None, None,
None, None,
self.value self.copy()
) / Equation( ) / Equation(
Operation.CONST, Operation.CONST,
None, None,
@ -137,7 +156,7 @@ class Const:
Operation.CONST, Operation.CONST,
None, None,
None, None,
self.value self.copy()
) / Equation( ) / Equation(
Operation.VAR, Operation.VAR,
None, None,
@ -149,8 +168,12 @@ class Const:
Operation.CONST, Operation.CONST,
None, None,
None, None,
self.value self.copy()
) / other ) / other
def __truediv__(self, other):
if isinstance(other, (int, float)):
return Const(other) / self
# var class # var class
class Var: class Var:
@ -159,13 +182,22 @@ class Var:
self.type = "Var" self.type = "Var"
self.degree = degree self.degree = degree
def copy(self):
return Var(self.name, self.degree)
def diff(self, n=1):
return Var("d_"+self.name, self.degree+n)
def evaluate(self, dico):
return dico[self.name]
def __add__(self, other): def __add__(self, other):
if other.type == "Const": if other.type == "Const":
return Equation( return Equation(
Operation.VAR, Operation.VAR,
None, None,
None, None,
self.name self.copy()
) + Equation( ) + Equation(
Operation.CONST, Operation.CONST,
None, None,
@ -177,7 +209,7 @@ class Var:
Operation.VAR, Operation.VAR,
None, None,
None, None,
self.name self.copy()
) + Equation( ) + Equation(
Operation.VAR, Operation.VAR,
None, None,
@ -189,16 +221,20 @@ class Var:
Operation.VAR, Operation.VAR,
None, None,
None, None,
self.name self.copy()
) + other ) + other
def __radd__(self, other):
if isinstance(other, (int, float)):
return Const(other) + self
def __sub__(self, other): def __sub__(self, other):
if other.type == "Const": if other.type == "Const":
return Equation( return Equation(
Operation.VAR, Operation.VAR,
None, None,
None, None,
self.name self.copy()
) - Equation( ) - Equation(
Operation.CONST, Operation.CONST,
None, None,
@ -210,7 +246,7 @@ class Var:
Operation.VAR, Operation.VAR,
None, None,
None, None,
self.name self.copy()
) - Equation( ) - Equation(
Operation.VAR, Operation.VAR,
None, None,
@ -222,16 +258,20 @@ class Var:
Operation.VAR, Operation.VAR,
None, None,
None, None,
self.name self.copy()
) - other ) - other
def __rsub__(self, other):
if isinstance(other, (int, float)):
return Const(other) - self
def __mul__(self, other): def __mul__(self, other):
if other.type == "Const": if other.type == "Const":
return Equation( return Equation(
Operation.VAR, Operation.VAR,
None, None,
None, None,
self.name self.copy()
) * Equation( ) * Equation(
Operation.CONST, Operation.CONST,
None, None,
@ -243,7 +283,7 @@ class Var:
Operation.VAR, Operation.VAR,
None, None,
None, None,
self.name self.copy()
) * Equation( ) * Equation(
Operation.VAR, Operation.VAR,
None, None,
@ -255,16 +295,20 @@ class Var:
Operation.VAR, Operation.VAR,
None, None,
None, None,
self.name self.copy()
) * other ) * other
def __rmul__(self, other):
if isinstance(other, (int, float)):
return Const(other) * self
def __truediv__(self, other): def __truediv__(self, other):
if other.type == "Const": if other.type == "Const":
return Equation( return Equation(
Operation.VAR, Operation.VAR,
None, None,
None, None,
self.name self.copy()
) / Equation( ) / Equation(
Operation.CONST, Operation.CONST,
None, None,
@ -276,7 +320,7 @@ class Var:
Operation.VAR, Operation.VAR,
None, None,
None, None,
self.name self.copy()
) / Equation( ) / Equation(
Operation.VAR, Operation.VAR,
None, None,
@ -288,8 +332,12 @@ class Var:
Operation.VAR, Operation.VAR,
None, None,
None, None,
self.name self.copy()
) / other ) / other
def __rtruediv__(self, other):
if isinstance(other, (int, float)):
return Const(other) / self
# equation class # equation class
class Equation: class Equation:
@ -305,13 +353,13 @@ class Equation:
return Const(self.value.value) return Const(self.value.value)
if self.op == Operation.VAR: if self.op == Operation.VAR:
return Var(self.value.name, self.value.degree) return Var(self.value.name, self.value.degree)
return Operation(self.op, self.left.copy(), self.right.copy(), None) return Equation(self.op, self.left.copy(), self.right.copy(), None)
def diff(self): def diff(self):
if self.op == Operation.CONST: if self.op == Operation.CONST:
return Const(0) return Equation(Operation.CONST, None, None, Const(0))
if self.op == Operation.VAR: if self.op == Operation.VAR:
return Var(self.value.name, self.value.degree+1) return Equation(Operation.VAR, None, None, Var("d_"+self.value.name, self.value.degree+1))
if self.op == Operation.ADD: if self.op == Operation.ADD:
return self.left.diff() + self.right.diff() return self.left.diff() + self.right.diff()
if self.op == Operation.SUB: if self.op == Operation.SUB:
@ -322,6 +370,39 @@ class Equation:
return (self.left.diff()*self.right.copy() - self.left.copy()*self.right.diff()) \ return (self.left.diff()*self.right.copy() - self.left.copy()*self.right.diff()) \
/ (self.right.copy()*self.right.copy()) / (self.right.copy()*self.right.copy())
def partial(self, var_name):
if self.op == Operation.CONST:
return Equation(Operation.CONST, None, None, Const(0))
if self.op == Operation.VAR:
if self.value.name == var_name:
return Equation(Operation.CONST, None, None, Const(1))
else:
return Equation(Operation.CONST, None, None, Const(0))
if self.op == Operation.ADD:
return self.left.partial(var_name) + self.right.partial(var_name)
if self.op == Operation.SUB:
return self.left.partial(var_name) - self.right.partial(var_name)
if self.op == Operation.MULT:
return self.left.partial(var_name)*self.right.copy() + self.left.copy()*self.right.partial(var_name)
if self.op == Operation.DIV:
return (self.left.partial(var_name)*self.right.copy() - self.left.copy()*self.right.partial(var_name)) \
/ (self.right.copy()*self.right.copy())
def evaluate(self, dico):
if self.op == Operation.CONST:
return self.value.value
if self.op == Operation.VAR:
return dico[self.value.name]
if self.op == Operation.ADD:
return self.left.evaluate(dico) + self.right.evaluate(dico)
if self.op == Operation.SUB:
return self.left.evaluate(dico) - self.right.evaluate(dico)
if self.op == Operation.MULT:
return self.left.evaluate(dico) * self.right.evaluate(dico)
if self.op == Operation.DIV:
return self.left.evaluate(dico) / self.right.evaluate(dico)
def __add__(self, other): def __add__(self, other):
if other.type == "Const": if other.type == "Const":
return self + Equation( return self + Equation(
@ -340,6 +421,10 @@ class Equation:
if other.type == "Equation": if other.type == "Equation":
return Equation(Operation.ADD, self, other, None) return Equation(Operation.ADD, self, other, None)
def __radd__(self, other):
if isinstance(other, (int, float)):
return Const(other) + self
def __sub__(self, other): def __sub__(self, other):
if other.type == "Const": if other.type == "Const":
return self - Equation( return self - Equation(
@ -358,6 +443,10 @@ class Equation:
if other.type == "Equation": if other.type == "Equation":
return Equation(Operation.SUB, self, other, None) return Equation(Operation.SUB, self, other, None)
def __rsub__(self, other):
if isinstance(other, (int, float)):
return Const(other) - self
def __mul__(self, other): def __mul__(self, other):
if other.type == "Const": if other.type == "Const":
return self * Equation( return self * Equation(
@ -376,6 +465,10 @@ class Equation:
if other.type == "Equation": if other.type == "Equation":
return Equation(Operation.MULT, self, other, None) return Equation(Operation.MULT, self, other, None)
def __rmul__(self, other):
if isinstance(other, (int, float)):
return Const(other) * self
def __truediv__(self, other): def __truediv__(self, other):
if other.type == "Const": if other.type == "Const":
return self / Equation( return self / Equation(
@ -393,3 +486,7 @@ class Equation:
) )
if other.type == "Equation": if other.type == "Equation":
return Equation(Operation.DIV, self, other, None) return Equation(Operation.DIV, self, other, None)
def __rtruediv__(self, other):
if isinstance(other, (int, float)):
return Const(other) / self