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2.56-2.57 derivation.py
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2.56-2.57 derivation.py
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from orderedPair import *
from symbolic import *
def number(e):
if isinstance(e, (int, float)):
return True
elif isinstance(e, str):
if e.isdigit():
return True
else:
return False
else:
return False
def variable(e):
if symt(e):
if e.isdigit():
return False
else:
return True
else:
pass
def _make_sum(a1, a2):
if a1 is '0':
return a2
elif a2 is '0':
return a1
elif symt(a1) and symt(a2):
try:
return str(int(a1) + int(a2))
except ValueError:
return lister(a1, '+', a2)
else:
return lister(a1, '+', a2)
def same_variable(v1, v2):
if symt(v1) and symt(v2) and eq(v1, v2):
return True
else:
return False
def sum_formula(f):
if memq('+', f):
return True
else:
return False
def addend(f):
return car(f)
def augend(f):
return car(cdr(cdr(f)))
def _make_product(m1, m2):
if m1 is '0' or m2 is '0':
return '0'
elif m1 is '1':
return m2
elif m2 is '1':
return m1
elif symt(m1) and symt(m2):
try:
return str(int(m1) * int(m2))
except ValueError:
return lister(m1, '*', m2)
else:
return lister(m1, '*', m2)
def product_formula(f):
if memq('*', f):
return True
else:
return False
def multiplier(f):
return car(f)
def multiplicand(f):
return car(cdr(cdr(f)))
def deriv(exp, var):
if number(exp):
return '0'
elif variable(exp):
if same_variable(exp, var):
return '1'
else:
return '0'
elif sum_formula(exp):
return make_sum(deriv(addend(exp), var),
deriv(augend(exp), var))
elif product_formula(exp):
return make_sum(
make_product(multiplier(exp),
deriv(multiplicand(exp), var)),
make_product(multiplicand(exp),
deriv(multiplier(exp), var)))
elif exponentiation(exp):
return make_product(exponent(exp),
make_product(
make_exponentiation(
base(exp),
make_sum(exponent(exp), '-1')),
deriv(base(exp), var)))
else:
return print('error, unknown expression type--Deriv')
# 2.56
def make_exponentiation(b, e):
if e is '0':
return '1'
elif e is '1':
return b
elif symt(b) and symt(e):
try:
return str(int(b) ** int(e))
except ValueError:
return lister(b, '**', e)
else:
return lister(b, '**', e)
def exponentiation(f):
if memq('**', f):
return True
else:
return False
def base(f):
return car(f)
def exponent(f):
return car(cdr(cdr(f)))
# 2.57
def make_sum(*args):
exp = lister(*args)
def _sum(first, other):
if other is None:
return first
elif first is '0':
return _sum(other, cdr(other))
elif car(other) is '0':
return _sum(first, cdr(other))
elif symt(first) and symt(car(other)):
try:
return _sum(str(int(first) + int(car(other))), cdr(other))
except ValueError:
return lister(first, '+', _sum(car(other), cdr(other)))
else:
return lister(first, '+', _sum(car(other), cdr(other)))
return _sum(car(exp), cdr(exp))
def make_product(*args):
exp = lister(*args)
def _mul(first, other):
if other is None:
return first
elif symt(first) and symt(car(other)):
try:
return _mul(str(int(first) * int(car(other))), cdr(other))
except ValueError:
return lister(first, '*', _mul(car(other), cdr(other)))
else:
return lister(first, '*', _mul(car(other), cdr(other)))
if memq('0', exp):
return '0'
elif memq('1', exp):
def picker(s):
if s is None:
return None
elif eq(car(s), '1'):
return picker(cdr(s))
else:
return cons(car(s), picker(cdr(s)))
exp = picker(exp)
return _mul(car(exp), cdr(exp))
else:
return _mul(car(exp), cdr(exp))
# 2.58 a, b
# 使用新版make_sum和make_product之后程序基本上能正确表示
if __name__ == '__main__':
exp1 = make_sum('x', '3')
exp2 = make_product('x', 'y')
exp3 = make_product(exp2, exp1)
exp4 = make_exponentiation('x', '3')
exp5 = make_sum('1', '0', 'y', '4', 'x')
exp6 = make_product('1', '0', '-3', '4', 'x')
display(exp1)
display(exp2)
display(exp3)
display(exp4)
display(exp5)
display(exp6)
display(deriv(exp1, 'x'))
display(deriv(exp2, 'x'))
display(deriv(exp3, 'x'))
display(deriv(exp4, 'x'))
display(make_sum(exp1, exp2, exp4))
display(deriv(exp3, 'x'))
display(deriv(make_product('x', 'y', exp1), 'x'))
display(deriv(exp5, 'x'))