def try_limit(term, x, to, directory=''):
try:
return sympy.Limit(term, x, to, directory).doit()
except sympy.SympifyError:
return 'Error'
except NotImplementedError:
return "Sorry, cannot solve..."
def noevaluate(self, expr, t, s):
t0 = sympify('t0')
return sym.Limit(sym.Integral(expr * sym.exp(-s * t), (t, t0, sym.oo)),
t0,
0,
dir='-')
def laplace_transform(expr, t, s, evaluate=True):
"""Compute unilateral Laplace transform of expr with lower limit 0-.
Undefined functions such as v(t) are converted to V(s)."""
if expr.is_Equality:
return sym.Eq(laplace_transform(expr.args[0], t, s),
laplace_transform(expr.args[1], t, s))
if not evaluate:
t0 = sympify('t0')
result = sym.Limit(sym.Integral(expr * sym.exp(-s * t),
(t, t0, sym.oo)),
t0,
0,
dir='-')
return result
const, expr = factor_const(expr, t)
key = (expr, t, s)
if key in laplace_cache:
return const * laplace_cache[key]
if expr.has(s):
raise ValueError(
'Cannot Laplace transform for expression %s that depends on %s' %
(expr, s))
# The variable may have been created with different attributes,
# say when using sympify('Heaviside(t)') since this will
# default to assuming that t is complex. So if the symbol has the
# same representation, convert to the desired one.
var = sym.Symbol(str(t))
if isinstance(expr, Expr):
expr = expr.expr
else:
expr = sympify(expr)
# SymPy laplace barfs on Piecewise but unilateral LT ignores expr
# for t < 0 so remove Piecewise.
expr = expr.replace(var, t)
if expr.is_Piecewise and expr.args[0].args[1].has(t >= 0):
expr = expr.args[0].args[0]
expr = sym.expand(expr)
terms = expr.as_ordered_terms()
result = 0
try:
for term in terms:
result += laplace_term(term, t, s)
except ValueError:
raise
result = result.simplify()
laplace_cache[key] = result
return const * result
def handle_limit(func):
sub = func.limit_sub()
if sub.LETTER():
var = sympy.Symbol(sub.LETTER().getText())
elif sub.SYMBOL():
var = sympy.Symbol(sub.SYMBOL().getText()[1:])
else:
var = sympy.Symbol('x')
if sub.SUB():
direction = "-"
else:
direction = "+"
approaching = convert_expr(sub.expr())
content = convert_mp(func.mp())
return sympy.Limit(content, var, approaching, direction)
def handle_limit(func):
sub = func.limit_sub()
if sub.LETTER_NO_E():
var = sympy.Symbol(sub.LETTER_NO_E().getText(), real=is_real)
elif sub.GREEK_CMD():
var = sympy.Symbol(sub.GREEK_CMD().getText()[1:].strip(), real=is_real)
else:
var = sympy.Symbol('x', real=is_real)
if sub.SUB():
direction = "-"
else:
direction = "+"
approaching = convert_expr(sub.expr())
content = convert_mp(func.mp())
return sympy.Limit(content, var, approaching, direction)
#!/usr/bin/env python
# coding: utf-8
# In[1]:
#!/usr/bin/env python
# coding: utf-8
# In[4]:
import sympy as sym
sym.init_printing()
x = sym.symbols('x')
sym.Limit(1 / x, x, sym.oo)
# In[2]:
# In[2]:
print("grup 1")
sym.Limit((x**2 - 1) / (x - 1), x, 1)
# In[3]:
print("jawaban")
sym.Limit((x**2 - 1) / (x - 1), x, 1).doit()
# In[ ]:
def format_limit(node, visitor):
if len(node.args) >= 3:
return sympy.latex(
sympy.Limit(
*[visitor.evaluator.eval_node(arg) for arg in node.args]))
def try_limit(term, x, to, directory=''):
try:
return sympy.Limit(term, x, to, directory).doit()
except sympy.SympifyError:
return 'Error'
sym1.series(x,x0,n)
sym1.removeO()
###########################################################
# 3.1 # 3.2
sym.solveset(f,x,domain=sym.S.Complexes)
sym.solveset(f<0,domain=sym.S.Reals)
sym.roots(f,x) # multiple roots not only once {0:1 , 3:2} 0 order 1 and 3 order 2
sym.solve(f)
sym.nsolve(f,x0)
#####
# 4.1
#use limit instead of subs when necessary
sym.limit(f,x,x0)
sym.limit(f,x,x0,'+') # or '-'
sym.Limit(f,x,x0)
#####
sym.singularities(f,x)
#####
is_monotonic
is_increasing
is_decreasing
is_strictly_increasing
is_strictly_decreasing
#####
# 4.2 #4.3
sym1.diff(x,y,z,z)
sym.diff(f,x,y,z,z)
sym1.diff( (x,n) ) # unspecified n is sym or int. float?
sym.Derivative(f,x,y,z) # unevaluated , later can be by:
_Mul(sympy.Pow(5, 3, evaluate=False), sympy.Pow(a, 2, evaluate=False))),
("a^{32}b^2", _Mul(a**32, b**2)),
("5^{38}b^3", _Mul(sympy.Pow(5, 38, evaluate=False), b**3)),
("6a^3b^4", _Mul(6, _Mul(a**3, b**4))),
("4a^{b^7}",
4 * sympy.Pow(a, sympy.Pow(b, 7, evaluate=False), evaluate=False)),
("\\frac{d}{d\\theta} x", sympy.Derivative(x, theta)),
("\\sin \\theta", sympy.sin(theta)), ("\\sin(\\theta)", sympy.sin(theta)),
("\\sin^{-1} a", sympy.asin(a)),
("\\sin a \\cos b", _Mul(sympy.sin(a), sympy.cos(b))),
("\\sin \\cos \\theta", sympy.sin(sympy.cos(theta))),
("\\sin(\\cos \\theta)", sympy.sin(sympy.cos(theta))),
("\\frac{a}{b}", a / b), ("\\frac{a + b}{c}", _Mul(a + b, _Pow(c, -1))),
("\\frac{7}{3}", _Mul(7, _Pow(3, -1))),
("(\\csc x)(\\sec y)", sympy.csc(x) * sympy.sec(y)),
("\\lim_{x \\to 3} a", sympy.Limit(a, x, 3)),
("\\lim_{x \\rightarrow 3} a", sympy.Limit(a, x, 3)),
("\\lim_{x \\Rightarrow 3} a", sympy.Limit(a, x, 3)),
("\\lim_{x \\longrightarrow 3} a", sympy.Limit(a, x, 3)),
("\\lim_{x \\Longrightarrow 3} a", sympy.Limit(a, x, 3)),
("\\lim_{x \\to 3^{+}} a", sympy.Limit(a, x, 3, dir='+')),
("\\lim_{x \\to 3^{-}} a", sympy.Limit(a, x, 3, dir='-')),
("\\infty", sympy.oo),
("\\lim_{x \\to \\infty} \\frac{1}{x}",
sympy.Limit(_Mul(1, _Pow(x, -1)), x, sympy.oo)),
("\\frac{d}{dx} x", sympy.Derivative(x, x)),
("\\frac{d}{dt} x", sympy.Derivative(x, t)), ("f(x)", f(x)),
("f(x, y)", f(x, y)), ("f(x, y, z)", f(x, y, z)),
("\\frac{d f(x)}{dx}", sympy.Derivative(f(x), x)),
("\\frac{d\\theta(x)}{dx}", sympy.Derivative(theta(x),
x)), ("|x|", _Abs(x)),