def latex(self):
r"""
Print a LaTeX representation of a linear multistep formula.
**Example**::
>>> from nodepy import lm
>>> print(lm.Adams_Bashforth(2).latex())
\begin{align} y_{n + 2} - y_{n + 1} = \frac{3}{2}h f(y_{n + 1}) - \frac{1}{2}h f(y_{n})\end{align}
"""
from sympy import symbols, latex
n = symbols('n')
from nodepy.snp import printable
k = len(self)
alpha_terms = []
beta_terms = []
for i in range(k+1):
subscript = latex(n+k-i)
if self.alpha[k-i] != 0:
alpha_terms.append(printable(self.alpha[k-i],return_one=False)
+ ' y_{'+subscript+'}')
if self.beta[k-i] != 0:
beta_terms.append(printable(self.beta[k-i],return_one=False)
+ 'h f(y_{'+subscript+'})')
lhs = ' + '.join(alpha_terms)
rhs = ' + '.join(beta_terms)
s = r'\begin{align}'+ ' = '.join([lhs,rhs]) + r'\end{align}'
s = s.replace('+ -','-')
return s
def latex(self):
r"""
Print a LaTeX representation of a linear multistep formula.
**Example**::
>>> from nodepy import lm
>>> print(lm.Adams_Bashforth(2).latex())
\begin{align} y_{n + 2} - y_{n + 1} = \frac{3}{2}h f(y_{n + 1}) - \frac{1}{2}h f(y_{n})\end{align}
"""
from sympy import symbols, latex
n = symbols('n')
from nodepy.snp import printable
k = len(self)
alpha_terms = []
beta_terms = []
for i in range(k + 1):
subscript = latex(n + k - i)
if self.alpha[k - i] != 0:
alpha_terms.append(
printable(self.alpha[k - i], return_one=False) + ' y_{' +
subscript + '}')
if self.beta[k - i] != 0:
beta_terms.append(
printable(self.beta[k - i], return_one=False) + 'h f(y_{' +
subscript + '})')
lhs = ' + '.join(alpha_terms)
rhs = ' + '.join(beta_terms)
s = r'\begin{align}' + ' = '.join([lhs, rhs]) + r'\end{align}'
s = s.replace('+ -', '-')
return s