On 11/01/2012 10:26 AM, Jason Grout wrote:
>
> Here's a conversation about this:
>
> https://groups.google.com/forum/?fromgroups=#!searchin/sage-support/Is$20there$20an$20efficient$20method$20of$20producing$20indexed$20variables?/sage-support/qj8q21wr7-0/Qs-Qxr8A0dAJ
>
> In particular, this is a nice solution:
>
> class SymbolicVariables(SageObject):
> def __init__(self, prefix='x'):
> self._prefix = prefix
> def __getitem__(self, i):
> return var("%s%s"%(self._prefix, i))
>
>
> a = SymbolicVariables('a')
> sum(a[i]*x^i for i in range(3))
>
> would give a2*x^2 + a1*x + a0
>
I need to do this a lot. We already have SR.symbol(), does anyone think
it would make sense to have this available as SR.symbols()?
Here's my first shot at it. I could clean it up and add more examples.
class SymbolCollection:
"""
An indexed collection of symbolic variables.
INPUT:
- ``prefix`` -- The string with which to prefix the symbol
names.
- ``latex_prefix`` -- An optional latex expression (string) to
use instead of `prefix` when converting the symbols to latex.
- ``domain`` -- A string representing the domain of the symbol,
either 'real', 'complex', or 'positive'.
OUTPUT:
An object which supports indexing. Each index references a
particular symbolic variable.
EXAMPLES:
Create coefficients for polynomials of arbitrary degree::
sage: a = SymbolCollection('a')
sage: p = sum([ a[i]*x^i for i in range(0,5)])
sage: p
a4*x^4 + a3*x^3 + a2*x^2 + a1*x + a0
Using a different latex name since 'lambda' is reserved::
sage: l = SymbolCollection('l', '\lambda')
sage: l[0]
l0
sage: latex(l[0])
$\lambda_{0}$
TESTS:
We shouldn't overwrite variables in the global namespace::
sage: a = SymbolCollection('a')
sage: a0 = 4
sage: a[0]
a0
sage: a0
4
The symbol at a given index should always be the same, even when
the symbols themselves are unnamed. We store the string
representation and compare because the output is unpredictable::
sage: a = SymbolCollection()
sage: a0str = str(a[0])
sage: str(a[0]) == a0str
True
"""
def __init__(self, prefix=None, latex_prefix=None, domain=None):
# We store a dict of already-created symbols so that we don't
# recreate a symbol which already exists. This is especially
# helpful when using unnamed variables, if you want e.g. a[0]
# to return the same variable each time.
self._symbols = {}
self._prefix = prefix
if latex_prefix is None:
# Note: this can set the latex_prefix to None, so we check
# this condition later.
self._latex_prefix = prefix
else:
# Strip latex math-mode delimiters, since we'll add them
# ourselves later.
self._latex_prefix = latex_prefix.strip('$')
self._domain = domain
def create_symbol(self, i):
if self._prefix is None:
# Allow creating unnamed symbols, for consistency with
# SR.symbol().
name = None
else:
name = '%s%d' % (self._prefix, i)
if self._latex_prefix is None:
latex_name = None
else:
latex_name = r'$%s_{%d}$' % (self._latex_prefix, i)
return SR.symbol(name, latex_name, self._domain)
def __getitem__(self, i):
if i < 0:
# Cowardly refuse to create a variable named "a-1".
raise IndexError('Index must be nonnegative')
try:
return self._symbols[i]
except KeyError:
self._symbols[i] = self.create_symbol(i)
return self._symbols[i]
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