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Fix conversion from symbolic expressions with nonintegral exponents to power series ring #39809

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Fix conversion from symbolic expressions with nonintegral exponents to power series ring #39809

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694550e
fix issue #39736 with enhancement tackling conversion from symbolic e…
TinaJin0228 Mar 28, 2025
b12e871
modified with more test examples
TinaJin0228 Mar 29, 2025
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24 changes: 24 additions & 0 deletions src/sage/rings/power_series_ring.py
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Original file line number Diff line number Diff line change
Expand Up @@ -820,6 +820,20 @@ def _element_constructor_(self, f, prec=infinity, check=True):
sage: R(ex)
1 + euler_gamma*y + (1/2*euler_gamma^2 + 1/12*pi^2)*y^2 + O(y^3)

Conversion from general symbolic expressions (see :issue:`39736`)::

sage: # Conversion from non-polynomial symbolic expressions, e.g. sqrt(1+x)
sage: R.<x> = PowerSeriesRing(QQ, default_prec=7)
sage: f = R(sqrt(1+x))
sage: f
1 + 1/2*x - 1/8*x^2 + 1/16*x^3 - 5/128*x^4 + 7/256*x^5 - 21/1024*x^6 + O(x^7)
sage: g = R(sin(x))
sage: g
x - 1/6*x^3 + 1/120*x^5 + O(x^7)
sage: t = R(e^x)
sage: t
1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + O(x^7)

Laurent series with nonnegative valuation are accepted (see
:issue:`6431`)::

Expand Down Expand Up @@ -878,6 +892,16 @@ def _element_constructor_(self, f, prec=infinity, check=True):
check=check)
else:
raise TypeError("Can only convert series into ring with same variable name.")
else:
from sage.symbolic.ring import SR
sym_var = SR.var(self.variable_name())
if f.is_polynomial(sym_var):
poly_ring = self._poly_ring()
return self.element_class(self, poly_ring(f), prec, check=check)
func = f.function(sym_var) # test for exception
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what does this comment mean here (I thought we're not testing for exception here…?)

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my fault, I forget to delete it after the testing...

L = LazyPowerSeriesRing(self.base_ring(), self.variable_name())
series_lazy = L.taylor(func)
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There's another way to get the Taylor expansion

sage: (1/(x+1)).series(x, 10)
1 + (-1)*x + 1*x^2 + (-1)*x^3 + 1*x^4 + (-1)*x^5 + 1*x^6 + (-1)*x^7 + 1*x^8 + (-1)*x^9 + Order(x^10)

Are they equivalent, if not is there any significant difference (e.g. which one is faster?)

return self(series_lazy, prec=prec, check=check)
else:
from sage.rings.lazy_series import LazyPowerSeries
if isinstance(f, LazyPowerSeries):
Expand Down