Hello,
I am quite new to Sage. I have a science background but am a stranger to
rings, fields and other advanced mathematical topics which seem central in
working with Sage. Having struggled with the issue below for quite a while
though, I decided to post it.
I have a power series f in x1 and x2 and want to substitute x1 and x2 with
a power series in y to finally obtain a power series in y. The code below
is an example of the idea and seems to work fine:
c= var('c')
R.<x1,x2>=PowerSeriesRing(SR)
Y.<y>=PowerSeriesRing(SR)
f=x1*x2+R.O(3)
g1=y
g2=c*y
r=f.substitute(x1=g1,x2=g2);r
c*y^2 + O(y^3)
The issue is that at first instance I obtain f as a symbolic expression f_symb,
not as a power series. So the
idea is to convert the symbolic expression to a power series first and then
carry out the same substitution as
above
f_symb(x1,x2)=x1*x2
P.<x1,x2>=PolynomialRing(QQ)
f_poly = P(f_symb)
f2 = R(f_poly)+R.O(3)
It appears that f2 is exactly the same as f:
f;type(f);f2;type(f2)
x1*x2 + O(x1, x2)^3
<class 'sage.rings.multi_power_series_ring_element.MPowerSeries'>
x1*x2 + O(x1, x2)^3
<class 'sage.rings.multi_power_series_ring_element.MPowerSeries'>
However, if I now try to carry out the substitution, an error appears:
r=f2.substitute(x1=g1,x2=g2)
Traceback (click to the left of this block for traceback)
...
AttributeError: 'sage.symbolic.expression.Expression' object has no
attribute 'add_bigoh'
It turns out that the error is due to the part "+R.O(3)" in the definition
of f2. Leaving out this part, there is no error. But then Sage does not
know anymore till what order it should expand.
My apologies if this is a basic question, which it seems to be. But as I
said, I have been stuck with this for quite a while.
Thanks for any help provided!
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