### `uinv_as_power_series`, `ureverse_inv_as_power_series`

uinv_as_power_series(p,d)
ureverse_inv_as_power_series(p,d)
:: Computes the truncated inverse as a power series.
return
univariate polynomial
p
univariate polynomial
d
non-negative integer
• For a polynomial p with a non zero constant term, `uinv_as_power_series(p,d)` computes a polynomial r whose degree is at most d such that p*r = 1 mod x^(d+1), where x is the variable of p.
• Let e be the degree of p. `ureverse_inv_as_power_series(p,d)` computes `uinv_as_power_series(p1,d)` for p1=`ureverse(p,e)`.
• The output of `ureverse_inv_as_power_series()` can be used as the input of `rembymul_precomp()`.
```[123] A=(x+1)^5;
x^5+5*x^4+10*x^3+10*x^2+5*x+1
[124] uinv_as_power_series(A,5);
-126*x^5+70*x^4-35*x^3+15*x^2-5*x+1
[126] A*R;
-126*x^10-560*x^9-945*x^8-720*x^7-210*x^6+1
[127] A=x^10+x^9;
x^10+x^9
[128] R=ureverse_inv_as_power_series(A,5);
-x^5+x^4-x^3+x^2-x+1
[129] ureverse(A)*R;
-x^6+1
```
References
section `utrunc`, `udecomp`, `ureverse`, section `udiv`, `urem`, `urembymul`, `urembymul_precomp`, `ugcd`.