Suppose given polynomials e,q,h,r in R[x], p in R (R a ring), how can I use Sage to find f in R[x] so f*e = q*h + r (mod p)?

Similarly, given f,g in R[x] (gcd(f,g)=1), what function can I use to compute s,t in R[x] so s*f + g*h = 1 (mod p) ?

1 | initial version |

Suppose given polynomials e,q,h,r in R[x], p in R (R a ring), how can I use Sage to find f in R[x] so f*e = q*h + r (mod p)?

Similarly, given f,g in R[x] (gcd(f,g)=1), what function can I use to compute s,t in R[x] so s*f + g*h = 1 (mod p) ?

2 | No.2 Revision |

Suppose given polynomials ~~e,q,h,r ~~$e,q,h,r$ in ~~R[x], p in R ~~$R[x]$, $p \in R$ (R a ring), how can I use Sage to find ~~f ~~$f$ in ~~R[x] ~~$R[x]$ so ~~f~~$f*e = q*h + r ~~(mod p)?~~(\text{mod} p)$?

Similarly, given ~~f,g ~~$f,g$ in ~~R[x] (gcd(f,g)=1), ~~$R[x]$ with $\text{gcd}(f,g)=1$, what function can I use to compute ~~s,t ~~$s,t$ in ~~R[x] ~~$R[x]$ so ~~s~~$s*f + g*h = 1 ~~(mod p) ~~(\text{mod} p)$ ?

3 | No.3 Revision |

Suppose given polynomials $e,q,h,r$ in $R[x]$, $p \in R$ (R a ring), how can I use Sage to find $f$ in $R[x]$ so ~~$f~~*$f e = q*q h + r

Similarly, given $f,g$ in $R[x]$ with $\text{gcd}(f,g)=1$, what function can I use to compute $s,t$ in $R[x]$ so ~~$s~~*$s f + g*g h = 1

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.