** suivant:** Rational fractions
** monter:** Gröbner basis and Gröbner
** précédent:** Gröbner reduction : greduce
** Table des matières**
** Index**

##

Build a polynomial from it's evaluation : `genpoly`

`genpoly` takes three arguments : a polynomial *P* with *n* - 1
variables, an integer *b* and the name of a variable `var`.

`genpoly` returns the polynomial *Q* with *n* variables (the *P* variables
and the variable `var` given as second argument), such that :
`subst(Q,var=b)==P`
- the coefficients of
*Q* belongs to the interval
] - *b*/2 ; *b*/2]

In other words, *P* is written in base *b* but using the convention
that the euclidean remainder belongs to
] - *b*/2 ; *b*/2]
(this convention is also known as s-mod representation).
Input :
`genpoly(61,6,x) `

Output :
`2*x``^`

2-2*x+1

Indeed 61 divided by 6 is 10, remains 1, then 10 divided by 6 is 2
remains -2 (instead of the usual quotient 1 and remainder 4 out of bounds),

61 = 2*6^{2} - 2*6 + 1

Input :
`genpoly(5,6,x) `

Output :
`x-1`

Indeed : 5 = 6 - 1

Input :
`genpoly(7,6,x) `

Output :
`x+1`

Indeed : 7 = 6 + 1

Input :
`genpoly(7*y+5,6,x) `

Output :
`x*y+x+y-1`

Indeed :
*x***y* + *x* + *y* - 1 = *y*(*x* + 1) + (*x* - 1)

Input :
`genpoly(7*y+5*z``^2`

,6,x)

Output :
`x*y+x*z+y-z`

Indeed :
*x***y* + *x***z* + *y* - *z* = *y**(*x* + 1) + *z**(*x* - 1)

** suivant:** Rational fractions
** monter:** Gröbner basis and Gröbner
** précédent:** Gröbner reduction : greduce
** Table des matières**
** Index**
giac documentation written by Renée De Graeve and Bernard Parisse