i want to just modify my code so that it performs multivariate polynomial division, the main problem is in ig in while loop, its infinite: from sympy import symbols, degree, LC$,$ expand

def fun$($f$,$ g$,$ var $=$ symbols$(\text{'}$x y$\text{'}),$ Order$=$'lex'$)$:

$$ x$,$ y $=$ var

$$ r $=$ f

$$ q $=0$

$$ while degree$($r$,$ gen$=$x$)>=$ degree$($g$,$ gen$=$x$)$ and degree$($r$,$ gen$=$y$)>=$ degree$($g$,$ gen$=$y$)$:

$$ LT$\_$r$\_$xy $=$ LC$($r$,$ x$,$ y$)$

$$ LT$\_$g$\_$xy $=$ LC$($g$,$ x$,$ y$)$

$$ TempQ $=$ LT$\_$r$\_$xy $/$ LT$\_$g$\_$xy $*$ x$**($degree$($r$,$ gen$=$x$)-$ degree$($g$,$ gen$=$x$))*$ y$**($degree$($r$,$ gen$=$y$)-$ degree$($g$,$ gen$=$y$))$

$$ q $+=$ TempQ

$$ r $=($r $-$ TempQ $*$ g$).$expand$()$

$$ return q$,$ r

x$,$ y $=$ symbols$(\text{'}$x y$\text{'})$

f $=$ x$**2+$ y$**2+3*$x$*$y $-1$

g $=$ x $+$ y

quotient, remainder $=$ fun$($f$,$ g$,($x$,$ y$))$

print$($f$"$Quotient: $\{$quotient$\}")$

print$($f$"$Remainder: $\{$remainder$\}")$