#1716 resultant & algebraic : true --> quotient not exact

[Barton Willis]

I should look for a smaller example... With algebraic = false, OK:

(%i1) resultant(658952*x^3+((-1776*sqrt(37)-9647)*((1776*sqrt(37)-9647)^(1/3))^2+82369*(1776*sqrt(37)-9647)^(1/3)+4036081)*x^2+
((-7104*sqrt(37)-38588)*((1776*sqrt(37)-9647)^(1/3))^2+329476*(1776*sqrt(37)-9647)^(1/3)+6260044)*x+(-7104*sqrt(37)-38588)*((1776*sqrt(37)-9647)^(1/3))^2+329476*
(1776*sqrt(37)-9647)^(1/3)+5601092,((1776*sqrt(37)+9647)*((1776*sqrt(37)-9647)^(1/3))^2-82369*(1776*sqrt(37)-9647)^(1/3)-4036081)*x^2+
((14208*sqrt(37)+77176)*((1776*sqrt(37)-9647)^(1/3))^2-658952*(1776*sqrt(37)-9647)^(1/3)-12520088)*x+(21312*sqrt(37)+115764)*((1776*sqrt(37)-9647)^(1/3))^2-988428*
(1776*sqrt(37)-9647)^(1/3)-16803276,x);
(%o1) -63259392*((1776*sqrt(37)-9647)^(4/3)*(149550664320828645840*sqrt(37)+996465692476197624289)+(1776*sqrt(37)-9647)^(5/3)*(7886642286489394848*sqrt(37)+51019025130868750039)+(1776*sqrt(37)-9647)^2*(410349627024955632*sqrt(37)+2552620562180128391)+(1776*sqrt(37)-9647)^(8/3)*(14375957813878848*sqrt(37)+87447323236375873)+(-231659666025286464*sqrt(37)-1408621778456986940)*(1776*sqrt(37)-9647)^(7/3)+(-1709100058195259761248*sqrt(37)-8501072671220284640149)*(1776*sqrt(37)-9647)+(-33676814212905551079504*sqrt(37)-143294929822723634925032)*(1776*sqrt(37)-9647)^(2/3)+1561894994314649401389451*(1776*sqrt(37)-9647)^(1/3)+15098241559200034610148158)

Simplify to zero

(%i2) ratsimp(expand(%));
(%o2) 0

With algebraic : true, error:

(%i3) resultant(658952*x^3+((-1776*sqrt(37)-9647)*((1776*sqrt(37)-9647)^(1/3))^2+82369*(1776*sqrt(37)-9647)^(1/3)+4036081)*x^2+
((-7104*sqrt(37)-38588)*((1776*sqrt(37)-9647)^(1/3))^2+329476*(1776*sqrt(37)-9647)^(1/3)+6260044)*x+(-7104*sqrt(37)-38588)*((1776*sqrt(37)-9647)^(1/3))^2+329476*
(1776*sqrt(37)-9647)^(1/3)+5601092,((1776*sqrt(37)+9647)*((1776*sqrt(37)-9647)^(1/3))^2-82369*(1776*sqrt(37)-9647)^(1/3)-4036081)*x^2+
((14208*sqrt(37)+77176)*((1776*sqrt(37)-9647)^(1/3))^2-658952*(1776*sqrt(37)-9647)^(1/3)-12520088)*x+(21312*sqrt(37)+115764)*((1776*sqrt(37)-9647)^(1/3))^2-988428*
(1776*sqrt(37)-9647)^(1/3)-16803276,x), algebraic : true;
quotient is not exact
-- an error. To debug this try debugmode(true);