tangent() doesn't work when non-integers are involved

[niccolo]

There's a problem creating tangents to ellipses and parabolas (but there's no problem with circles) when we use non-integer numbers.

For example, the following code works:

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el := ellipse(-1,1,point(1+i));
A := point(-3+3*i);
tn := tangent(el, A);

But the following code doesn't work:

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el := ellipse(-1,1,point(1+i));
A := point(-3.1+3*i);
tn := tangent(el, A);

I simply changed the "-3" to "-3.1". When I do this, the tangent() fails and prints:

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Warning! Algebraic extension not implemented yet for poly [100,-1185520711848600,5832385641982111064112389540,-3790135019015975345440561800,-2729701128580087121698805869] 

I have the same problem with parabolas. The following code works:

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A := point(-3+3*i);
B := point(5+i);
C := point(4-i);
prb := parabola(B,C);
tn := tangent(prb,A);

BUT, when I change the "B := point(5+i)" to "B := point(5.1+i)", I get a message telling me "Computing..." and it doesn't return (I can stop it).

The output of my "dpkg -l giac":

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||/ Name                                Version                Architecture           Description
+++-===================================-======================-======================-============================
ii  giac                                1.1.0-44               i386                   computer algebra system by Bernard Parisse

[parisse]

Indeed, the reason is that it is using the trigonometric parametric equation instead of the rational one. I'll fix that for the next release.

[niccolo]

I'll fix that for the next release.

Thank you!