Revision history [back]

Solution via ideals machinery

R.<x, y, z> = QQbar[]
eq1 = x + y + z - 2
eq2 = x^2 + 2*y + 3*z - 4
eq3 = x + y + z^2 - 10
show(ideal([eq1,eq2,eq3]).variety())

It gives

$$\displaystyle \left[\verb|{z:|\verb| |\verb|-2.372281323269015?,|\verb| |\verb|y:|\verb| |\verb|1.535904095336525?,|\verb| |\verb|x:|\verb| |\verb|2.836377227932490?}|, \verb|{z:|\verb| |\verb|-2.372281323269015?,|\verb| |\verb|y:|\verb| |\verb|5.208658551201504?,|\verb| |\verb|x:|\verb| |\verb|-0.8363772279324894?}|, \verb|{z:|\verb| |\verb|3.372281323269015?,|\verb| |\verb|y:|\verb| |\verb|-2.372281323269015?|\verb| |\verb|-|\verb| |\verb|1.540221192968405?I,|\verb| |\verb|x:|\verb| |\verb|1.000000000000000?|\verb| |\verb|+|\verb| |\verb|1.540221192968405?I}|, \verb|{z:|\verb| |\verb|3.372281323269015?,|\verb| |\verb|y:|\verb| |\verb|-2.372281323269015?|\verb| |\verb|+|\verb| |\verb|1.540221192968405?I,|\verb| |\verb|x:|\verb| |\verb|1.000000000000000?|\verb| |\verb|-|\verb| |\verb|1.540221192968405?I}|\right]$$

Solution via ideals machinery

R.<x, y, z> = QQbar[]
eq1 = x + y + z - 2
eq2 = x^2 + 2*y + 3*z - 4
eq3 = x + y + z^2 - 10
show(ideal([eq1,eq2,eq3]).variety())
V = ideal([eq1,eq2,eq3]).variety()
for p in V:
    show( {v:e.radical_expression() for v,e in p.items()} )

It givesResults can be seen at Sagecell.