Reduce (CSL, rev 6657), 10-Dec-2023 ...

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=====> submit number 0 done <=====

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5: 
 off nat;

7: write "=====> submit number ", 1, " done <=====" ;
=====> submit number 1 done <=====$


8: ;

9: solve({x+3y=7,y-x=1},{x,y});
{{x=1,y=2}}$


10: write "=====> submit number ", 2, " done <=====" ;
=====> submit number 2 done <=====$


11: ;

12: solve({x^7-x^6+x^2=1},{x});
{x=root_of(x_**6 + x_ + 1,x_,tag_1),x=1}$


13: write "=====> submit number ", 3, " done <=====" ;
=====> submit number 3 done <=====$


14: ;

15: solve({x^2=2x-1},{x});
{x=1}$


16: write "=====> submit number ", 4, " done <=====" ;
=====> submit number 4 done <=====$


17: ;

18: on multiplicities;

19: write "=====> submit number ", 5, " done <=====" ;
=====> submit number 5 done <=====$


20: ;

21: solve({x^2=2x-1},{x});
{x=1,x=1}$


22: write "=====> submit number ", 6, " done <=====" ;
=====> submit number 6 done <=====$


23: ;

24: solve({x=2*z,z=2*y},{z});
{}$


25: write "=====> submit number ", 7, " done <=====" ;
=====> submit number 7 done <=====$


26: ;

27: solve({x = a, x = b, y = c, y = d},{x, y});
{}$


28: write "=====> submit number ", 8, " done <=====" ;
=====> submit number 8 done <=====$


29: ;

30: solve({x2 = a, x2 = b, y2 = c, y2 = d},{x, y});
{}$


31: write "=====> submit number ", 9, " done <=====" ;
=====> submit number 9 done <=====$


32: ;

33: on rounded;

34: write "=====> submit number ", 10, " done <=====" ;
=====> submit number 10 done <=====$


35: ;

36: solve({x+y+z = 0, x^2 + y^2 + z^2 = 9, x^2 + y^2 = z^2},{x, y, z});
{{x=2.12132034356,y=0,z=-2.12132034356},
{x=-2.12132034356,y=0,z=2.12132034356},
{x=0,y=2.12132034356,z=-2.12132034356},
{x=0,y=-2.12132034356,z=2.12132034356}}$


37: write "=====> submit number ", 11, " done <=====" ;
=====> submit number 11 done <=====$


38: ;

39: off rounded;

40: write "=====> submit number ", 12, " done <=====" ;
=====> submit number 12 done <=====$


41: ;

42: solve({x+y+z = 0, x^2 + y^2 + z^2 = 9, x^2 + y^2 = z},{x, y, z});
{{x=(2*sqrt( - sqrt(37) - 7)*sqrt(3) + sqrt(74) + sqrt(2))/(4*sqrt(2)),
y=( - 2*sqrt( - sqrt(37) - 7)*sqrt(3) + sqrt(74) + sqrt(2))/(4*sqrt(2)),
z=( - (sqrt(37) + 1))/2},
{x=( - 2*sqrt( - sqrt(37) - 7)*sqrt(3) + sqrt(74) + sqrt(2))/(4*sqrt(2)),
y=(2*sqrt( - sqrt(37) - 7)*sqrt(3) + sqrt(74) + sqrt(2))/(4*sqrt(2)),
z=( - (sqrt(37) + 1))/2},
{x=(2*sqrt(sqrt(37) - 7)*sqrt(3) - sqrt(74) + sqrt(2))/(4*sqrt(2)),
y=( - 2*sqrt(sqrt(37) - 7)*sqrt(3) - sqrt(74) + sqrt(2))/(4*sqrt(2)),
z=(sqrt(37) - 1)/2},
{x=( - 2*sqrt(sqrt(37) - 7)*sqrt(3) - sqrt(74) + sqrt(2))/(4*sqrt(2)),
y=(2*sqrt(sqrt(37) - 7)*sqrt(3) - sqrt(74) + sqrt(2))/(4*sqrt(2)),
z=(sqrt(37) - 1)/2}}$


43: write "=====> submit number ", 13, " done <=====" ;
=====> submit number 13 done <=====$


44: 




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