The second input is optional, and indicates the alternative ways to provide output either using an exact rational interval QQi, a real interval RRi, or by taking a rational or real approximation of the midpoint of the intervals.
i1 : R = QQ[x,y]
o1 = R
o1 : PolynomialRing
|
i2 : I = ideal {(x-1)*x, y^2-5}
2 2
o2 = ideal (x - x, y - 5)
o2 : Ideal of R
|
i3 : rationalIntervalSols = msolveRealSolutions I
1198219063
o3 = {{{- ----------------------------------------------------,
1496577676626844588240573268701473812127674924007424
------------------------------------------------------------------------
2808835777 4801919417
----------------------------------------------------}, {----------,
5986310706507378352962293074805895248510699696029696 2147483648
------------------------------------------------------------------------
9603838835 8589934591 8589934593 4801919417 9603838835
----------}}, {{----------, ----------}, {----------, ----------}}, {{-
4294967296 8589934592 8589934592 2147483648 4294967296
------------------------------------------------------------------------
6513514217
----------------------------------------------------,
1496577676626844588240573268701473812127674924007424
------------------------------------------------------------------------
1825522629 9603838835
---------------------------------------------------}, {- ----------, -
374144419156711147060143317175368453031918731001856 4294967296
------------------------------------------------------------------------
4801919417 8589934591 8589934593 9603838835 4801919417
----------}}, {{----------, ----------}, {- ----------, - ----------}}}
2147483648 8589934592 8589934592 4294967296 2147483648
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
1984040475 19207677669
o4 = {{- -----------------------------------------------------, -----------},
11972621413014756705924586149611790497021399392059392 8589934592
------------------------------------------------------------------------
19207677669 788576299
{1, -----------}, {----------------------------------------------------,
8589934592 2993155353253689176481146537402947624255349848014848
------------------------------------------------------------------------
19207677669 19207677669
- -----------}, {1, - -----------}}
8589934592 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[-8.00639e-43,4.6921e-43], [2.23607,2.23607]}, {[1,1],
------------------------------------------------------------------------
[2.23607,2.23607]}, {[-4.35227e-42,4.87919e-42], [-2.23607,-2.23607]},
------------------------------------------------------------------------
{[1,1], [-2.23607,-2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[-8.00842e-43,4.69435e-43], [2.23535,2.23633]}, {[.999512,1.00049],
------------------------------------------------------------------------
[2.23535,2.23633]}, {[-4.35243e-42,4.87932e-42], [-2.23633,-2.23535]},
------------------------------------------------------------------------
{[.999512,1.00049], [-2.23633,-2.23535]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{-1.65715e-43, 2.23607}, {1, 2.23607}, {2.6346e-43, -2.23607}, {1,
------------------------------------------------------------------------
-2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{-1.65704e-43, 2.23584}, {1, 2.23584}, {2.63444e-43, -2.23584}, {1,
------------------------------------------------------------------------
-2.23584}}
o8 : List
|
i9 : I = ideal {(x-1)*x^3, (y^2-5)^2}
4 3 4 2
o9 = ideal (x - x , y - 10y + 25)
o9 : Ideal of R
|
i10 : floatApproxSols = msolveRealSolutions(I, RRi)
o10 = {{[-8.00639e-43,4.6921e-43], [2.23607,2.23607]}, {[1,1],
-----------------------------------------------------------------------
[2.23607,2.23607]}, {[-4.35227e-42,4.87919e-42], [-2.23607,-2.23607]},
-----------------------------------------------------------------------
{[1,1], [-2.23607,-2.23607]}}
o10 : List
|