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
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i2 : I = ideal {(x-1)*x, y^2-5}
2 2
o2 = ideal (x - x, y - 5)
o2 : Ideal of R
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i3 : rationalIntervalSols = msolveRealSolutions I
8589934591 8589934593 9603838835 4801919417 8589934591
o3 = {{{----------, ----------}, {- ----------, - ----------}}, {{----------,
8589934592 8589934592 4294967296 2147483648 8589934592
------------------------------------------------------------------------
8589934593 4801919417 9603838835
----------}, {----------, ----------}}, {{-
8589934592 2147483648 4294967296
------------------------------------------------------------------------
3694478609
----------------------------------------------------,
1496577676626844588240573268701473812127674924007424
------------------------------------------------------------------------
39285932913 9603838835
----------------------------------------------------}, {- ----------, -
2993155353253689176481146537402947624255349848014848 4294967296
------------------------------------------------------------------------
4801919417 12346786025
----------}}, {{- ----------------------------------------------------,
2147483648 5986310706507378352962293074805895248510699696029696
------------------------------------------------------------------------
6645529979 4801919417
-----------------------------------------------------}, {----------,
11972621413014756705924586149611790497021399392059392 2147483648
------------------------------------------------------------------------
9603838835
----------}}}
4294967296
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
19207677669 19207677669
o4 = {{1, - -----------}, {1, -----------},
8589934592 8589934592
------------------------------------------------------------------------
31896975695 19207677669
{----------------------------------------------------, - -----------},
5986310706507378352962293074805895248510699696029696 8589934592
------------------------------------------------------------------------
18048042071 19207677669
{- -----------------------------------------------------, -----------}}
23945242826029513411849172299223580994042798784118784 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[1,1], [2.23607,2.23607]}, {[-1.1424e-41,1.12702e-41],
------------------------------------------------------------------------
[2.23607,2.23607]}, {[1,1], [-2.23607,-2.23607]},
------------------------------------------------------------------------
{[-1.9607e-40,1.58153e-40], [-2.23607,-2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[-6.37276e-59,8.18132e-59], [2.23535,2.23633]}, {[.999512,1.00049],
------------------------------------------------------------------------
[2.23535,2.23633]}, {[-9.77636e-58,9.17272e-58], [-2.23633,-2.23535]},
------------------------------------------------------------------------
{[.999512,1.00049], [-2.23633,-2.23535]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{1, -2.23607}, {-1.43368e-40, -2.23607}, {1, 2.23607}, {-5.93459e-42,
------------------------------------------------------------------------
2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{1, 2.23584}, {-2.68212e-58, 2.23584}, {1, -2.23584}, {5.84186e-59,
------------------------------------------------------------------------
-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 = {{[-1.77739e-39,8.46482e-40], [2.23607,2.23607]}, {[1,1],
-----------------------------------------------------------------------
[2.23607,2.23607]}, {[-1.05389e-57,7.711e-58], [-2.23607,-2.23607]},
-----------------------------------------------------------------------
{[1,1], [-2.23607,-2.23607]}}
o10 : List
|