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 4801919417 9603838835
o3 = {{{----------, ----------}, {----------, ----------}}, {{-
8589934592 8589934592 2147483648 4294967296
------------------------------------------------------------------------
1954906941
------------------------------------------------,
182687704666362864775460604089535377456991567872
------------------------------------------------------------------------
9650665747 4801919417
------------------------------------------------}, {----------,
730750818665451459101842416358141509827966271488 2147483648
------------------------------------------------------------------------
9603838835 8589934591 8589934593 9603838835 4801919417
----------}}, {{----------, ----------}, {- ----------, - ----------}},
4294967296 8589934592 8589934592 4294967296 2147483648
------------------------------------------------------------------------
1831481139
{{- ----------------------------------------------------,
1496577676626844588240573268701473812127674924007424
------------------------------------------------------------------------
8013980059 9603838835
----------------------------------------------------}, {- ----------, -
2993155353253689176481146537402947624255349848014848 4294967296
------------------------------------------------------------------------
4801919417
----------}}}
2147483648
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
19207677669 1831037983
o4 = {{1, -----------}, {-------------------------------------------------,
8589934592 1461501637330902918203684832716283019655932542976
------------------------------------------------------------------------
19207677669 19207677669
-----------}, {1, - -----------},
8589934592 8589934592
------------------------------------------------------------------------
4351017781 19207677669
{----------------------------------------------------, - -----------}}
5986310706507378352962293074805895248510699696029696 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[1,1], [2.23607,2.23607]}, {[-2.76171e-57,3.27268e-57],
------------------------------------------------------------------------
[2.23607,2.23607]}, {[1,1], [-2.23607,-2.23607]},
------------------------------------------------------------------------
{[-3.83127e-40,9.34251e-41], [-2.23607,-2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[.999512,1.00049], [2.23535,2.23633]}, {[-2.76177e-57,3.27331e-57],
------------------------------------------------------------------------
[2.23535,2.23633]}, {[.999512,1.00049], [-2.23633,-2.23535]},
------------------------------------------------------------------------
{[-3.83171e-40,9.34498e-41], [-2.23633,-2.23535]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{1, 2.23607}, {2.55487e-58, 2.23607}, {1, -2.23607}, {-1.44851e-40,
------------------------------------------------------------------------
-2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{1, 2.23584}, {2.55766e-58, 2.23584}, {1, -2.23584}, {-1.44861e-40,
------------------------------------------------------------------------
-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 = {{[1,1], [2.23607,2.23607]}, {[-2.76171e-57,3.27268e-57],
-----------------------------------------------------------------------
[2.23607,2.23607]}, {[1,1], [-2.23607,-2.23607]},
-----------------------------------------------------------------------
{[-3.83127e-40,9.34251e-41], [-2.23607,-2.23607]}}
o10 : List
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