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
2296185875
o3 = {{{- -----------------------------------------------------,
95780971304118053647396689196894323976171195136475136
------------------------------------------------------------------------
10294793213 9603838835
------------------------------------------------------}, {- ----------,
383123885216472214589586756787577295904684780545900544 4294967296
------------------------------------------------------------------------
4801919417 8589934591 8589934593 9603838835
- ----------}}, {{----------, ----------}, {- ----------, -
2147483648 8589934592 8589934592 4294967296
------------------------------------------------------------------------
4801919417 5266333839
----------}}, {{- ---------------------------------------------------,
2147483648 187072209578355573530071658587684226515959365500928
------------------------------------------------------------------------
5829290567 4801919417
---------------------------------------------------}, {----------,
187072209578355573530071658587684226515959365500928 2147483648
------------------------------------------------------------------------
9603838835 8589934591 8589934593 4801919417 9603838835
----------}}, {{----------, ----------}, {----------, ----------}}}
4294967296 8589934592 8589934592 2147483648 4294967296
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
1110049713
o4 = {{------------------------------------------------------, -
766247770432944429179173513575154591809369561091801088
------------------------------------------------------------------------
19207677669 19207677669
-----------}, {1, - -----------},
8589934592 8589934592
------------------------------------------------------------------------
70369591 19207677669
{--------------------------------------------------, -----------}, {1,
46768052394588893382517914646921056628989841375232 8589934592
------------------------------------------------------------------------
19207677669
-----------}}
8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[-2.39733e-44,2.68707e-44], [-2.23607,-2.23607]}, {[1,1],
------------------------------------------------------------------------
[-2.23607,-2.23607]}, {[-2.81513e-41,3.11606e-41], [2.23607,2.23607]},
------------------------------------------------------------------------
{[1,1], [2.23607,2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[-2.39753e-44,2.68765e-44], [-2.23633,-2.23535]}, {[.999512,1.00049],
------------------------------------------------------------------------
[-2.23633,-2.23535]}, {[-2.81605e-41,3.11649e-41], [2.23535,2.23633]},
------------------------------------------------------------------------
{[.999512,1.00049], [2.23535,2.23633]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{1.44868e-45, -2.23607}, {1, -2.23607}, {1.50465e-42, 2.23607}, {1,
------------------------------------------------------------------------
2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{1.45056e-45, -2.23584}, {1, -2.23584}, {1.50219e-42, 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 = {{[-2.39733e-44,2.68707e-44], [-2.23607,-2.23607]}, {[1,1],
-----------------------------------------------------------------------
[-2.23607,-2.23607]}, {[-2.81513e-41,3.11606e-41], [2.23607,2.23607]},
-----------------------------------------------------------------------
{[1,1], [2.23607,2.23607]}}
o10 : List
|