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
------------------------------------------------------------------------
6509393705
--------------------------------------------------,
11692013098647223345629478661730264157247460343808
------------------------------------------------------------------------
1144627437 4801919417
-------------------------------------------------}, {----------,
1461501637330902918203684832716283019655932542976 2147483648
------------------------------------------------------------------------
9603838835 8589934591 8589934593 9603838835 4801919417
----------}}, {{----------, ----------}, {- ----------, - ----------}},
4294967296 8589934592 8589934592 4294967296 2147483648
------------------------------------------------------------------------
3125430191
{{- --------------------------------------------------,
23384026197294446691258957323460528314494920687616
------------------------------------------------------------------------
6204544777 9603838835
--------------------------------------------------}, {- ----------, -
46768052394588893382517914646921056628989841375232 4294967296
------------------------------------------------------------------------
4801919417
----------}}}
2147483648
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
19207677669 122086863
o4 = {{1, - -----------}, {--------------------------------------------------
8589934592 18707220957835557353007165858768422651595936550092
------------------------------------------------------------------------
19207677669 19207677669
-, - -----------}, {1, -----------},
8 8589934592 8589934592
------------------------------------------------------------------------
2989030409 19207677669
{--------------------------------------------------, -----------}}
23384026197294446691258957323460528314494920687616 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[-1.3685e-58,8.4798e-59], [2.23607,2.23607]}, {[1,1],
------------------------------------------------------------------------
[2.23607,2.23607]}, {[-1.40299e-58,1.7592e-58], [-2.23607,-2.23607]},
------------------------------------------------------------------------
{[1,1], [-2.23607,-2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[.999512,1.00049], [2.23535,2.23633]}, {[.999512,1.00049],
------------------------------------------------------------------------
[-2.23633,-2.23535]}, {[-6.42215e-58,8.24238e-58], [2.23535,2.23633]},
------------------------------------------------------------------------
{[-3.62376e-42,9.27099e-42], [-2.23633,-2.23535]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{3.47491e-40, -2.23607}, {1, -2.23607}, {6.98069e-41, 2.23607}, {1,
------------------------------------------------------------------------
2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{1, 2.23584}, {-4.37906e-47, 2.23584}, {1, -2.23584}, {-1.9194e-44,
------------------------------------------------------------------------
-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 = {{[-5.40736e-42,8.74172e-42], [-2.23607,-2.23607]}, {[1,1],
-----------------------------------------------------------------------
[-2.23607,-2.23607]}, {[-4.4274e-42,4.90009e-42], [2.23607,2.23607]},
-----------------------------------------------------------------------
{[1,1], [2.23607,2.23607]}}
o10 : List
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