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
8589934591 8589934593 9603838835 4801919417
o3 = {{{----------, ----------}, {- ----------, - ----------}}, {{-
8589934592 8589934592 4294967296 2147483648
------------------------------------------------------------------------
1508080353
----------------------------------------------------,
2993155353253689176481146537402947624255349848014848
------------------------------------------------------------------------
16471737921 9603838835
-----------------------------------------------------}, {- ----------, -
47890485652059026823698344598447161988085597568237568 4294967296
------------------------------------------------------------------------
4801919417 8589934591 8589934593 4801919417 9603838835
----------}}, {{----------, ----------}, {----------, ----------}}, {{-
2147483648 8589934592 8589934592 2147483648 4294967296
------------------------------------------------------------------------
3396933269
-------------------------------------------------------,
3064991081731777716716694054300618367237478244367204352
------------------------------------------------------------------------
11693166607 4801919417
-------------------------------------------------------}, {----------,
6129982163463555433433388108601236734474956488734408704 2147483648
------------------------------------------------------------------------
9603838835
----------}}}
4294967296
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
19207677669
o4 = {{1, - -----------}, {-
8589934592
------------------------------------------------------------------------
7657547727 19207677669
-----------------------------------------------------, - -----------},
95780971304118053647396689196894323976171195136475136 8589934592
------------------------------------------------------------------------
19207677669 4899300069
{1, -----------}, {-----------------------------------------------------
8589934592 12259964326927110866866776217202473468949912977468817
------------------------------------------------------------------------
19207677669
---, -----------}}
408 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[1,1], [-2.23607,-2.23607]}, {[-5.03843e-43,3.43946e-43],
------------------------------------------------------------------------
[-2.23607,-2.23607]}, {[1,1], [2.23607,2.23607]},
------------------------------------------------------------------------
{[-1.1083e-45,1.90754e-45], [2.23607,2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[.999512,1.00049], [-2.23633,-2.23535]}, {[-5.03854e-43,3.44019e-43],
------------------------------------------------------------------------
[-2.23633,-2.23535]}, {[.999512,1.00049], [2.23535,2.23633]},
------------------------------------------------------------------------
{[-1.10845e-45,1.90763e-45], [2.23535,2.23633]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{1, -2.23607}, {-7.99485e-44, -2.23607}, {1, 2.23607}, {3.99618e-46,
------------------------------------------------------------------------
2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{1, -2.23584}, {-7.99178e-44, -2.23584}, {1, 2.23584}, {3.99589e-46,
------------------------------------------------------------------------
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]}, {[-5.03843e-43,3.43946e-43],
-----------------------------------------------------------------------
[-2.23607,-2.23607]}, {[1,1], [2.23607,2.23607]},
-----------------------------------------------------------------------
{[-1.1083e-45,1.90754e-45], [2.23607,2.23607]}}
o10 : List
|