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
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i3 : rationalIntervalSols = msolveRealSolutions I
8589934591 8589934593 9603838835 4801919417
o3 = {{{----------, ----------}, {- ----------, - ----------}}, {{-
8589934592 8589934592 4294967296 2147483648
------------------------------------------------------------------------
2704575355
-------------------------------------------------------------------,
3369993333393829974333376885877453834204643052817571560137951281152
------------------------------------------------------------------------
3149266357
-------------------------------------------------------------------}, {-
3369993333393829974333376885877453834204643052817571560137951281152
------------------------------------------------------------------------
9603838835 4801919417 8589934591 8589934593 4801919417
----------, - ----------}}, {{----------, ----------}, {----------,
4294967296 2147483648 8589934592 8589934592 2147483648
------------------------------------------------------------------------
9603838835 1734104385
----------}}, {{- -----------------------------------------------------,
4294967296 47890485652059026823698344598447161988085597568237568
------------------------------------------------------------------------
10873247245 4801919417
-----------------------------------------------------}, {----------,
95780971304118053647396689196894323976171195136475136 2147483648
------------------------------------------------------------------------
9603838835
----------}}}
4294967296
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
19207677669 441211623
o4 = {{1, -----------}, {- --------------------------------------------------
8589934592 13479973333575319897333507543509815336818572211270
------------------------------------------------------------------------
19207677669 19207677669
------------------, -----------}, {1, - -----------},
286240551805124608 8589934592 8589934592
------------------------------------------------------------------------
3406373727
{-----------------------------------------------------------, -
12554203470773361527671578846415332832204710888928069025792
------------------------------------------------------------------------
19207677669
-----------}}
8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[1,1], [-2.23607,-2.23607]}, {[-9.74921e-58,1.45125e-57],
------------------------------------------------------------------------
[-2.23607,-2.23607]}, {[1,1], [2.23607,2.23607]},
------------------------------------------------------------------------
{[-5.07182e-40,5.85425e-40], [2.23607,2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[.999512,1.00049], [2.23535,2.23633]}, {[-7.60513e-39,7.96673e-39],
------------------------------------------------------------------------
[2.23535,2.23633]}, {[.999512,1.00049], [-2.23633,-2.23535]},
------------------------------------------------------------------------
{[-2.31069e-40,5.35408e-41], [-2.23633,-2.23535]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{1, -2.23607}, {-1.116e-58, -2.23607}, {1, 2.23607}, {-9.91327e-42,
------------------------------------------------------------------------
2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{7.85428e-43, 2.23584}, {1, 2.23584}, {2.67745e-58, -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 = {{[1,1], [2.23607,2.23607]}, {[-1.83932e-41,1.58489e-41],
-----------------------------------------------------------------------
[2.23607,2.23607]}, {[1,1], [-2.23607,-2.23607]},
-----------------------------------------------------------------------
{[-1.05639e-40,2.21871e-40], [-2.23607,-2.23607]}}
o10 : List
|