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 4801919417 9603838835
o3 = {{{----------, ----------}, {----------, ----------}}, {{-
8589934592 8589934592 2147483648 4294967296
------------------------------------------------------------------------
317944045
------------------------------------------------------------------,
421249166674228746791672110734681729275580381602196445017243910144
------------------------------------------------------------------------
7036295741
-------------------------------------------------------------------},
6739986666787659948666753771754907668409286105635143120275902562304
------------------------------------------------------------------------
4801919417 9603838835 8589934591 8589934593 9603838835
{----------, ----------}}, {{----------, ----------}, {- ----------, -
2147483648 4294967296 8589934592 8589934592 4294967296
------------------------------------------------------------------------
4801919417 5296878921
----------}}, {{- --------------------------------------------------,
2147483648 93536104789177786765035829293842113257979682750464
------------------------------------------------------------------------
615866991 9603838835
-------------------------------------------------}, {- ----------, -
5846006549323611672814739330865132078623730171904 4294967296
------------------------------------------------------------------------
4801919417
----------}}}
2147483648
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
19207677669 1949191021
o4 = {{1, -----------}, {----------------------------------------------------
8589934592 1347997333357531989733350754350981533681857221127028
------------------------------------------------------------------------
19207677669 19207677669
----------------, -----------}, {1, - -----------},
6240551805124608 8589934592 8589934592
------------------------------------------------------------------------
4556992935 19207677669
{---------------------------------------------------, - -----------}}
187072209578355573530071658587684226515959365500928 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[1,1], [2.23607,2.23607]}, {[-7.54765e-58,1.04396e-57],
------------------------------------------------------------------------
[2.23607,2.23607]}, {[1,1], [-2.23607,-2.23607]},
------------------------------------------------------------------------
{[-5.66292e-41,1.05348e-40], [-2.23607,-2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[.999512,1.00049], [2.23535,2.23633]}, {[-7.54852e-58,1.04422e-57],
------------------------------------------------------------------------
[2.23535,2.23633]}, {[.999512,1.00049], [-2.23633,-2.23535]},
------------------------------------------------------------------------
{[-5.66349e-41,1.05378e-40], [-2.23633,-2.23535]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{1, 2.23607}, {1.44599e-58, 2.23607}, {1, -2.23607}, {2.43595e-41,
------------------------------------------------------------------------
-2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{1, 2.23584}, {1.44685e-58, 2.23584}, {1, -2.23584}, {2.43714e-41,
------------------------------------------------------------------------
-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]}, {[-7.54765e-58,1.04396e-57],
-----------------------------------------------------------------------
[2.23607,2.23607]}, {[1,1], [-2.23607,-2.23607]},
-----------------------------------------------------------------------
{[-5.66292e-41,1.05348e-40], [-2.23607,-2.23607]}}
o10 : List
|