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 9603838835 4801919417
o3 = {{{----------, ----------}, {- ----------, - ----------}}, {{-
8589934592 8589934592 4294967296 2147483648
------------------------------------------------------------------------
17289631723
--------------------------------------------------------------------,
13479973333575319897333507543509815336818572211270286240551805124608
------------------------------------------------------------------------
14871302675
--------------------------------------------------------------------},
13479973333575319897333507543509815336818572211270286240551805124608
------------------------------------------------------------------------
9603838835 4801919417 8589934591 8589934593 4801919417
{- ----------, - ----------}}, {{----------, ----------}, {----------,
4294967296 2147483648 8589934592 8589934592 2147483648
------------------------------------------------------------------------
9603838835 4782210831
----------}}, {{- ---------------------------------------------------,
4294967296 187072209578355573530071658587684226515959365500928
------------------------------------------------------------------------
3782910073 4801919417
--------------------------------------------------}, {----------,
93536104789177786765035829293842113257979682750464 2147483648
------------------------------------------------------------------------
9603838835
----------}}}
4294967296
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
19207677669
o4 = {{1, - -----------}, {-
8589934592
------------------------------------------------------------------------
302291131
-------------------------------------------------------------------, -
3369993333393829974333376885877453834204643052817571560137951281152
------------------------------------------------------------------------
19207677669 19207677669
-----------}, {1, -----------},
8589934592 8589934592
------------------------------------------------------------------------
2783609315 19207677669
{---------------------------------------------------, -----------}}
374144419156711147060143317175368453031918731001856 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[1,1], [-2.23607,-2.23607]}, {[-1.28262e-57,1.10321e-57],
------------------------------------------------------------------------
[-2.23607,-2.23607]}, {[1,1], [2.23607,2.23607]},
------------------------------------------------------------------------
{[-2.55634e-41,4.04433e-41], [2.23607,2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[.999512,1.00049], [-2.23633,-2.23535]}, {[-1.28287e-57,1.10334e-57],
------------------------------------------------------------------------
[-2.23633,-2.23535]}, {[.999512,1.00049], [2.23535,2.23633]},
------------------------------------------------------------------------
{[-2.55821e-41,4.04471e-41], [2.23535,2.23633]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{1, -2.23607}, {-8.97008e-59, -2.23607}, {1, 2.23607}, {7.43993e-42,
------------------------------------------------------------------------
2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{1, -2.23584}, {-8.9767e-59, -2.23584}, {1, 2.23584}, {7.43249e-42,
------------------------------------------------------------------------
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]}, {[-1.28262e-57,1.10321e-57],
-----------------------------------------------------------------------
[-2.23607,-2.23607]}, {[1,1], [2.23607,2.23607]},
-----------------------------------------------------------------------
{[-2.55634e-41,4.04433e-41], [2.23607,2.23607]}}
o10 : List
|