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
2795222235
o3 = {{{- --------------------------------------------------,
93536104789177786765035829293842113257979682750464
------------------------------------------------------------------------
1189718579 9603838835
--------------------------------------------------}, {- ----------, -
46768052394588893382517914646921056628989841375232 4294967296
------------------------------------------------------------------------
4801919417 8902618511
----------}}, {{- --------------------------------------------------,
2147483648 46768052394588893382517914646921056628989841375232
------------------------------------------------------------------------
9574038757 4801919417
--------------------------------------------------}, {----------,
46768052394588893382517914646921056628989841375232 2147483648
------------------------------------------------------------------------
9603838835 8589934591 8589934593 9603838835 4801919417
----------}}, {{----------, ----------}, {- ----------, - ----------}},
4294967296 8589934592 8589934592 4294967296 2147483648
------------------------------------------------------------------------
8589934591 8589934593 4801919417 9603838835
{{----------, ----------}, {----------, ----------}}}
8589934592 8589934592 2147483648 4294967296
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
415785077 19207677669
o4 = {{- ---------------------------------------------------, - -----------},
187072209578355573530071658587684226515959365500928 8589934592
------------------------------------------------------------------------
335710123 19207677669
{--------------------------------------------------, -----------}, {1, -
46768052394588893382517914646921056628989841375232 8589934592
------------------------------------------------------------------------
19207677669 19207677669
-----------}, {1, -----------}}
8589934592 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[-2.98839e-41,2.54387e-41], [-2.23607,-2.23607]},
------------------------------------------------------------------------
{[-1.90357e-40,2.04713e-40], [2.23607,2.23607]}, {[1,1],
------------------------------------------------------------------------
[-2.23607,-2.23607]}, {[1,1], [2.23607,2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[-2.98869e-41,2.54476e-41], [-2.23633,-2.23535]},
------------------------------------------------------------------------
{[-1.90397e-40,2.04747e-40], [2.23535,2.23633]}, {[.999512,1.00049],
------------------------------------------------------------------------
[-2.23633,-2.23535]}, {[.999512,1.00049], [2.23535,2.23633]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{-2.22259e-42, -2.23607}, {7.17819e-42, 2.23607}, {1, -2.23607}, {1,
------------------------------------------------------------------------
2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{-2.21966e-42, -2.23584}, {7.17465e-42, 2.23584}, {1, -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 = {{[-2.98839e-41,2.54387e-41], [-2.23607,-2.23607]},
-----------------------------------------------------------------------
{[-1.90357e-40,2.04713e-40], [2.23607,2.23607]}, {[1,1],
-----------------------------------------------------------------------
[-2.23607,-2.23607]}, {[1,1], [2.23607,2.23607]}}
o10 : List
|