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
6386010711
o3 = {{{- ---------------------------------------------------,
748288838313422294120286634350736906063837462003712
------------------------------------------------------------------------
7357884637 9603838835
---------------------------------------------------}, {- ----------, -
748288838313422294120286634350736906063837462003712 4294967296
------------------------------------------------------------------------
4801919417 8589934591 8589934593 9603838835 4801919417
----------}}, {{----------, ----------}, {- ----------, - ----------}},
2147483648 8589934592 8589934592 4294967296 2147483648
------------------------------------------------------------------------
2284884155
{{- -------------------------------------------------------------------,
3369993333393829974333376885877453834204643052817571560137951281152
------------------------------------------------------------------------
5237502109
-------------------------------------------------------------------},
6739986666787659948666753771754907668409286105635143120275902562304
------------------------------------------------------------------------
4801919417 9603838835 8589934591 8589934593 4801919417
{----------, ----------}}, {{----------, ----------}, {----------,
2147483648 4294967296 8589934592 8589934592 2147483648
------------------------------------------------------------------------
9603838835
----------}}}
4294967296
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
485936963 19207677669
o4 = {{---------------------------------------------------, - -----------},
748288838313422294120286634350736906063837462003712 8589934592
------------------------------------------------------------------------
19207677669 667733799
{1, - -----------}, {---------------------------------------------------
8589934592 134799733335753198973335075435098153368185722112702
------------------------------------------------------------------------
19207677669 19207677669
-----------------, -----------}, {1, -----------}}
86240551805124608 8589934592 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[-8.53415e-42,9.83295e-42], [-2.23607,-2.23607]}, {[1,1],
------------------------------------------------------------------------
[-2.23607,-2.23607]}, {[-6.78009e-58,7.77079e-58], [2.23607,2.23607]},
------------------------------------------------------------------------
{[1,1], [2.23607,2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[-8.53671e-42,9.83712e-42], [-2.23633,-2.23535]}, {[.999512,1.00049],
------------------------------------------------------------------------
[-2.23633,-2.23535]}, {[-6.78309e-58,7.77255e-58], [2.23535,2.23633]},
------------------------------------------------------------------------
{[.999512,1.00049], [2.23535,2.23633]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{6.49398e-43, -2.23607}, {1, -2.23607}, {4.95352e-59, 2.23607}, {1,
------------------------------------------------------------------------
2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{6.50202e-43, -2.23584}, {1, -2.23584}, {4.9473e-59, 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 = {{[-8.53415e-42,9.83295e-42], [-2.23607,-2.23607]}, {[1,1],
-----------------------------------------------------------------------
[-2.23607,-2.23607]}, {[-6.78009e-58,7.77079e-58], [2.23607,2.23607]},
-----------------------------------------------------------------------
{[1,1], [2.23607,2.23607]}}
o10 : List
|