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
8589934591 8589934593 9603838835 4801919417
o3 = {{{----------, ----------}, {- ----------, - ----------}}, {{-
8589934592 8589934592 4294967296 2147483648
------------------------------------------------------------------------
442534401
-------------------------------------------------,
1461501637330902918203684832716283019655932542976
------------------------------------------------------------------------
5099045269 9603838835
--------------------------------------------------}, {- ----------, -
23384026197294446691258957323460528314494920687616 4294967296
------------------------------------------------------------------------
4801919417 8589934591 8589934593 4801919417 9603838835
----------}}, {{----------, ----------}, {----------, ----------}}, {{-
2147483648 8589934592 8589934592 2147483648 4294967296
------------------------------------------------------------------------
3152700129
--------------------------------------------------,
23384026197294446691258957323460528314494920687616
------------------------------------------------------------------------
2933365597 4801919417
--------------------------------------------------}, {----------,
11692013098647223345629478661730264157247460343808 2147483648
------------------------------------------------------------------------
9603838835
----------}}}
4294967296
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
19207677669
o4 = {{1, - -----------}, {-
8589934592
------------------------------------------------------------------------
1981505147 19207677669
--------------------------------------------------, - -----------}, {1,
46768052394588893382517914646921056628989841375232 8589934592
------------------------------------------------------------------------
19207677669 2714031065
-----------}, {--------------------------------------------------,
8589934592 46768052394588893382517914646921056628989841375232
------------------------------------------------------------------------
19207677669
-----------}}
8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[1,1], [-2.23607,-2.23607]}, {[-3.02794e-40,2.18057e-40],
------------------------------------------------------------------------
[-2.23607,-2.23607]}, {[1,1], [2.23607,2.23607]},
------------------------------------------------------------------------
{[-1.34823e-40,2.50886e-40], [2.23607,2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[.999512,1.00049], [-2.23633,-2.23535]}, {[-3.0286e-40,2.18109e-40],
------------------------------------------------------------------------
[-2.23633,-2.23535]}, {[.999512,1.00049], [2.23535,2.23633]},
------------------------------------------------------------------------
{[-1.34883e-40,2.50933e-40], [2.23535,2.23633]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{1, -2.23607}, {-4.23688e-41, -2.23607}, {1, 2.23607}, {5.80317e-41,
------------------------------------------------------------------------
2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{1, -2.23584}, {-4.23753e-41, -2.23584}, {1, 2.23584}, {5.8025e-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]}, {[-3.02794e-40,2.18057e-40],
-----------------------------------------------------------------------
[-2.23607,-2.23607]}, {[1,1], [2.23607,2.23607]},
-----------------------------------------------------------------------
{[-1.34823e-40,2.50886e-40], [2.23607,2.23607]}}
o10 : List
|