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
10807333717
o3 = {{{- --------------------------------------------------,
11692013098647223345629478661730264157247460343808
------------------------------------------------------------------------
3740617515 9603838835
-------------------------------------------------}, {- ----------, -
2923003274661805836407369665432566039311865085952 4294967296
------------------------------------------------------------------------
4801919417 8589934591 8589934593 9603838835 4801919417
----------}}, {{----------, ----------}, {- ----------, - ----------}},
2147483648 8589934592 8589934592 4294967296 2147483648
------------------------------------------------------------------------
4421104533
{{- -------------------------------------------------,
1461501637330902918203684832716283019655932542976
------------------------------------------------------------------------
4718512383 4801919417
-------------------------------------------------}, {----------,
2923003274661805836407369665432566039311865085952 2147483648
------------------------------------------------------------------------
9603838835 8589934591 8589934593 4801919417 9603838835
----------}}, {{----------, ----------}, {----------, ----------}}}
4294967296 8589934592 8589934592 2147483648 4294967296
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
4155136343 19207677669
o4 = {{--------------------------------------------------, - -----------},
23384026197294446691258957323460528314494920687616 8589934592
------------------------------------------------------------------------
19207677669 4123696683
{1, - -----------}, {- -------------------------------------------------
8589934592 5846006549323611672814739330865132078623730171904
------------------------------------------------------------------------
19207677669 19207677669
, -----------}, {1, -----------}}
8589934592 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[-9.24335e-40,1.27972e-39], [-2.23607,-2.23607]}, {[1,1],
------------------------------------------------------------------------
[-2.23607,-2.23607]}, {[-3.02504e-39,1.61427e-39], [2.23607,2.23607]},
------------------------------------------------------------------------
{[1,1], [2.23607,2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[-9.24453e-40,1.27996e-39], [-2.23633,-2.23535]}, {[.999512,1.00049],
------------------------------------------------------------------------
[-2.23633,-2.23535]}, {[-3.02627e-39,1.6143e-39], [2.23535,2.23633]},
------------------------------------------------------------------------
{[.999512,1.00049], [2.23535,2.23633]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{1.77691e-40, -2.23607}, {1, -2.23607}, {-7.05387e-40, 2.23607}, {1,
------------------------------------------------------------------------
2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{1.77752e-40, -2.23584}, {1, -2.23584}, {-7.05985e-40, 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 = {{[-9.24335e-40,1.27972e-39], [-2.23607,-2.23607]}, {[1,1],
-----------------------------------------------------------------------
[-2.23607,-2.23607]}, {[-3.02504e-39,1.61427e-39], [2.23607,2.23607]},
-----------------------------------------------------------------------
{[1,1], [2.23607,2.23607]}}
o10 : List
|