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
------------------------------------------------------------------------
16784049227
-------------------------------------------------,
2923003274661805836407369665432566039311865085952
------------------------------------------------------------------------
11360448879 9603838835
-------------------------------------------------}, {- ----------, -
2923003274661805836407369665432566039311865085952 4294967296
------------------------------------------------------------------------
4801919417 8589934591 8589934593 4801919417 9603838835
----------}}, {{----------, ----------}, {----------, ----------}}, {{-
2147483648 8589934592 8589934592 2147483648 4294967296
------------------------------------------------------------------------
7878213377
---------------------------------------------------,
374144419156711147060143317175368453031918731001856
------------------------------------------------------------------------
9979808539 4801919417
---------------------------------------------------}, {----------,
374144419156711147060143317175368453031918731001856 2147483648
------------------------------------------------------------------------
9603838835
----------}}}
4294967296
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
19207677669 2327763537
o4 = {{1, -----------}, {----------------------------------------------------
8589934592 1347997333357531989733350754350981533681857221127028
------------------------------------------------------------------------
19207677669 19207677669
----------------, -----------}, {1, - -----------},
6240551805124608 8589934592 8589934592
------------------------------------------------------------------------
2875659845 19207677669
{-------------------------------------------------, - -----------}}
5846006549323611672814739330865132078623730171904 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[1,1], [2.23607,2.23607]}, {[-7.47884e-40,6.24894e-40],
------------------------------------------------------------------------
[2.23607,2.23607]}, {[1,1], [-2.23607,-2.23607]},
------------------------------------------------------------------------
{[-3.36221e-40,5.39147e-40], [-2.23607,-2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[.999512,1.00049], [-2.23633,-2.23535]}, {[-1.05231e-57,9.50877e-58],
------------------------------------------------------------------------
[-2.23633,-2.23535]}, {[.999512,1.00049], [2.23535,2.23633]},
------------------------------------------------------------------------
{[-2.36333e-39,7.48675e-40], [2.23535,2.23633]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{4.36134e-40, -2.23607}, {1, -2.23607}, {-5.8035e-40, 2.23607}, {1,
------------------------------------------------------------------------
2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{4.36129e-40, -2.23584}, {1, -2.23584}, {-5.79712e-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 = {{[-3.25047e-41,3.42848e-41], [-2.23607,-2.23607]}, {[1,1],
-----------------------------------------------------------------------
[-2.23607,-2.23607]}, {[-1.25974e-44,1.01052e-44], [2.23607,2.23607]},
-----------------------------------------------------------------------
{[1,1], [2.23607,2.23607]}}
o10 : List
|