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
3719580123
o3 = {{{- -------------------------------------------------,
2923003274661805836407369665432566039311865085952
------------------------------------------------------------------------
11832722507 4801919417
-------------------------------------------------}, {----------,
2923003274661805836407369665432566039311865085952 2147483648
------------------------------------------------------------------------
9603838835 8589934591 8589934593 4801919417 9603838835
----------}}, {{----------, ----------}, {----------, ----------}}, {{-
4294967296 8589934592 8589934592 2147483648 4294967296
------------------------------------------------------------------------
11810530867
-------------------------------------------------,
1461501637330902918203684832716283019655932542976
------------------------------------------------------------------------
11881524399 9603838835
-------------------------------------------------}, {- ----------, -
1461501637330902918203684832716283019655932542976 4294967296
------------------------------------------------------------------------
4801919417 8589934591 8589934593 9603838835 4801919417
----------}}, {{----------, ----------}, {- ----------, - ----------}}}
2147483648 8589934592 8589934592 4294967296 2147483648
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
507071399 19207677669
o4 = {{------------------------------------------------, -----------}, {1,
365375409332725729550921208179070754913983135744 8589934592
------------------------------------------------------------------------
19207677669 17748383
-----------}, {------------------------------------------------, -
8589934592 730750818665451459101842416358141509827966271488
------------------------------------------------------------------------
19207677669 19207677669
-----------}, {1, - -----------}}
8589934592 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[-1.27252e-39,4.04814e-39], [2.23607,2.23607]}, {[1,1],
------------------------------------------------------------------------
[2.23607,2.23607]}, {[-8.08109e-39,8.12967e-39], [-2.23607,-2.23607]},
------------------------------------------------------------------------
{[1,1], [-2.23607,-2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[-1.27278e-39,4.04865e-39], [2.23535,2.23633]}, {[.999512,1.00049],
------------------------------------------------------------------------
[2.23535,2.23633]}, {[-8.08152e-39,8.13031e-39], [-2.23633,-2.23535]},
------------------------------------------------------------------------
{[.999512,1.00049], [-2.23633,-2.23535]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{1.38781e-39, 2.23607}, {1, 2.23607}, {2.42879e-41, -2.23607}, {1,
------------------------------------------------------------------------
-2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{1.38794e-39, 2.23584}, {1, 2.23584}, {2.43938e-41, -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 = {{[-1.27252e-39,4.04814e-39], [2.23607,2.23607]}, {[1,1],
-----------------------------------------------------------------------
[2.23607,2.23607]}, {[-8.08109e-39,8.12967e-39], [-2.23607,-2.23607]},
-----------------------------------------------------------------------
{[1,1], [-2.23607,-2.23607]}}
o10 : List
|