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
7417372621
o3 = {{{- -------------------------------------------------,
5846006549323611672814739330865132078623730171904
------------------------------------------------------------------------
2503396909 4801919417
-------------------------------------------------}, {----------,
5846006549323611672814739330865132078623730171904 2147483648
------------------------------------------------------------------------
9603838835 8589934591 8589934593 4801919417 9603838835
----------}}, {{----------, ----------}, {----------, ----------}}, {{-
4294967296 8589934592 8589934592 2147483648 4294967296
------------------------------------------------------------------------
5690967285
-------------------------------------------------------------------,
1684996666696914987166688442938726917102321526408785780068975640576
------------------------------------------------------------------------
4677445355
-------------------------------------------------------------------}, {-
1684996666696914987166688442938726917102321526408785780068975640576
------------------------------------------------------------------------
9603838835 4801919417 8589934591 8589934593 9603838835
----------, - ----------}}, {{----------, ----------}, {- ----------, -
4294967296 2147483648 8589934592 8589934592 4294967296
------------------------------------------------------------------------
4801919417
----------}}}
2147483648
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
153561741 19207677669
o4 = {{- ------------------------------------------------, -----------}, {1,
365375409332725729550921208179070754913983135744 8589934592
------------------------------------------------------------------------
19207677669 506760965
-----------}, {- -------------------------------------------------------
8589934592 1684996666696914987166688442938726917102321526408785780
------------------------------------------------------------------------
19207677669 19207677669
------------, - -----------}, {1, - -----------}}
068975640576 8589934592 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[-1.26879e-39,4.28223e-40], [2.23607,2.23607]}, {[1,1],
------------------------------------------------------------------------
[2.23607,2.23607]}, {[-3.37744e-57,2.77594e-57], [-2.23607,-2.23607]},
------------------------------------------------------------------------
{[1,1], [-2.23607,-2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[-1.2692e-39,4.28326e-40], [2.23535,2.23633]}, {[.999512,1.00049],
------------------------------------------------------------------------
[2.23535,2.23633]}, {[-3.37785e-57,2.77795e-57], [-2.23633,-2.23535]},
------------------------------------------------------------------------
{[.999512,1.00049], [-2.23633,-2.23535]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{-4.20285e-40, 2.23607}, {1, 2.23607}, {-3.00749e-58, -2.23607}, {1,
------------------------------------------------------------------------
-2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{-4.20434e-40, 2.23584}, {1, 2.23584}, {-2.99949e-58, -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 = {{[-1.26879e-39,4.28223e-40], [2.23607,2.23607]}, {[1,1],
-----------------------------------------------------------------------
[2.23607,2.23607]}, {[-3.37744e-57,2.77594e-57], [-2.23607,-2.23607]},
-----------------------------------------------------------------------
{[1,1], [-2.23607,-2.23607]}}
o10 : List
|