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
1606984755
o3 = {{{- --------------------------------------------------,
93536104789177786765035829293842113257979682750464
------------------------------------------------------------------------
6734057533 9603838835
---------------------------------------------------}, {- ----------, -
374144419156711147060143317175368453031918731001856 4294967296
------------------------------------------------------------------------
4801919417 8589934591 8589934593 9603838835 4801919417
----------}}, {{----------, ----------}, {- ----------, - ----------}},
2147483648 8589934592 8589934592 4294967296 2147483648
------------------------------------------------------------------------
7150524515
{{- -------------------------------------------------,
5846006549323611672814739330865132078623730171904
------------------------------------------------------------------------
5693192295 4801919417
-------------------------------------------------}, {----------,
5846006549323611672814739330865132078623730171904 2147483648
------------------------------------------------------------------------
9603838835 8589934591 8589934593 4801919417 9603838835
----------}}, {{----------, ----------}, {----------, ----------}}}
4294967296 8589934592 8589934592 2147483648 4294967296
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
306118513 19207677669
o4 = {{---------------------------------------------------, - -----------},
748288838313422294120286634350736906063837462003712 8589934592
------------------------------------------------------------------------
19207677669 364333055
{1, - -----------}, {- -------------------------------------------------
8589934592 2923003274661805836407369665432566039311865085952
------------------------------------------------------------------------
19207677669 19207677669
, -----------}, {1, -----------}}
8589934592 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[-1.71804e-41,1.79986e-41], [-2.23607,-2.23607]}, {[1,1],
------------------------------------------------------------------------
[-2.23607,-2.23607]}, {[-1.22315e-39,9.7386e-40], [2.23607,2.23607]},
------------------------------------------------------------------------
{[1,1], [2.23607,2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[-1.71855e-41,1.80039e-41], [-2.23633,-2.23535]}, {[.999512,1.00049],
------------------------------------------------------------------------
[-2.23633,-2.23535]}, {[-1.22328e-39,9.74317e-40], [2.23535,2.23633]},
------------------------------------------------------------------------
{[.999512,1.00049], [2.23535,2.23633]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{4.09091e-43, -2.23607}, {1, -2.23607}, {-1.24643e-40, 2.23607}, {1,
------------------------------------------------------------------------
2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{4.09179e-43, -2.23584}, {1, -2.23584}, {-1.2448e-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 = {{[-1.71804e-41,1.79986e-41], [-2.23607,-2.23607]}, {[1,1],
-----------------------------------------------------------------------
[-2.23607,-2.23607]}, {[-1.22315e-39,9.7386e-40], [2.23607,2.23607]},
-----------------------------------------------------------------------
{[1,1], [2.23607,2.23607]}}
o10 : List
|