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
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i2 : I = ideal {(x-1)*x, y^2-5}
2 2
o2 = ideal (x - x, y - 5)
o2 : Ideal of R
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i3 : rationalIntervalSols = msolveRealSolutions I
8589934591 8589934593 9603838835 4801919417
o3 = {{{----------, ----------}, {- ----------, - ----------}}, {{-
8589934592 8589934592 4294967296 2147483648
------------------------------------------------------------------------
13142973925
--------------------------------------------------------------------,
26959946667150639794667015087019630673637144422540572481103610249216
------------------------------------------------------------------------
14281864989
--------------------------------------------------------------------},
26959946667150639794667015087019630673637144422540572481103610249216
------------------------------------------------------------------------
9603838835 4801919417 8589934591 8589934593 4801919417
{- ----------, - ----------}}, {{----------, ----------}, {----------,
4294967296 2147483648 8589934592 8589934592 2147483648
------------------------------------------------------------------------
9603838835 7062415609
----------}}, {{- -------------------------------------------------,
4294967296 2923003274661805836407369665432566039311865085952
------------------------------------------------------------------------
7350005263 4801919417
-------------------------------------------------}, {----------,
5846006549323611672814739330865132078623730171904 2147483648
------------------------------------------------------------------------
9603838835
----------}}}
4294967296
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
19207677669 142361383
o4 = {{1, - -----------}, {--------------------------------------------------
8589934592 67399866667876599486667537717549076684092861056351
------------------------------------------------------------------------
19207677669 19207677669
-----------------, - -----------}, {1, -----------}, {-
43120275902562304 8589934592 8589934592
------------------------------------------------------------------------
6774825955 19207677669
--------------------------------------------------, -----------}}
11692013098647223345629478661730264157247460343808 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[1,1], [-2.23607,-2.23607]}, {[-4.875e-58,5.29744e-58],
------------------------------------------------------------------------
[-2.23607,-2.23607]}, {[1,1], [2.23607,2.23607]},
------------------------------------------------------------------------
{[-2.41615e-39,1.25727e-39], [2.23607,2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[.999512,1.00049], [-2.23633,-2.23535]}, {[-4.87573e-58,5.2989e-58],
------------------------------------------------------------------------
[-2.23633,-2.23535]}, {[.999512,1.00049], [2.23535,2.23633]},
------------------------------------------------------------------------
{[-2.41642e-39,1.25772e-39], [2.23535,2.23633]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{1, -2.23607}, {2.11219e-59, -2.23607}, {1, 2.23607}, {-5.79441e-40,
------------------------------------------------------------------------
2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{1, -2.23584}, {2.11583e-59, -2.23584}, {1, 2.23584}, {-5.79353e-40,
------------------------------------------------------------------------
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 = {{[1,1], [-2.23607,-2.23607]}, {[-4.875e-58,5.29744e-58],
-----------------------------------------------------------------------
[-2.23607,-2.23607]}, {[1,1], [2.23607,2.23607]},
-----------------------------------------------------------------------
{[-2.41615e-39,1.25727e-39], [2.23607,2.23607]}}
o10 : List
|