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 4801919417 9603838835
o3 = {{{----------, ----------}, {----------, ----------}}, {{-
8589934592 8589934592 2147483648 4294967296
------------------------------------------------------------------------
4727067509
-------------------------------------------------,
1461501637330902918203684832716283019655932542976
------------------------------------------------------------------------
16261142833 4801919417
-------------------------------------------------}, {----------,
2923003274661805836407369665432566039311865085952 2147483648
------------------------------------------------------------------------
9603838835 8589934591 8589934593 9603838835 4801919417
----------}}, {{----------, ----------}, {- ----------, - ----------}},
4294967296 8589934592 8589934592 4294967296 2147483648
------------------------------------------------------------------------
13169698205
{{- -------------------------------------------------,
5846006549323611672814739330865132078623730171904
------------------------------------------------------------------------
11884277689 9603838835
-------------------------------------------------}, {- ----------, -
5846006549323611672814739330865132078623730171904 4294967296
------------------------------------------------------------------------
4801919417
----------}}}
2147483648
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
19207677669 6807007815
o4 = {{1, -----------}, {-------------------------------------------------,
8589934592 5846006549323611672814739330865132078623730171904
------------------------------------------------------------------------
19207677669 19207677669
-----------}, {1, - -----------}, {-
8589934592 8589934592
------------------------------------------------------------------------
321355129 19207677669
-------------------------------------------------, - -----------}}
2923003274661805836407369665432566039311865085952 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[1,1], [2.23607,2.23607]}, {[-3.23439e-39,5.56316e-39],
------------------------------------------------------------------------
[2.23607,2.23607]}, {[1,1], [-2.23607,-2.23607]},
------------------------------------------------------------------------
{[-2.25277e-39,2.03289e-39], [-2.23607,-2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[.999512,1.00049], [2.23535,2.23633]}, {[-3.23577e-39,5.56322e-39],
------------------------------------------------------------------------
[2.23535,2.23633]}, {[.999512,1.00049], [-2.23633,-2.23535]},
------------------------------------------------------------------------
{[-2.25284e-39,2.0333e-39], [-2.23633,-2.23535]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{1, 2.23607}, {1.16439e-39, 2.23607}, {1, -2.23607}, {-1.0994e-40,
------------------------------------------------------------------------
-2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{1, 2.23584}, {1.16373e-39, 2.23584}, {1, -2.23584}, {-1.09772e-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]}, {[-3.23439e-39,5.56316e-39],
-----------------------------------------------------------------------
[2.23607,2.23607]}, {[1,1], [-2.23607,-2.23607]},
-----------------------------------------------------------------------
{[-2.25277e-39,2.03289e-39], [-2.23607,-2.23607]}}
o10 : List
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