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
8589934591 8589934593 4801919417 9603838835
o3 = {{{----------, ----------}, {----------, ----------}}, {{-
8589934592 8589934592 2147483648 4294967296
------------------------------------------------------------------------
5246946157
-------------------------------------------------------------------,
6739986666787659948666753771754907668409286105635143120275902562304
------------------------------------------------------------------------
11486277351
--------------------------------------------------------------------},
13479973333575319897333507543509815336818572211270286240551805124608
------------------------------------------------------------------------
4801919417 9603838835 8589934591 8589934593 9603838835
{----------, ----------}}, {{----------, ----------}, {- ----------, -
2147483648 4294967296 8589934592 8589934592 4294967296
------------------------------------------------------------------------
4801919417 3033417661
----------}}, {{- -------------------------------------------------,
2147483648 2923003274661805836407369665432566039311865085952
------------------------------------------------------------------------
4689256689 9603838835
-------------------------------------------------}, {- ----------, -
5846006549323611672814739330865132078623730171904 4294967296
------------------------------------------------------------------------
4801919417
----------}}}
2147483648
o3 : List
|
i4 : rationalApproxSols = msolveRealSolutions(I, QQ)
19207677669 992385037
o4 = {{1, -----------}, {----------------------------------------------------
8589934592 2695994666715063979466701508701963067363714442254057
------------------------------------------------------------------------
19207677669 19207677669
----------------, -----------}, {1, - -----------}, {-
2481103610249216 8589934592 8589934592
------------------------------------------------------------------------
1377578633 19207677669
--------------------------------------------------, - -----------}}
11692013098647223345629478661730264157247460343808 8589934592
o4 : List
|
i5 : floatIntervalSols = msolveRealSolutions(I, RRi)
o5 = {{[1,1], [2.23607,2.23607]}, {[-7.7848e-58,8.52099e-58],
------------------------------------------------------------------------
[2.23607,2.23607]}, {[1,1], [-2.23607,-2.23607]},
------------------------------------------------------------------------
{[-1.03777e-39,8.0213e-40], [-2.23607,-2.23607]}}
o5 : List
|
i6 : floatIntervalSols = msolveRealSolutions(I, RRi_10)
o6 = {{[.999512,1.00049], [2.23535,2.23633]}, {[-7.78499e-58,8.52242e-58],
------------------------------------------------------------------------
[2.23535,2.23633]}, {[.999512,1.00049], [-2.23633,-2.23535]},
------------------------------------------------------------------------
{[-1.03781e-39,8.02484e-40], [-2.23633,-2.23535]}}
o6 : List
|
i7 : floatApproxSols = msolveRealSolutions(I, RR)
o7 = {{1, 2.23607}, {3.68096e-59, 2.23607}, {1, -2.23607}, {-1.17822e-40,
------------------------------------------------------------------------
-2.23607}}
o7 : List
|
i8 : floatApproxSols = msolveRealSolutions(I, RR_10)
o8 = {{1, 2.23584}, {3.68714e-59, 2.23584}, {1, -2.23584}, {-1.17664e-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]}, {[1,1], [-2.23607,-2.23607]},
-----------------------------------------------------------------------
{[-7.04666e-42,9.26628e-42], [2.23607,2.23607]},
-----------------------------------------------------------------------
{[-2.16329e-44,8.10164e-44], [-2.23607,-2.23607]}}
o10 : List
|