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ApproxSolve

Approximate real solutions for polynomial system

Syntax
ApproxSolve(L: LIST of RINGELEM): LIST of LIST of RAT

Description
This function returns the list of real solutions (points) of a 0-dimensional polynomial system L . Works only if with rational coefficients. Approximate coordinates are given for non-rational solutions.

Verbosity 20.

See also RationalSolve

Example
/**/ Use QQ[x,y,z];
/**/ L := [x^3-y^2+z-1, x-2, (y-3)*(y+2)];
/**/ RationalSolve(L);
[[2, -2, -3], [2, 3, 2]]
/**/ ApproxSolve(L);
[[2, -2, -3], [2, 3, 2]]

/**/ L := [x^3-y^2+1, (y-3)*(y+2), z];
/**/ indent(ApproxSolve(L));
[
  [167001090947516369641767378634802431634869700965461961120334511774287062707365/115792089237316195423570985008687907853269984665640564039457584007913129639936, -3105036184601417870297958976925005110513772034233393222278104076052101905372785086417905610616594068048936176388754598241094647389028646910227375835339689773298904914910878292075930186409206203488239052651022151060681311443956437155/1552518092300708935148979488462502555256886017116696611139052038026050952686376886330878408828646477950487730697131073206171580044114814391444287275041181139204454976020849905550265285631598444825262999193716468750892846853816057856, 0],
  [2, 3, 0]
]

/**/ L := [x^3-y^2+z-1, x^2-2, (y-3)*(y+2)];
/**/ Pts := ApproxSolve(L);
--> [[17564737135690137373...
/**/ indent([[ DecimalStr(coord,10) | coord in pt] | pt in Pts]);
[
  ["1.4142135624", "-2.0000000000", "2.1715728753"],
  ["1.4142135624", "3.0000000000", "7.1715728753"],
  ["-1.4142135624", "-2.0000000000", "7.8284271247"],
  ["-1.4142135624", "3.0000000000", "12.8284271247"]
]

-- Verify we have an approximate answer:
/**/ indent([ [ FloatStr(eval(f, pt)) | f in L ] | pt in Pts]);
[
  ["-3.2567*10^(-76)", "-6.2932*10^(-77)", "2.3668*10^(-76)"],
  ["-1.3971*10^(-77)", "8.1808*10^(-78)", "2.5541*10^(-77)"],
  ["-3.7110*10^(-77)", "8.1808*10^(-78)", "2.5541*10^(-77)"],
  ["7.7208*10^(-77)", "3.2902*10^(-77)", "-1.2374*10^(-76)"]
]

See Also