Reducing system of 10 inequalities
$begingroup$
I have the following system of inequalities of real variables
sys = 0.383706 x1 + 0.720204 x2 + 1.4568 x3 - 0.000244875 y > 0 && -0.0941312 x1 - 0.176681 x2 - 0.357383 x3 + 0.0000592689 y > 0 && 1.41819 x1 + 3.079 x2 + 2.53801 x3 - 0.00182772 y > 0 && -0.00258971 x1 - 0.00562247 x2 - 0.00463458 x3 + 3.93843*10^-6 y > 0 && 0.129511 x1 + 0.214698 x2 + 0.286739 x3 - 0.0000795243 y > 0 && -0.660462 x1 - 1.09489 x2 - 1.46227 x3 + 0.000405426 y > 0 && 0.351966 x1 + 3.44019 x2 + 7.59863 x3 + 0.00257072 y > 0 && -0.00265509 x1 - 0.0259514 x2 - 0.0573209 x3 - 0.0000199557 y > 0 && 1.34471 x1 + 2.58639 x2 + 3.39561 x3 + 0.0000742173 y > 0 && -0.0314846 x1 - 0.0605571 x2 - 0.079504 x3 - 1.69328*10^-6 y > 0
I want to Reduce
the system in order to see if it admits solutions or not. However, the command Reduce
takes too much time and gets stuck. How can you check if this system admits solutions?
I have tried with FindInstance[sys,{x1,x2,x3,y},Reals]
which returns {}
. However, I am not sure this is a fully proof that the system does not admit solution. Indeed, If I run the command on a subsystem of inequalities I experience the following behaviour
FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals]
(* {} *)
but If I ask for more instances, Mathematica found the points
FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals, 2]
(*{{x1 -> -33., x2 -> 13.5619, x3 -> 1.98727, y -> 0.255564}, {x1 -> -51., x2 -> 20.9595, x3 -> 3.07117, y -> 0.601467}}*)
So, the subsystem [[1;;4]] admits at least a solution. I have run FindInstance[sys, {x1, x2, x3, y}, Reals, 2]
for all the night and got the output {}
. Still, is this a proof that the system does not admits solution?
equation-solving inequalities findinstance
$endgroup$
add a comment |
$begingroup$
I have the following system of inequalities of real variables
sys = 0.383706 x1 + 0.720204 x2 + 1.4568 x3 - 0.000244875 y > 0 && -0.0941312 x1 - 0.176681 x2 - 0.357383 x3 + 0.0000592689 y > 0 && 1.41819 x1 + 3.079 x2 + 2.53801 x3 - 0.00182772 y > 0 && -0.00258971 x1 - 0.00562247 x2 - 0.00463458 x3 + 3.93843*10^-6 y > 0 && 0.129511 x1 + 0.214698 x2 + 0.286739 x3 - 0.0000795243 y > 0 && -0.660462 x1 - 1.09489 x2 - 1.46227 x3 + 0.000405426 y > 0 && 0.351966 x1 + 3.44019 x2 + 7.59863 x3 + 0.00257072 y > 0 && -0.00265509 x1 - 0.0259514 x2 - 0.0573209 x3 - 0.0000199557 y > 0 && 1.34471 x1 + 2.58639 x2 + 3.39561 x3 + 0.0000742173 y > 0 && -0.0314846 x1 - 0.0605571 x2 - 0.079504 x3 - 1.69328*10^-6 y > 0
I want to Reduce
the system in order to see if it admits solutions or not. However, the command Reduce
takes too much time and gets stuck. How can you check if this system admits solutions?
I have tried with FindInstance[sys,{x1,x2,x3,y},Reals]
which returns {}
. However, I am not sure this is a fully proof that the system does not admit solution. Indeed, If I run the command on a subsystem of inequalities I experience the following behaviour
FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals]
(* {} *)
but If I ask for more instances, Mathematica found the points
FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals, 2]
(*{{x1 -> -33., x2 -> 13.5619, x3 -> 1.98727, y -> 0.255564}, {x1 -> -51., x2 -> 20.9595, x3 -> 3.07117, y -> 0.601467}}*)
So, the subsystem [[1;;4]] admits at least a solution. I have run FindInstance[sys, {x1, x2, x3, y}, Reals, 2]
for all the night and got the output {}
. Still, is this a proof that the system does not admits solution?
equation-solving inequalities findinstance
$endgroup$
1
$begingroup$
Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals]
givesFalse
.
$endgroup$
– kglr
Nov 19 '18 at 7:28
1
$begingroup$
andRegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys))
givesEmptyRegion[4]
.
$endgroup$
– kglr
Nov 19 '18 at 7:33
add a comment |
$begingroup$
I have the following system of inequalities of real variables
sys = 0.383706 x1 + 0.720204 x2 + 1.4568 x3 - 0.000244875 y > 0 && -0.0941312 x1 - 0.176681 x2 - 0.357383 x3 + 0.0000592689 y > 0 && 1.41819 x1 + 3.079 x2 + 2.53801 x3 - 0.00182772 y > 0 && -0.00258971 x1 - 0.00562247 x2 - 0.00463458 x3 + 3.93843*10^-6 y > 0 && 0.129511 x1 + 0.214698 x2 + 0.286739 x3 - 0.0000795243 y > 0 && -0.660462 x1 - 1.09489 x2 - 1.46227 x3 + 0.000405426 y > 0 && 0.351966 x1 + 3.44019 x2 + 7.59863 x3 + 0.00257072 y > 0 && -0.00265509 x1 - 0.0259514 x2 - 0.0573209 x3 - 0.0000199557 y > 0 && 1.34471 x1 + 2.58639 x2 + 3.39561 x3 + 0.0000742173 y > 0 && -0.0314846 x1 - 0.0605571 x2 - 0.079504 x3 - 1.69328*10^-6 y > 0
I want to Reduce
the system in order to see if it admits solutions or not. However, the command Reduce
takes too much time and gets stuck. How can you check if this system admits solutions?
I have tried with FindInstance[sys,{x1,x2,x3,y},Reals]
which returns {}
. However, I am not sure this is a fully proof that the system does not admit solution. Indeed, If I run the command on a subsystem of inequalities I experience the following behaviour
FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals]
(* {} *)
but If I ask for more instances, Mathematica found the points
FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals, 2]
(*{{x1 -> -33., x2 -> 13.5619, x3 -> 1.98727, y -> 0.255564}, {x1 -> -51., x2 -> 20.9595, x3 -> 3.07117, y -> 0.601467}}*)
So, the subsystem [[1;;4]] admits at least a solution. I have run FindInstance[sys, {x1, x2, x3, y}, Reals, 2]
for all the night and got the output {}
. Still, is this a proof that the system does not admits solution?
equation-solving inequalities findinstance
$endgroup$
I have the following system of inequalities of real variables
sys = 0.383706 x1 + 0.720204 x2 + 1.4568 x3 - 0.000244875 y > 0 && -0.0941312 x1 - 0.176681 x2 - 0.357383 x3 + 0.0000592689 y > 0 && 1.41819 x1 + 3.079 x2 + 2.53801 x3 - 0.00182772 y > 0 && -0.00258971 x1 - 0.00562247 x2 - 0.00463458 x3 + 3.93843*10^-6 y > 0 && 0.129511 x1 + 0.214698 x2 + 0.286739 x3 - 0.0000795243 y > 0 && -0.660462 x1 - 1.09489 x2 - 1.46227 x3 + 0.000405426 y > 0 && 0.351966 x1 + 3.44019 x2 + 7.59863 x3 + 0.00257072 y > 0 && -0.00265509 x1 - 0.0259514 x2 - 0.0573209 x3 - 0.0000199557 y > 0 && 1.34471 x1 + 2.58639 x2 + 3.39561 x3 + 0.0000742173 y > 0 && -0.0314846 x1 - 0.0605571 x2 - 0.079504 x3 - 1.69328*10^-6 y > 0
I want to Reduce
the system in order to see if it admits solutions or not. However, the command Reduce
takes too much time and gets stuck. How can you check if this system admits solutions?
I have tried with FindInstance[sys,{x1,x2,x3,y},Reals]
which returns {}
. However, I am not sure this is a fully proof that the system does not admit solution. Indeed, If I run the command on a subsystem of inequalities I experience the following behaviour
FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals]
(* {} *)
but If I ask for more instances, Mathematica found the points
FindInstance[sys[[1 ;; 4]], {x1, x2, x3, y}, Reals, 2]
(*{{x1 -> -33., x2 -> 13.5619, x3 -> 1.98727, y -> 0.255564}, {x1 -> -51., x2 -> 20.9595, x3 -> 3.07117, y -> 0.601467}}*)
So, the subsystem [[1;;4]] admits at least a solution. I have run FindInstance[sys, {x1, x2, x3, y}, Reals, 2]
for all the night and got the output {}
. Still, is this a proof that the system does not admits solution?
equation-solving inequalities findinstance
equation-solving inequalities findinstance
asked Nov 19 '18 at 7:18
apt45apt45
561211
561211
1
$begingroup$
Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals]
givesFalse
.
$endgroup$
– kglr
Nov 19 '18 at 7:28
1
$begingroup$
andRegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys))
givesEmptyRegion[4]
.
$endgroup$
– kglr
Nov 19 '18 at 7:33
add a comment |
1
$begingroup$
Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals]
givesFalse
.
$endgroup$
– kglr
Nov 19 '18 at 7:28
1
$begingroup$
andRegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys))
givesEmptyRegion[4]
.
$endgroup$
– kglr
Nov 19 '18 at 7:33
1
1
$begingroup$
Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals]
gives False
.$endgroup$
– kglr
Nov 19 '18 at 7:28
$begingroup$
Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals]
gives False
.$endgroup$
– kglr
Nov 19 '18 at 7:28
1
1
$begingroup$
and
RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys))
gives EmptyRegion[4]
.$endgroup$
– kglr
Nov 19 '18 at 7:33
$begingroup$
and
RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys))
gives EmptyRegion[4]
.$endgroup$
– kglr
Nov 19 '18 at 7:33
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] // RepeatedTiming
{0.24878, False}
RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) //
RepeatedTiming
{0.0152, EmptyRegion[4]}
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "387"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f186279%2freducing-system-of-10-inequalities%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] // RepeatedTiming
{0.24878, False}
RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) //
RepeatedTiming
{0.0152, EmptyRegion[4]}
$endgroup$
add a comment |
$begingroup$
Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] // RepeatedTiming
{0.24878, False}
RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) //
RepeatedTiming
{0.0152, EmptyRegion[4]}
$endgroup$
add a comment |
$begingroup$
Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] // RepeatedTiming
{0.24878, False}
RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) //
RepeatedTiming
{0.0152, EmptyRegion[4]}
$endgroup$
Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals] // RepeatedTiming
{0.24878, False}
RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys)) //
RepeatedTiming
{0.0152, EmptyRegion[4]}
answered Nov 19 '18 at 7:59
kglrkglr
181k10200413
181k10200413
add a comment |
add a comment |
Thanks for contributing an answer to Mathematica Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f186279%2freducing-system-of-10-inequalities%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
Reduce[Rationalize[sys, 2^-12], {x1, x2, x3, y}, Reals]
givesFalse
.$endgroup$
– kglr
Nov 19 '18 at 7:28
1
$begingroup$
and
RegionIntersection @@ (ImplicitRegion[#, {x1, x2, x3, y}] & /@ (List @@ sys))
givesEmptyRegion[4]
.$endgroup$
– kglr
Nov 19 '18 at 7:33