Possible bug in Solve function?
$begingroup$
Bug introduced in 10.0 and persisting through 11.3 or later
In 11.3.0 for Microsoft Windows (64-bit) (March 7, 2018) writing:
f[w_, x_, y_, z_] := w*x^2*y^3 - z*(w^2 + x^2 + y^2 - 1)
eqn = {D[f[w, x, y, z], w] == 0,
D[f[w, x, y, z], x] == 0,
D[f[w, x, y, z], y] == 0,
D[f[w, x, y, z], z] == 0};
sol = Solve[eqn];
Table[eqn /. sol[[n]], {n, Length[sol]}]
I get:
{{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True}}
from which there are four wrong solutions.
Am I wrong or is it a Solve bug?
EDIT: through the email address support@wolfram.com I contacted Wolfram Technical Support who in less than three working days have confirmed that it is a bug and have already proceeded to report to their developers.
equation-solving bugs
edited Jan 8 at 11:37
Szabolcs
163k14448945
asked Jan 5 at 21:50
TeMTeM
2,029621
$endgroup$
add a comment |
$begingroup$
Bug introduced in 10.0 and persisting through 11.3 or later
In 11.3.0 for Microsoft Windows (64-bit) (March 7, 2018) writing:
f[w_, x_, y_, z_] := w*x^2*y^3 - z*(w^2 + x^2 + y^2 - 1)
eqn = {D[f[w, x, y, z], w] == 0,
D[f[w, x, y, z], x] == 0,
D[f[w, x, y, z], y] == 0,
D[f[w, x, y, z], z] == 0};
sol = Solve[eqn];
Table[eqn /. sol[[n]], {n, Length[sol]}]
I get:
{{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True}}
from which there are four wrong solutions.
Am I wrong or is it a Solve bug?
EDIT: through the email address support@wolfram.com I contacted Wolfram Technical Support who in less than three working days have confirmed that it is a bug and have already proceeded to report to their developers.
equation-solving bugs
edited Jan 8 at 11:37
Szabolcs
163k14448945
asked Jan 5 at 21:50
TeMTeM
2,029621
$endgroup$
1
$begingroup$
You could useList@ToRules@Reduce[eqn, {x, y, z, w}]to get all valid solutions. Filter for those that only have numeric values on the RHS of->.
$endgroup$
– Szabolcs
Jan 5 at 22:30
$begingroup$
Select[sol, And @@ eqn /. # &]
$endgroup$
– Bob Hanlon
Jan 5 at 23:53
5
$begingroup$
Next time, please do not add the bugs tag yourself on a question. The tag is only supposed to be added after your observations have been confirmed by other users.
$endgroup$
– J. M. is away♦
Jan 6 at 2:45
add a comment |
$begingroup$
Bug introduced in 10.0 and persisting through 11.3 or later
In 11.3.0 for Microsoft Windows (64-bit) (March 7, 2018) writing:
f[w_, x_, y_, z_] := w*x^2*y^3 - z*(w^2 + x^2 + y^2 - 1)
eqn = {D[f[w, x, y, z], w] == 0,
D[f[w, x, y, z], x] == 0,
D[f[w, x, y, z], y] == 0,
D[f[w, x, y, z], z] == 0};
sol = Solve[eqn];
Table[eqn /. sol[[n]], {n, Length[sol]}]
I get:
{{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True}}
from which there are four wrong solutions.
Am I wrong or is it a Solve bug?
EDIT: through the email address support@wolfram.com I contacted Wolfram Technical Support who in less than three working days have confirmed that it is a bug and have already proceeded to report to their developers.
equation-solving bugs
edited Jan 8 at 11:37
Szabolcs
163k14448945
asked Jan 5 at 21:50
TeMTeM
2,029621
$endgroup$
Bug introduced in 10.0 and persisting through 11.3 or later
In 11.3.0 for Microsoft Windows (64-bit) (March 7, 2018) writing:
f[w_, x_, y_, z_] := w*x^2*y^3 - z*(w^2 + x^2 + y^2 - 1)
eqn = {D[f[w, x, y, z], w] == 0,
D[f[w, x, y, z], x] == 0,
D[f[w, x, y, z], y] == 0,
D[f[w, x, y, z], z] == 0};
sol = Solve[eqn];
Table[eqn /. sol[[n]], {n, Length[sol]}]
I get:
{{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True},
{False, True, True, False},
{True, True, True, True},
{True, True, True, True}}
from which there are four wrong solutions.
Am I wrong or is it a Solve bug?
EDIT: through the email address support@wolfram.com I contacted Wolfram Technical Support who in less than three working days have confirmed that it is a bug and have already proceeded to report to their developers.
equation-solving bugs
equation-solving bugs
edited Jan 8 at 11:37
Szabolcs
163k14448945
asked Jan 5 at 21:50
TeMTeM
2,029621
edited Jan 8 at 11:37
Szabolcs
163k14448945
asked Jan 5 at 21:50
TeMTeM
2,029621
edited Jan 8 at 11:37
Szabolcs
163k14448945
edited Jan 8 at 11:37
Szabolcs
163k14448945
edited Jan 8 at 11:37
Szabolcs
163k14448945
163k14448945
asked Jan 5 at 21:50
TeMTeM
2,029621
asked Jan 5 at 21:50
TeMTeM
2,029621
asked Jan 5 at 21:50
TeMTeM
2,029621
2,029621
1
$begingroup$
You could useList@ToRules@Reduce[eqn, {x, y, z, w}]to get all valid solutions. Filter for those that only have numeric values on the RHS of->.
$endgroup$
– Szabolcs
Jan 5 at 22:30
$begingroup$
Select[sol, And @@ eqn /. # &]
$endgroup$
– Bob Hanlon
Jan 5 at 23:53
5
$begingroup$
Next time, please do not add the bugs tag yourself on a question. The tag is only supposed to be added after your observations have been confirmed by other users.
$endgroup$
– J. M. is away♦
Jan 6 at 2:45
add a comment |
1
$begingroup$
You could useList@ToRules@Reduce[eqn, {x, y, z, w}]to get all valid solutions. Filter for those that only have numeric values on the RHS of->.
$endgroup$
– Szabolcs
Jan 5 at 22:30
$begingroup$
Select[sol, And @@ eqn /. # &]
$endgroup$
– Bob Hanlon
Jan 5 at 23:53
5
$begingroup$
Next time, please do not add the bugs tag yourself on a question. The tag is only supposed to be added after your observations have been confirmed by other users.
$endgroup$
– J. M. is away♦
Jan 6 at 2:45
1
1
$begingroup$
You could use
List@ToRules@Reduce[eqn, {x, y, z, w}] to get all valid solutions. Filter for those that only have numeric values on the RHS of ->.$endgroup$
– Szabolcs
Jan 5 at 22:30
$begingroup$
You could use
List@ToRules@Reduce[eqn, {x, y, z, w}] to get all valid solutions. Filter for those that only have numeric values on the RHS of ->.$endgroup$
– Szabolcs
Jan 5 at 22:30
$begingroup$
Select[sol, And @@ eqn /. # &]$endgroup$
– Bob Hanlon
Jan 5 at 23:53
$begingroup$
Select[sol, And @@ eqn /. # &]$endgroup$
– Bob Hanlon
Jan 5 at 23:53
5
5
$begingroup$
Next time, please do not add the bugs tag yourself on a question. The tag is only supposed to be added after your observations have been confirmed by other users.
$endgroup$
– J. M. is away♦
Jan 6 at 2:45
$begingroup$
Next time, please do not add the bugs tag yourself on a question. The tag is only supposed to be added after your observations have been confirmed by other users.
$endgroup$
– J. M. is away♦
Jan 6 at 2:45
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Thanks for asking! In version 9.0 only 16 solutions are returned and they are all valid. In version 10.2 there are 20 solutions, with the extra 4 all being invalid. Contragulations! I think you found a bug. You may want to click "Help", then "Give Feedback...", and then fill out the form in your browser to report.
As another answer notes, you can always try Reduce instead which may give better results in some cases, but Solve is usually what you want.
answered Jan 5 at 22:05
SomosSomos
1,7451110
$endgroup$
$begingroup$
Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
$endgroup$
– TeM
Jan 5 at 22:11
2
$begingroup$
@TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
$endgroup$
– Szabolcs
Jan 5 at 22:31
$begingroup$
@Szabolcs: Could you direct me where I can do it correctly?
$endgroup$
– TeM
Jan 5 at 22:44
4
$begingroup$
@TeM wolfram.com/support/contact
$endgroup$
– Szabolcs
Jan 5 at 23:49
add a comment |
$begingroup$
You can use Reduce
f[w_, x_, y_, z_] := w*x^2*y^3 - z*(w^2 + x^2 + y^2 - 1)
eqn = {D[f[w, x, y, z], w] == 0, D[f[w, x, y, z], x] == 0,
D[f[w, x, y, z], y] == 0, D[f[w, x, y, z], z] == 0};
red = Reduce[eqn, Backsubstitution -> True]
$left(z=0land x=0land w=-sqrt{1-y^2}right)lor left(z=0land x=0land w=sqrt{1-y^2}right)lor left(z=0land y=0land
w=-sqrt{1-x^2}right)lor left(z=0land y=0land w=sqrt{1-x^2}right)lor (z=0land y=-1land x=0land w=0)lor (z=0land y=0land x=0land
w=-1)lor (z=0land y=0land x=0land w=1)lor (z=0land y=1land x=0land w=0)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land
x=-frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)\
lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)$
First@eqn //. {ToRules[red]}
{True, True, True, True, True, True, True, True, True, True, True,
True, True, True, True, True}
answered Jan 6 at 1:09
Okkes DulgerciOkkes Dulgerci
5,4241919
$endgroup$
$begingroup$
Yes, of course, I had already tried. I was almost certain it was a bug fromSolve, so I pointed out. Thank you very much anyway, always very kind!
$endgroup$
– TeM
Jan 6 at 1:14
4
$begingroup$
I believeSolveuse the functionReduceunder the hood. when you removeBacksubstitution -> True, you'll find implicit solution, somehowSolvemesses up somewhere and it is definitely a bug..
$endgroup$
– Okkes Dulgerci
Jan 6 at 1:18
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%2f188900%2fpossible-bug-in-solve-function%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Thanks for asking! In version 9.0 only 16 solutions are returned and they are all valid. In version 10.2 there are 20 solutions, with the extra 4 all being invalid. Contragulations! I think you found a bug. You may want to click "Help", then "Give Feedback...", and then fill out the form in your browser to report.
As another answer notes, you can always try Reduce instead which may give better results in some cases, but Solve is usually what you want.
answered Jan 5 at 22:05
SomosSomos
1,7451110
$endgroup$
$begingroup$
Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
$endgroup$
– TeM
Jan 5 at 22:11
2
$begingroup$
@TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
$endgroup$
– Szabolcs
Jan 5 at 22:31
$begingroup$
@Szabolcs: Could you direct me where I can do it correctly?
$endgroup$
– TeM
Jan 5 at 22:44
4
$begingroup$
@TeM wolfram.com/support/contact
$endgroup$
– Szabolcs
Jan 5 at 23:49
add a comment |
$begingroup$
Thanks for asking! In version 9.0 only 16 solutions are returned and they are all valid. In version 10.2 there are 20 solutions, with the extra 4 all being invalid. Contragulations! I think you found a bug. You may want to click "Help", then "Give Feedback...", and then fill out the form in your browser to report.
As another answer notes, you can always try Reduce instead which may give better results in some cases, but Solve is usually what you want.
answered Jan 5 at 22:05
SomosSomos
1,7451110
$endgroup$
$begingroup$
Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
$endgroup$
– TeM
Jan 5 at 22:11
2
$begingroup$
@TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
$endgroup$
– Szabolcs
Jan 5 at 22:31
$begingroup$
@Szabolcs: Could you direct me where I can do it correctly?
$endgroup$
– TeM
Jan 5 at 22:44
4
$begingroup$
@TeM wolfram.com/support/contact
$endgroup$
– Szabolcs
Jan 5 at 23:49
add a comment |
$begingroup$
Thanks for asking! In version 9.0 only 16 solutions are returned and they are all valid. In version 10.2 there are 20 solutions, with the extra 4 all being invalid. Contragulations! I think you found a bug. You may want to click "Help", then "Give Feedback...", and then fill out the form in your browser to report.
As another answer notes, you can always try Reduce instead which may give better results in some cases, but Solve is usually what you want.
answered Jan 5 at 22:05
SomosSomos
1,7451110
$endgroup$
Thanks for asking! In version 9.0 only 16 solutions are returned and they are all valid. In version 10.2 there are 20 solutions, with the extra 4 all being invalid. Contragulations! I think you found a bug. You may want to click "Help", then "Give Feedback...", and then fill out the form in your browser to report.
As another answer notes, you can always try Reduce instead which may give better results in some cases, but Solve is usually what you want.
answered Jan 5 at 22:05
SomosSomos
1,7451110
edited Jan 6 at 1:16
answered Jan 5 at 22:05
SomosSomos
1,7451110
answered Jan 5 at 22:05
SomosSomos
1,7451110
answered Jan 5 at 22:05
SomosSomos
1,7451110
1,7451110
$begingroup$
Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
$endgroup$
– TeM
Jan 5 at 22:11
2
$begingroup$
@TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
$endgroup$
– Szabolcs
Jan 5 at 22:31
$begingroup$
@Szabolcs: Could you direct me where I can do it correctly?
$endgroup$
– TeM
Jan 5 at 22:44
4
$begingroup$
@TeM wolfram.com/support/contact
$endgroup$
– Szabolcs
Jan 5 at 23:49
add a comment |
$begingroup$
Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
$endgroup$
– TeM
Jan 5 at 22:11
2
$begingroup$
@TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
$endgroup$
– Szabolcs
Jan 5 at 22:31
$begingroup$
@Szabolcs: Could you direct me where I can do it correctly?
$endgroup$
– TeM
Jan 5 at 22:44
4
$begingroup$
@TeM wolfram.com/support/contact
$endgroup$
– Szabolcs
Jan 5 at 23:49
$begingroup$
Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
$endgroup$
– TeM
Jan 5 at 22:11
$begingroup$
Well, it will mean that the next version will be the first calculation I will perform. Thank you! ^_^
$endgroup$
– TeM
Jan 5 at 22:11
2
2
$begingroup$
@TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
$endgroup$
– Szabolcs
Jan 5 at 22:31
$begingroup$
@TeM You should report it to Wolfram first, otherwise there's no chance for it to get fixed.
$endgroup$
– Szabolcs
Jan 5 at 22:31
$begingroup$
@Szabolcs: Could you direct me where I can do it correctly?
$endgroup$
– TeM
Jan 5 at 22:44
$begingroup$
@Szabolcs: Could you direct me where I can do it correctly?
$endgroup$
– TeM
Jan 5 at 22:44
4
4
$begingroup$
@TeM wolfram.com/support/contact
$endgroup$
– Szabolcs
Jan 5 at 23:49
$begingroup$
@TeM wolfram.com/support/contact
$endgroup$
– Szabolcs
Jan 5 at 23:49
add a comment |
$begingroup$
You can use Reduce
f[w_, x_, y_, z_] := w*x^2*y^3 - z*(w^2 + x^2 + y^2 - 1)
eqn = {D[f[w, x, y, z], w] == 0, D[f[w, x, y, z], x] == 0,
D[f[w, x, y, z], y] == 0, D[f[w, x, y, z], z] == 0};
red = Reduce[eqn, Backsubstitution -> True]
$left(z=0land x=0land w=-sqrt{1-y^2}right)lor left(z=0land x=0land w=sqrt{1-y^2}right)lor left(z=0land y=0land
w=-sqrt{1-x^2}right)lor left(z=0land y=0land w=sqrt{1-x^2}right)lor (z=0land y=-1land x=0land w=0)lor (z=0land y=0land x=0land
w=-1)lor (z=0land y=0land x=0land w=1)lor (z=0land y=1land x=0land w=0)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land
x=-frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)\
lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)$
First@eqn //. {ToRules[red]}
{True, True, True, True, True, True, True, True, True, True, True,
True, True, True, True, True}
answered Jan 6 at 1:09
Okkes DulgerciOkkes Dulgerci
5,4241919
$endgroup$
$begingroup$
Yes, of course, I had already tried. I was almost certain it was a bug fromSolve, so I pointed out. Thank you very much anyway, always very kind!
$endgroup$
– TeM
Jan 6 at 1:14
4
$begingroup$
I believeSolveuse the functionReduceunder the hood. when you removeBacksubstitution -> True, you'll find implicit solution, somehowSolvemesses up somewhere and it is definitely a bug..
$endgroup$
– Okkes Dulgerci
Jan 6 at 1:18
add a comment |
$begingroup$
You can use Reduce
f[w_, x_, y_, z_] := w*x^2*y^3 - z*(w^2 + x^2 + y^2 - 1)
eqn = {D[f[w, x, y, z], w] == 0, D[f[w, x, y, z], x] == 0,
D[f[w, x, y, z], y] == 0, D[f[w, x, y, z], z] == 0};
red = Reduce[eqn, Backsubstitution -> True]
$left(z=0land x=0land w=-sqrt{1-y^2}right)lor left(z=0land x=0land w=sqrt{1-y^2}right)lor left(z=0land y=0land
w=-sqrt{1-x^2}right)lor left(z=0land y=0land w=sqrt{1-x^2}right)lor (z=0land y=-1land x=0land w=0)lor (z=0land y=0land x=0land
w=-1)lor (z=0land y=0land x=0land w=1)lor (z=0land y=1land x=0land w=0)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land
x=-frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)\
lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)$
First@eqn //. {ToRules[red]}
{True, True, True, True, True, True, True, True, True, True, True,
True, True, True, True, True}
answered Jan 6 at 1:09
Okkes DulgerciOkkes Dulgerci
5,4241919
$endgroup$
$begingroup$
Yes, of course, I had already tried. I was almost certain it was a bug fromSolve, so I pointed out. Thank you very much anyway, always very kind!
$endgroup$
– TeM
Jan 6 at 1:14
4
$begingroup$
I believeSolveuse the functionReduceunder the hood. when you removeBacksubstitution -> True, you'll find implicit solution, somehowSolvemesses up somewhere and it is definitely a bug..
$endgroup$
– Okkes Dulgerci
Jan 6 at 1:18
add a comment |
$begingroup$
You can use Reduce
f[w_, x_, y_, z_] := w*x^2*y^3 - z*(w^2 + x^2 + y^2 - 1)
eqn = {D[f[w, x, y, z], w] == 0, D[f[w, x, y, z], x] == 0,
D[f[w, x, y, z], y] == 0, D[f[w, x, y, z], z] == 0};
red = Reduce[eqn, Backsubstitution -> True]
$left(z=0land x=0land w=-sqrt{1-y^2}right)lor left(z=0land x=0land w=sqrt{1-y^2}right)lor left(z=0land y=0land
w=-sqrt{1-x^2}right)lor left(z=0land y=0land w=sqrt{1-x^2}right)lor (z=0land y=-1land x=0land w=0)lor (z=0land y=0land x=0land
w=-1)lor (z=0land y=0land x=0land w=1)lor (z=0land y=1land x=0land w=0)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land
x=-frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)\
lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)$
First@eqn //. {ToRules[red]}
{True, True, True, True, True, True, True, True, True, True, True,
True, True, True, True, True}
answered Jan 6 at 1:09
Okkes DulgerciOkkes Dulgerci
5,4241919
$endgroup$
You can use Reduce
f[w_, x_, y_, z_] := w*x^2*y^3 - z*(w^2 + x^2 + y^2 - 1)
eqn = {D[f[w, x, y, z], w] == 0, D[f[w, x, y, z], x] == 0,
D[f[w, x, y, z], y] == 0, D[f[w, x, y, z], z] == 0};
red = Reduce[eqn, Backsubstitution -> True]
$left(z=0land x=0land w=-sqrt{1-y^2}right)lor left(z=0land x=0land w=sqrt{1-y^2}right)lor left(z=0land y=0land
w=-sqrt{1-x^2}right)lor left(z=0land y=0land w=sqrt{1-x^2}right)lor (z=0land y=-1land x=0land w=0)lor (z=0land y=0land x=0land
w=-1)lor (z=0land y=0land x=0land w=1)lor (z=0land y=1land x=0land w=0)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land
x=-frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=-frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=-frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land
w=-frac{1}{sqrt{6}}right)lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=-frac{1}{sqrt{3}}land
w=frac{1}{sqrt{6}}right)\
lor left(z=frac{1}{4 sqrt{3}}land y=frac{1}{sqrt{2}}land x=frac{1}{sqrt{3}}land w=frac{1}{sqrt{6}}right)$
First@eqn //. {ToRules[red]}
{True, True, True, True, True, True, True, True, True, True, True,
True, True, True, True, True}
answered Jan 6 at 1:09
Okkes DulgerciOkkes Dulgerci
5,4241919
answered Jan 6 at 1:09
Okkes DulgerciOkkes Dulgerci
5,4241919
answered Jan 6 at 1:09
Okkes DulgerciOkkes Dulgerci
5,4241919
answered Jan 6 at 1:09
Okkes DulgerciOkkes Dulgerci
5,4241919
5,4241919
$begingroup$
Yes, of course, I had already tried. I was almost certain it was a bug fromSolve, so I pointed out. Thank you very much anyway, always very kind!
$endgroup$
– TeM
Jan 6 at 1:14
4
$begingroup$
I believeSolveuse the functionReduceunder the hood. when you removeBacksubstitution -> True, you'll find implicit solution, somehowSolvemesses up somewhere and it is definitely a bug..
$endgroup$
– Okkes Dulgerci
Jan 6 at 1:18
add a comment |
$begingroup$
Yes, of course, I had already tried. I was almost certain it was a bug fromSolve, so I pointed out. Thank you very much anyway, always very kind!
$endgroup$
– TeM
Jan 6 at 1:14
4
$begingroup$
I believeSolveuse the functionReduceunder the hood. when you removeBacksubstitution -> True, you'll find implicit solution, somehowSolvemesses up somewhere and it is definitely a bug..
$endgroup$
– Okkes Dulgerci
Jan 6 at 1:18
$begingroup$
Yes, of course, I had already tried. I was almost certain it was a bug from
Solve, so I pointed out. Thank you very much anyway, always very kind!$endgroup$
– TeM
Jan 6 at 1:14
$begingroup$
Yes, of course, I had already tried. I was almost certain it was a bug from
Solve, so I pointed out. Thank you very much anyway, always very kind!$endgroup$
– TeM
Jan 6 at 1:14
4
4
$begingroup$
I believe
Solve use the function Reduce under the hood. when you remove Backsubstitution -> True, you'll find implicit solution, somehow Solve messes up somewhere and it is definitely a bug..$endgroup$
– Okkes Dulgerci
Jan 6 at 1:18
$begingroup$
I believe
Solve use the function Reduce under the hood. when you remove Backsubstitution -> True, you'll find implicit solution, somehow Solve messes up somewhere and it is definitely a bug..$endgroup$
– Okkes Dulgerci
Jan 6 at 1:18
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%2f188900%2fpossible-bug-in-solve-function%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
$begingroup$
You could use
List@ToRules@Reduce[eqn, {x, y, z, w}]to get all valid solutions. Filter for those that only have numeric values on the RHS of->.$endgroup$
– Szabolcs
Jan 5 at 22:30
$begingroup$
Select[sol, And @@ eqn /. # &]$endgroup$
– Bob Hanlon
Jan 5 at 23:53
5
$begingroup$
Next time, please do not add the bugs tag yourself on a question. The tag is only supposed to be added after your observations have been confirmed by other users.
$endgroup$
– J. M. is away♦
Jan 6 at 2:45