Is $X + frac{2}{X}$ a rational quadratic form, where $X in mathbb{Q} setminus mathbb{Z}$?
$begingroup$
First of all, I apologize for the rather silly question. This came up while I was scouring the Internet on a mathematical terminology appropriate for a concept that I need for a paper which I am currently writing.
So here it is:
Is $X + frac{2}{X}$ a rational quadratic form, where $X in mathbb{Q} setminus mathbb{Z}$?
Or to put in another way:
Can the rational function $X + frac{2}{X}$ be represented by a quadratic form, where $X in mathbb{Q} setminus mathbb{Z}$?
I know that I can just check Cassels' Rational Quadratic Forms, unfortunately the nearest university library is a bit far from my place of residence (not to mention being closed during the holidays).
quadratic-forms representations-by-quadratic-forms
asked Dec 31 '18 at 8:50
Jose Arnaldo Bebita-DrisJose Arnaldo Bebita-Dris
5,27452045
$endgroup$
add a comment |
$begingroup$
First of all, I apologize for the rather silly question. This came up while I was scouring the Internet on a mathematical terminology appropriate for a concept that I need for a paper which I am currently writing.
So here it is:
Is $X + frac{2}{X}$ a rational quadratic form, where $X in mathbb{Q} setminus mathbb{Z}$?
Or to put in another way:
Can the rational function $X + frac{2}{X}$ be represented by a quadratic form, where $X in mathbb{Q} setminus mathbb{Z}$?
I know that I can just check Cassels' Rational Quadratic Forms, unfortunately the nearest university library is a bit far from my place of residence (not to mention being closed during the holidays).
quadratic-forms representations-by-quadratic-forms
asked Dec 31 '18 at 8:50
Jose Arnaldo Bebita-DrisJose Arnaldo Bebita-Dris
5,27452045
$endgroup$
$begingroup$
@flawr: I would go with the definition in Wikipedia, although honestly, I was not able to spot an actual definition for rational quadratic form but only for quadratic form per se.
$endgroup$
– Jose Arnaldo Bebita-Dris
Dec 31 '18 at 9:41
$begingroup$
My apologies! I meant to say $X in mathbb{Q} setminus mathbb{Z}$. Editing my question now to reflect this change.
$endgroup$
– Jose Arnaldo Bebita-Dris
Jan 25 at 8:09
add a comment |
$begingroup$
First of all, I apologize for the rather silly question. This came up while I was scouring the Internet on a mathematical terminology appropriate for a concept that I need for a paper which I am currently writing.
So here it is:
Is $X + frac{2}{X}$ a rational quadratic form, where $X in mathbb{Q} setminus mathbb{Z}$?
Or to put in another way:
Can the rational function $X + frac{2}{X}$ be represented by a quadratic form, where $X in mathbb{Q} setminus mathbb{Z}$?
I know that I can just check Cassels' Rational Quadratic Forms, unfortunately the nearest university library is a bit far from my place of residence (not to mention being closed during the holidays).
quadratic-forms representations-by-quadratic-forms
asked Dec 31 '18 at 8:50
Jose Arnaldo Bebita-DrisJose Arnaldo Bebita-Dris
5,27452045
$endgroup$
First of all, I apologize for the rather silly question. This came up while I was scouring the Internet on a mathematical terminology appropriate for a concept that I need for a paper which I am currently writing.
So here it is:
Is $X + frac{2}{X}$ a rational quadratic form, where $X in mathbb{Q} setminus mathbb{Z}$?
Or to put in another way:
Can the rational function $X + frac{2}{X}$ be represented by a quadratic form, where $X in mathbb{Q} setminus mathbb{Z}$?
I know that I can just check Cassels' Rational Quadratic Forms, unfortunately the nearest university library is a bit far from my place of residence (not to mention being closed during the holidays).
quadratic-forms representations-by-quadratic-forms
quadratic-forms representations-by-quadratic-forms
asked Dec 31 '18 at 8:50
Jose Arnaldo Bebita-DrisJose Arnaldo Bebita-Dris
5,27452045
asked Dec 31 '18 at 8:50
Jose Arnaldo Bebita-DrisJose Arnaldo Bebita-Dris
5,27452045
edited Jan 25 at 8:10
Jose Arnaldo Bebita-Dris
asked Dec 31 '18 at 8:50
Jose Arnaldo Bebita-DrisJose Arnaldo Bebita-Dris
5,27452045
asked Dec 31 '18 at 8:50
Jose Arnaldo Bebita-DrisJose Arnaldo Bebita-Dris
5,27452045
asked Dec 31 '18 at 8:50
Jose Arnaldo Bebita-DrisJose Arnaldo Bebita-Dris
5,27452045
5,27452045
$begingroup$
@flawr: I would go with the definition in Wikipedia, although honestly, I was not able to spot an actual definition for rational quadratic form but only for quadratic form per se.
$endgroup$
– Jose Arnaldo Bebita-Dris
Dec 31 '18 at 9:41
$begingroup$
My apologies! I meant to say $X in mathbb{Q} setminus mathbb{Z}$. Editing my question now to reflect this change.
$endgroup$
– Jose Arnaldo Bebita-Dris
Jan 25 at 8:09
add a comment |
$begingroup$
@flawr: I would go with the definition in Wikipedia, although honestly, I was not able to spot an actual definition for rational quadratic form but only for quadratic form per se.
$endgroup$
– Jose Arnaldo Bebita-Dris
Dec 31 '18 at 9:41
$begingroup$
My apologies! I meant to say $X in mathbb{Q} setminus mathbb{Z}$. Editing my question now to reflect this change.
$endgroup$
– Jose Arnaldo Bebita-Dris
Jan 25 at 8:09
$begingroup$
@flawr: I would go with the definition in Wikipedia, although honestly, I was not able to spot an actual definition for rational quadratic form but only for quadratic form per se.
$endgroup$
– Jose Arnaldo Bebita-Dris
Dec 31 '18 at 9:41
$begingroup$
@flawr: I would go with the definition in Wikipedia, although honestly, I was not able to spot an actual definition for rational quadratic form but only for quadratic form per se.
$endgroup$
– Jose Arnaldo Bebita-Dris
Dec 31 '18 at 9:41
$begingroup$
My apologies! I meant to say $X in mathbb{Q} setminus mathbb{Z}$. Editing my question now to reflect this change.
$endgroup$
– Jose Arnaldo Bebita-Dris
Jan 25 at 8:09
$begingroup$
My apologies! I meant to say $X in mathbb{Q} setminus mathbb{Z}$. Editing my question now to reflect this change.
$endgroup$
– Jose Arnaldo Bebita-Dris
Jan 25 at 8:09
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
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: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
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
},
noCode: 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%2fmath.stackexchange.com%2fquestions%2f3057522%2fis-x-frac2x-a-rational-quadratic-form-where-x-in-mathbbq-setminu%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics 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%2fmath.stackexchange.com%2fquestions%2f3057522%2fis-x-frac2x-a-rational-quadratic-form-where-x-in-mathbbq-setminu%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
$begingroup$
@flawr: I would go with the definition in Wikipedia, although honestly, I was not able to spot an actual definition for rational quadratic form but only for quadratic form per se.
$endgroup$
– Jose Arnaldo Bebita-Dris
Dec 31 '18 at 9:41
$begingroup$
My apologies! I meant to say $X in mathbb{Q} setminus mathbb{Z}$. Editing my question now to reflect this change.
$endgroup$
– Jose Arnaldo Bebita-Dris
Jan 25 at 8:09