Mdthbs

First amendment and employment: Can an employer terminate you for speech?

The pronunciation of "protester"

A stranger from Norway wants to have money delivered to me

Are there any financial disadvantages to living significantly "below your means"?

How can a surrogate pass on genes to a fertilized embryo?

Accidentals - some in brackets, some not

Dereferencing a pointer in a 'for' loop initializer creates a segmentation fault

Non-OR journals which regularly publish OR research

How would I as a DM create a smart phone-like spell/device my players could use?

Why isn’t SHA-3 in wider use?

Why do oscilloscopes use SMPS instead of linear power supply?

Author changing name

How should an administrative assistant reply to student addressing them as "Professor" or "Doctor"?

Why aren’t emergency services using callsigns?

Infeasibility in mathematical optimization models

Am I overreacting to my team leader's unethical requests?

Does two puncture wounds mean venomous snake?

As a 16 year old, how can I keep my money safe from my mother?

In a topological space if there exists a loop that cannot be contracted to a point does there exist a simple loop that cannot be contracted also?

Why did the RAAF procure the F/A-18 despite being purpose-built for carriers?

How can I tell if a flight itinerary is fake?

If a Contingency spell has been cast on a creature, does the Simulacrum spell transfer the contingent spell to its duplicate?

Are there any differences in causality between linear and logistic regression?

What are the uses and limitations of Persuasion, Insight, and Deception against other PCs?

Optimal way to extract “positive part” of a multivariate polynomial

Get the first positive coefficient in polynomial?Multivariate Polynomial ManipulationHow do I find the constant term of a multivariate polynomial?Fishing for monomials in a nested or partially factored polynomial streamFunny behavior when computing dot product of coefficients with high-order polynomialsEfficiently strip off coefficients in front of variables?Easiest way to extract the coefficient of a polynomialGet the homogeneous part of a polynomial

.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ margin-bottom:0;
}

4

$begingroup$

I've got multivariate polynomials with numerical coefficients, like e. g.

p - s - p q^2 s^2 + 3 r s^2 + 3 r^2 s^2 - p r^2 s^2 - 2 q r^2 s^2 - 2 r^3 s^2 + s^3

and I would like to take the sum of those monomials with positive coefficients only.

Although for my purposes

FromCoefficientRules[Select[CoefficientRules[poly],Last[#]>0&],Variables[poly]]

seems to be quick enough, it involves translating to another form and back, so I feel there must be a more optimal way to do it, probably using some tricks with the internal representation of polynomials.

Is there?

performance-tuning polynomials algebraic-manipulation

share|improve this question

asked 13 hours ago

მამუკა ჯიბლაძემამუკა ჯიბლაძე

1,07255 silver badges2020 bronze badges

$endgroup$

add a comment | 

4

$begingroup$

I've got multivariate polynomials with numerical coefficients, like e. g.

p - s - p q^2 s^2 + 3 r s^2 + 3 r^2 s^2 - p r^2 s^2 - 2 q r^2 s^2 - 2 r^3 s^2 + s^3

and I would like to take the sum of those monomials with positive coefficients only.

Although for my purposes

FromCoefficientRules[Select[CoefficientRules[poly],Last[#]>0&],Variables[poly]]

seems to be quick enough, it involves translating to another form and back, so I feel there must be a more optimal way to do it, probably using some tricks with the internal representation of polynomials.

Is there?

performance-tuning polynomials algebraic-manipulation

share|improve this question

asked 13 hours ago

მამუკა ჯიბლაძემამუკა ჯიბლაძე

1,07255 silver badges2020 bronze badges

$endgroup$

add a comment | 

$begingroup$

I've got multivariate polynomials with numerical coefficients, like e. g.

p - s - p q^2 s^2 + 3 r s^2 + 3 r^2 s^2 - p r^2 s^2 - 2 q r^2 s^2 - 2 r^3 s^2 + s^3

and I would like to take the sum of those monomials with positive coefficients only.

Although for my purposes

FromCoefficientRules[Select[CoefficientRules[poly],Last[#]>0&],Variables[poly]]

seems to be quick enough, it involves translating to another form and back, so I feel there must be a more optimal way to do it, probably using some tricks with the internal representation of polynomials.

Is there?

performance-tuning polynomials algebraic-manipulation

share|improve this question

asked 13 hours ago

მამუკა ჯიბლაძემამუკა ჯიბლაძე

1,07255 silver badges2020 bronze badges

$endgroup$

p - s - p q^2 s^2 + 3 r s^2 + 3 r^2 s^2 - p r^2 s^2 - 2 q r^2 s^2 - 2 r^3 s^2 + s^3

FromCoefficientRules[Select[CoefficientRules[poly],Last[#]>0&],Variables[poly]]

share|improve this question

asked 13 hours ago

მამუკა ჯიბლაძემამუკა ჯიბლაძე

1,07255 silver badges2020 bronze badges

share|improve this question

asked 13 hours ago

მამუკა ჯიბლაძემამუკა ჯიბლაძე

1,07255 silver badges2020 bronze badges

asked 13 hours ago

მამუკა ჯიბლაძემამუკა ჯიბლაძე

1,07255 silver badges2020 bronze badges

asked 13 hours ago

მამუკა ჯიბლაძემამუკა ჯიბლაძე

1,07255 silver badges2020 bronze badges

3 Answers
3

active

oldest

votes

3

$begingroup$

This will delete the terms written with a leading minus sign:

nixneg[p_Plus] := DeleteCases[p, _?Internal`SyntacticNegativeQ];

nixneg[_?Internal`SyntacticNegativeQ] := 0;  (* 1-term case: neg *)

nixneg[p_] := p;                             (* 1-term case: nonneg *)

OP's example:

nixneg[poly]  (* use nixneg[Expand@poly] if needed *)

(*  p + 3 r s^2 + 3 r^2 s^2 + s^3  *)

Deletes negative constant terms, too:

nixneg[poly + 100]

nixneg[poly - 100]

(*

  100 + p + 3 r s^2 + 3 r^2 s^2 + s^3

  p + 3 r s^2 + 3 r^2 s^2 + s^3

*)

share|improve this answer

answered 9 hours ago

Michael E2Michael E2

157k1313 gold badges215215 silver badges511511 bronze badges

$endgroup$

add a comment | 

4

$begingroup$

Assuming poly is homogeneous (as in the example in the OP),

poly /. Times[_?Negative, _] -> 0

share|improve this answer

answered 13 hours ago

AccidentalFourierTransformAccidentalFourierTransform

6,57911 gold badge1212 silver badges4545 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Nice! But you mean without constant term rather than homogeneous, right? My polynomials might have constant terms, actually, but I am sure one can deal with them very quickly too
  $endgroup$
  – მამუკა ჯიბლაძე
  11 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @მამუკაჯიბლაძე oh, yes, I meant without constant term!
  $endgroup$
  – AccidentalFourierTransform
  11 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry! - have to accept the most complete one
  $endgroup$
  – მამუკა ჯიბლაძე
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @მამუკაჯიბლაძე no need to apologise, those are great answers too, clearly better than mine :-)
  $endgroup$
  – AccidentalFourierTransform
  4 hours ago
  

  
  
  
  

add a comment | 

3

$begingroup$

exp = p - s - p q^2 s^2 + 3 r s^2 + 3 r^2 s^2 - p r^2 s^2 - 2 q r^2 s^2 - 2 r^3 s^2 + s^3

Few additional ways to use Internal`SyntacticNegativeQ:

Select[Not @* Internal`SyntacticNegativeQ] @ exp

p + 3 r s^2 + 3 r^2 s^2 + s^3

share|improve this answer

answered 8 hours ago

kglrkglr

210k1010 gold badges241241 silver badges480480 bronze badges

$endgroup$

add a comment | 

Your Answer

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
});


}
});

draft saved

draft discarded

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

Name

Email

Required, but never shown

StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f203555%2foptimal-way-to-extract-positive-part-of-a-multivariate-polynomial%23new-answer', 'question_page');
}
);

Post as a guest

Name

Email

Required, but never shown

3

$begingroup$

This will delete the terms written with a leading minus sign:

nixneg[p_Plus] := DeleteCases[p, _?Internal`SyntacticNegativeQ];

nixneg[_?Internal`SyntacticNegativeQ] := 0;  (* 1-term case: neg *)

nixneg[p_] := p;                             (* 1-term case: nonneg *)

OP's example:

nixneg[poly]  (* use nixneg[Expand@poly] if needed *)

(*  p + 3 r s^2 + 3 r^2 s^2 + s^3  *)

Deletes negative constant terms, too:

nixneg[poly + 100]

nixneg[poly - 100]

(*

  100 + p + 3 r s^2 + 3 r^2 s^2 + s^3

  p + 3 r s^2 + 3 r^2 s^2 + s^3

*)

share|improve this answer

answered 9 hours ago

Michael E2Michael E2

157k1313 gold badges215215 silver badges511511 bronze badges

$endgroup$

add a comment | 

3

$begingroup$

This will delete the terms written with a leading minus sign:

nixneg[p_Plus] := DeleteCases[p, _?Internal`SyntacticNegativeQ];

nixneg[_?Internal`SyntacticNegativeQ] := 0;  (* 1-term case: neg *)

nixneg[p_] := p;                             (* 1-term case: nonneg *)

OP's example:

nixneg[poly]  (* use nixneg[Expand@poly] if needed *)

(*  p + 3 r s^2 + 3 r^2 s^2 + s^3  *)

Deletes negative constant terms, too:

nixneg[poly + 100]

nixneg[poly - 100]

(*

  100 + p + 3 r s^2 + 3 r^2 s^2 + s^3

  p + 3 r s^2 + 3 r^2 s^2 + s^3

*)

share|improve this answer

answered 9 hours ago

Michael E2Michael E2

157k1313 gold badges215215 silver badges511511 bronze badges

$endgroup$

add a comment | 

$begingroup$

This will delete the terms written with a leading minus sign:

nixneg[p_Plus] := DeleteCases[p, _?Internal`SyntacticNegativeQ];

nixneg[_?Internal`SyntacticNegativeQ] := 0;  (* 1-term case: neg *)

nixneg[p_] := p;                             (* 1-term case: nonneg *)

OP's example:

nixneg[poly]  (* use nixneg[Expand@poly] if needed *)

(*  p + 3 r s^2 + 3 r^2 s^2 + s^3  *)

Deletes negative constant terms, too:

nixneg[poly + 100]

nixneg[poly - 100]

(*

  100 + p + 3 r s^2 + 3 r^2 s^2 + s^3

  p + 3 r s^2 + 3 r^2 s^2 + s^3

*)

share|improve this answer

answered 9 hours ago

Michael E2Michael E2

157k1313 gold badges215215 silver badges511511 bronze badges

$endgroup$

nixneg[p_Plus] := DeleteCases[p, _?Internal`SyntacticNegativeQ];

nixneg[_?Internal`SyntacticNegativeQ] := 0;  (* 1-term case: neg *)

nixneg[p_] := p;                             (* 1-term case: nonneg *)

nixneg[poly]  (* use nixneg[Expand@poly] if needed *)

(*  p + 3 r s^2 + 3 r^2 s^2 + s^3  *)

nixneg[poly + 100]

nixneg[poly - 100]

(*

  100 + p + 3 r s^2 + 3 r^2 s^2 + s^3

  p + 3 r s^2 + 3 r^2 s^2 + s^3

*)

share|improve this answer

answered 9 hours ago

Michael E2Michael E2

157k1313 gold badges215215 silver badges511511 bronze badges

answered 9 hours ago

Michael E2Michael E2

157k1313 gold badges215215 silver badges511511 bronze badges

answered 9 hours ago

Michael E2Michael E2

157k1313 gold badges215215 silver badges511511 bronze badges

4

$begingroup$

Assuming poly is homogeneous (as in the example in the OP),

poly /. Times[_?Negative, _] -> 0

share|improve this answer

answered 13 hours ago

AccidentalFourierTransformAccidentalFourierTransform

6,57911 gold badge1212 silver badges4545 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Nice! But you mean without constant term rather than homogeneous, right? My polynomials might have constant terms, actually, but I am sure one can deal with them very quickly too
  $endgroup$
  – მამუკა ჯიბლაძე
  11 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @მამუკაჯიბლაძე oh, yes, I meant without constant term!
  $endgroup$
  – AccidentalFourierTransform
  11 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry! - have to accept the most complete one
  $endgroup$
  – მამუკა ჯიბლაძე
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @მამუკაჯიბლაძე no need to apologise, those are great answers too, clearly better than mine :-)
  $endgroup$
  – AccidentalFourierTransform
  4 hours ago
  

  
  
  
  

add a comment | 

4

$begingroup$

Assuming poly is homogeneous (as in the example in the OP),

poly /. Times[_?Negative, _] -> 0

share|improve this answer

answered 13 hours ago

AccidentalFourierTransformAccidentalFourierTransform

6,57911 gold badge1212 silver badges4545 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Nice! But you mean without constant term rather than homogeneous, right? My polynomials might have constant terms, actually, but I am sure one can deal with them very quickly too
  $endgroup$
  – მამუკა ჯიბლაძე
  11 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @მამუკაჯიბლაძე oh, yes, I meant without constant term!
  $endgroup$
  – AccidentalFourierTransform
  11 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry! - have to accept the most complete one
  $endgroup$
  – მამუკა ჯიბლაძე
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @მამუკაჯიბლაძე no need to apologise, those are great answers too, clearly better than mine :-)
  $endgroup$
  – AccidentalFourierTransform
  4 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

Assuming poly is homogeneous (as in the example in the OP),

poly /. Times[_?Negative, _] -> 0

share|improve this answer

answered 13 hours ago

AccidentalFourierTransformAccidentalFourierTransform

6,57911 gold badge1212 silver badges4545 bronze badges

$endgroup$

poly /. Times[_?Negative, _] -> 0

share|improve this answer

answered 13 hours ago

AccidentalFourierTransformAccidentalFourierTransform

6,57911 gold badge1212 silver badges4545 bronze badges

answered 13 hours ago

AccidentalFourierTransformAccidentalFourierTransform

6,57911 gold badge1212 silver badges4545 bronze badges

answered 13 hours ago

AccidentalFourierTransformAccidentalFourierTransform

6,57911 gold badge1212 silver badges4545 bronze badges

3

$begingroup$

exp = p - s - p q^2 s^2 + 3 r s^2 + 3 r^2 s^2 - p r^2 s^2 - 2 q r^2 s^2 - 2 r^3 s^2 + s^3

Few additional ways to use Internal`SyntacticNegativeQ:

Select[Not @* Internal`SyntacticNegativeQ] @ exp

p + 3 r s^2 + 3 r^2 s^2 + s^3

share|improve this answer

answered 8 hours ago

kglrkglr

210k1010 gold badges241241 silver badges480480 bronze badges

$endgroup$

add a comment | 

3

$begingroup$

exp = p - s - p q^2 s^2 + 3 r s^2 + 3 r^2 s^2 - p r^2 s^2 - 2 q r^2 s^2 - 2 r^3 s^2 + s^3

Few additional ways to use Internal`SyntacticNegativeQ:

Select[Not @* Internal`SyntacticNegativeQ] @ exp

p + 3 r s^2 + 3 r^2 s^2 + s^3

share|improve this answer

answered 8 hours ago

kglrkglr

210k1010 gold badges241241 silver badges480480 bronze badges

$endgroup$

add a comment | 

$begingroup$

exp = p - s - p q^2 s^2 + 3 r s^2 + 3 r^2 s^2 - p r^2 s^2 - 2 q r^2 s^2 - 2 r^3 s^2 + s^3

Few additional ways to use Internal`SyntacticNegativeQ:

Select[Not @* Internal`SyntacticNegativeQ] @ exp

p + 3 r s^2 + 3 r^2 s^2 + s^3

share|improve this answer

answered 8 hours ago

kglrkglr

210k1010 gold badges241241 silver badges480480 bronze badges

$endgroup$

exp = p - s - p q^2 s^2 + 3 r s^2 + 3 r^2 s^2 - p r^2 s^2 - 2 q r^2 s^2 - 2 r^3 s^2 + s^3

Select[Not @* Internal`SyntacticNegativeQ] @ exp

share|improve this answer

answered 8 hours ago

kglrkglr

210k1010 gold badges241241 silver badges480480 bronze badges

answered 8 hours ago

kglrkglr

210k1010 gold badges241241 silver badges480480 bronze badges

answered 8 hours ago

kglrkglr

210k1010 gold badges241241 silver badges480480 bronze badges