Jump to navigation Jump to search

General

Display information for equation id:math.268136.10 on revision:268136

* Page found: Pseudo-Boolean function (eq math.268136.10)

(force rerendering)

Occurrences on the following pages:

Hash: 037935127383c734dcb152dc775276b2

TeX (original user input): 

 f(\boldsymbol{x}) + f(\boldsymbol{y}) \ge  f(\boldsymbol{x} \wedge \boldsymbol{y}) + f(\boldsymbol{x} \vee \boldsymbol{y})

TeX (checked): 

f({\boldsymbol {x}})+f({\boldsymbol {y}})\geq f({\boldsymbol {x}}\wedge {\boldsymbol {y}})+f({\boldsymbol {x}}\vee {\boldsymbol {y}})

LaTeXML (experimental; uses MathML) rendering

MathML (5.667 KB / 907 B) :

f ⁢ ( 𝒙 ) + f ⁢ ( 𝒚 ) ≥ f ⁢ ( 𝒙 ∧ 𝒚 ) + f ⁢ ( 𝒙 ∨ 𝒚 ) 𝑓 𝒙 𝑓 𝒚 𝑓 𝒙 𝒚 𝑓 𝒙 𝒚 {\displaystyle f({\boldsymbol{x}})+f({\boldsymbol{y}})\geq f({\boldsymbol{x}}% \wedge{\boldsymbol{y}})+f({\boldsymbol{x}}\vee{\boldsymbol{y}})} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle f({\boldsymbol{x}})+f({\boldsymbol{y}})\geq f({\boldsymbol{x}}%&#10;\wedge{\boldsymbol{y}})+f({\boldsymbol{x}}\vee{\boldsymbol{y}})}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">
      <mrow id="p1.1.m1.1.24.1" xref="p1.1.m1.1.24.1.cmml">
        <mrow id="p1.1.m1.1.24.1.1" xref="p1.1.m1.1.24.1.1.cmml">
          <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">f</mi>
          <mo id="p1.1.m1.1.24.1.1.1" xref="p1.1.m1.1.24.1.1.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.24.1.1.2" xref="p1.1.m1.1.24.1.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.2" xref="p1.1.m1.1.24.1.1.cmml">(</mo>
            <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">𝒙</mi>
            <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.24.1.1.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">+</mo>
        <mrow id="p1.1.m1.1.24.1.2" xref="p1.1.m1.1.24.1.2.cmml">
          <mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">f</mi>
          <mo id="p1.1.m1.1.24.1.2.1" xref="p1.1.m1.1.24.1.2.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.24.1.2.2" xref="p1.1.m1.1.24.1.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.7" xref="p1.1.m1.1.24.1.2.cmml">(</mo>
            <mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">𝒚</mi>
            <mo stretchy="false" id="p1.1.m1.1.9" xref="p1.1.m1.1.24.1.2.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">≥</mo>
      <mrow id="p1.1.m1.1.24.2" xref="p1.1.m1.1.24.2.cmml">
        <mrow id="p1.1.m1.1.24.2.1" xref="p1.1.m1.1.24.2.1.cmml">
          <mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">f</mi>
          <mo id="p1.1.m1.1.24.2.1.1" xref="p1.1.m1.1.24.2.1.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.24.2.1.2" xref="p1.1.m1.1.24.2.1.2.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.12" xref="p1.1.m1.1.24.2.1.2.2.cmml">(</mo>
            <mrow id="p1.1.m1.1.24.2.1.2.2" xref="p1.1.m1.1.24.2.1.2.2.cmml">
              <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">𝒙</mi>
              <mo id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">∧</mo>
              <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">𝒚</mi>
            </mrow>
            <mo stretchy="false" id="p1.1.m1.1.16" xref="p1.1.m1.1.24.2.1.2.2.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">+</mo>
        <mrow id="p1.1.m1.1.24.2.2" xref="p1.1.m1.1.24.2.2.cmml">
          <mi id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">f</mi>
          <mo id="p1.1.m1.1.24.2.2.1" xref="p1.1.m1.1.24.2.2.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.24.2.2.2" xref="p1.1.m1.1.24.2.2.2.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.19" xref="p1.1.m1.1.24.2.2.2.2.cmml">(</mo>
            <mrow id="p1.1.m1.1.24.2.2.2.2" xref="p1.1.m1.1.24.2.2.2.2.cmml">
              <mi id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">𝒙</mi>
              <mo id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">∨</mo>
              <mi id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">𝒚</mi>
            </mrow>
            <mo stretchy="false" id="p1.1.m1.1.23" xref="p1.1.m1.1.24.2.2.2.2.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">
        <geq id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10"/>
        <apply id="p1.1.m1.1.24.1.cmml" xref="p1.1.m1.1.24.1">
          <plus id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
          <apply id="p1.1.m1.1.24.1.1.cmml" xref="p1.1.m1.1.24.1.1">
            <times id="p1.1.m1.1.24.1.1.1.cmml" xref="p1.1.m1.1.24.1.1.1"/>
            <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑓</ci>
            <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝒙</ci>
          </apply>
          <apply id="p1.1.m1.1.24.1.2.cmml" xref="p1.1.m1.1.24.1.2">
            <times id="p1.1.m1.1.24.1.2.1.cmml" xref="p1.1.m1.1.24.1.2.1"/>
            <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">𝑓</ci>
            <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">𝒚</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.24.2.cmml" xref="p1.1.m1.1.24.2">
          <plus id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17"/>
          <apply id="p1.1.m1.1.24.2.1.cmml" xref="p1.1.m1.1.24.2.1">
            <times id="p1.1.m1.1.24.2.1.1.cmml" xref="p1.1.m1.1.24.2.1.1"/>
            <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">𝑓</ci>
            <apply id="p1.1.m1.1.24.2.1.2.2.cmml" xref="p1.1.m1.1.24.2.1.2">
              <and id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14"/>
              <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">𝒙</ci>
              <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">𝒚</ci>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.24.2.2.cmml" xref="p1.1.m1.1.24.2.2">
            <times id="p1.1.m1.1.24.2.2.1.cmml" xref="p1.1.m1.1.24.2.2.1"/>
            <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">𝑓</ci>
            <apply id="p1.1.m1.1.24.2.2.2.2.cmml" xref="p1.1.m1.1.24.2.2.2">
              <or id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21"/>
              <ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">𝒙</ci>
              <ci id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">𝒚</ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle f({\boldsymbol{x}})+f({\boldsymbol{y}})\geq f({\boldsymbol{x}}%
\wedge{\boldsymbol{y}})+f({\boldsymbol{x}}\vee{\boldsymbol{y}})}</annotation>
  </semantics>
</math>

SVG (8.181 KB / 2.592 KB) :

f times left-parenthesis 𝒙 right-parenthesis plus f times left-parenthesis 𝒚 right-parenthesis greater-than-or-equal-to f times left-parenthesis 𝒙 logical-and 𝒚 right-parenthesis plus f times left-parenthesis 𝒙 logical-or 𝒚 right-parenthesis

SVG (MathML can be enabled via browser plugin) rendering

MathML (1.672 KB / 393 B) :

f ( x ) + f ( y ) ≥ f ( x ∧ y ) + f ( x ∨ y ) {\displaystyle f({\boldsymbol {x}})+f({\boldsymbol {y}})\geq f({\boldsymbol {x}}\wedge {\boldsymbol {y}})+f({\boldsymbol {x}}\vee {\boldsymbol {y}})} 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle f({\boldsymbol {x}})+f({\boldsymbol {y}})\geq f({\boldsymbol {x}}\wedge {\boldsymbol {y}})+f({\boldsymbol {x}}\vee {\boldsymbol {y}})}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>f</mi>
        <mo stretchy="false">(</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="bold-italic">x</mi>
        </mrow>
        <mo stretchy="false">)</mo>
        <mo>+</mo>
        <mi>f</mi>
        <mo stretchy="false">(</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="bold-italic">y</mi>
        </mrow>
        <mo stretchy="false">)</mo>
        <mo>&#x2265;<!-- ≥ --></mo>
        <mi>f</mi>
        <mo stretchy="false">(</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="bold-italic">x</mi>
        </mrow>
        <mo>&#x2227;<!-- ∧ --></mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="bold-italic">y</mi>
        </mrow>
        <mo stretchy="false">)</mo>
        <mo>+</mo>
        <mi>f</mi>
        <mo stretchy="false">(</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="bold-italic">x</mi>
        </mrow>
        <mo>&#x2228;<!-- ∨ --></mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="bold-italic">y</mi>
        </mrow>
        <mo stretchy="false">)</mo>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle f({\boldsymbol {x}})+f({\boldsymbol {y}})\geq f({\boldsymbol {x}}\wedge {\boldsymbol {y}})+f({\boldsymbol {x}}\vee {\boldsymbol {y}})}</annotation>
  </semantics>
</math>

SVG (5.611 KB / 2.29 KB) :

{\displaystyle f({\boldsymbol {x}})+f({\boldsymbol {y}})\geq f({\boldsymbol {x}}\wedge {\boldsymbol {y}})+f({\boldsymbol {x}}\vee {\boldsymbol {y}})}

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Pseudo-Boolean function page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Retrieved from "https://en.formulasearchengine.com/wiki/Special:FormulaInfo"