Exemple : Simplification et réécriture d'expressions

Mathématiques symboliques > Utilisation des mathématiques symboliques > Simplification et réécriture d'expressions > Exemple : Simplification et réécriture d'expressions

Les mots-clés symboliques combine et rewrite permettent de combiner et de réécrire des expressions.

Mot-clé : simplify

• Simplifiez les expressions suivantes :

• Insérez l'opérateur d'évaluation symbolique.

• Insérez le mot-clé simplify dans la marque de réservation.

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  <math resultRef="24">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
        <apply>
          <pow />
          <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
          <apply>
            <mult />
            <real>2</real>
            <id xml:space="preserve">x</id>
          </apply>
        </apply>
        <apply>
          <pow />
          <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
          <apply>
            <mult />
            <real>7</real>
            <id xml:space="preserve">y</id>
          </apply>
        </apply>
      </apply>
      <command>
        <id xml:space="preserve">simplify</id>
      </command>
      <symResult>
        <apply>
          <pow />
          <id xml:space="preserve" labels="CONSTANT">e</id>
          <apply>
            <plus />
            <apply>
              <mult />
              <real>7</real>
              <id xml:space="preserve" labels="*">y</id>
            </apply>
            <apply>
              <mult />
              <real>2</real>
              <id xml:space="preserve" labels="*">x</id>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

Mot-clé : combine

• Le mot-clé combine permet de combiner l'expression suivante :

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  <math resultRef="26">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
        <apply>
          <mult />
          <real>2</real>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sin</id>
            <id xml:space="preserve">x</id>
          </apply>
        </apply>
        <apply>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">cos</id>
          <id xml:space="preserve">x</id>
        </apply>
      </apply>
      <command>
        <id xml:space="preserve">combine</id>
      </command>
      <symResult>
        <apply>
          <mult />
          <apply>
            <mult />
            <real>2</real>
            <apply>
              <id xml:space="preserve" labels="FUNCTION">cos</id>
              <id xml:space="preserve" labels="*">x</id>
            </apply>
          </apply>
          <apply>
            <id xml:space="preserve" labels="FUNCTION">sin</id>
            <id xml:space="preserve" labels="*">x</id>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

Le mot-clé combine n'affecte pas le résultat.

• Ajoutez le modificateur sincos pour indiquer de réécrire le résultat en termes de sinus ou cosinus.

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  <math resultRef="27">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
        <apply>
          <mult />
          <real>2</real>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sin</id>
            <id xml:space="preserve">x</id>
          </apply>
        </apply>
        <apply>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">cos</id>
          <id xml:space="preserve">x</id>
        </apply>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">combine</id>
          <id xml:space="preserve">sincos</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <id xml:space="preserve" labels="FUNCTION">sin</id>
          <apply>
            <mult />
            <real>2</real>
            <id xml:space="preserve" labels="*">x</id>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

• Utilisez le mot-clé combine avec d'autres modificateurs pour combiner plus d'expressions.

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      <apply>
        <mult />
        <apply>
          <pow />
          <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
          <id xml:space="preserve">x</id>
        </apply>
        <apply>
          <pow />
          <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
          <apply>
            <mult />
            <real>2</real>
            <id xml:space="preserve">y</id>
          </apply>
        </apply>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">combine</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">exp</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <pow />
          <id xml:space="preserve" labels="CONSTANT">e</id>
          <apply>
            <plus />
            <apply>
              <mult />
              <real>2</real>
              <id xml:space="preserve" labels="*">y</id>
            </apply>
            <id xml:space="preserve" labels="*">x</id>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <minus />
        <apply>
          <mult />
          <real>2</real>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">ln</id>
            <real>3</real>
          </apply>
        </apply>
        <apply>
          <mult />
          <real>3</real>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">ln</id>
            <real>2</real>
          </apply>
        </apply>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">combine</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">ln</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <id xml:space="preserve" labels="FUNCTION">ln</id>
          <apply>
            <div />
            <real>9</real>
            <real>8</real>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <minus />
        <apply>
          <mult />
          <real>2</real>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">log</id>
            <sequence>
              <real>3</real>
              <id xml:space="preserve">b</id>
            </sequence>
          </apply>
        </apply>
        <apply>
          <mult />
          <real>3</real>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">log</id>
            <sequence>
              <real>2</real>
              <id xml:space="preserve">b</id>
            </sequence>
          </apply>
        </apply>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">combine</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">log</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <id xml:space="preserve" labels="FUNCTION">log</id>
            <apply>
              <div />
              <real>9</real>
              <real>8</real>
            </apply>
          </apply>
          <apply>
            <id xml:space="preserve" labels="FUNCTION">log</id>
            <id xml:space="preserve" labels="*">b</id>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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  <math resultRef="31">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
        <apply>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sinh</id>
          <id xml:space="preserve">x</id>
        </apply>
        <apply>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sinh</id>
          <id xml:space="preserve">y</id>
        </apply>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">combine</id>
          <id xml:space="preserve">sinhcosh</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <minus />
            <apply>
              <id xml:space="preserve" labels="FUNCTION">cosh</id>
              <apply>
                <plus />
                <id xml:space="preserve" labels="*">y</id>
                <id xml:space="preserve" labels="*">x</id>
              </apply>
            </apply>
            <apply>
              <id xml:space="preserve" labels="FUNCTION">cosh</id>
              <apply>
                <minus />
                <id xml:space="preserve" labels="*">y</id>
                <id xml:space="preserve" labels="*">x</id>
              </apply>
            </apply>
          </apply>
          <real>2</real>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

Mot-clé : rewrite

• Le mot-clé rewrite permet de réécrire l'expression suivante en utilisant des types spécifiques d'identités :

PTC Mathcad renvoie une erreur car rewrite requiert un modificateur.

• Ajoutez le modificateur exp.

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sin</id>
        <id xml:space="preserve">x</id>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">exp</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <neg />
            <parens>
              <apply>
                <mult />
                <imag symbol="i">1</imag>
                <parens>
                  <apply>
                    <minus />
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="CONSTANT">e</id>
                      <apply>
                        <mult />
                        <id xml:space="preserve" labels="*">x</id>
                        <imag symbol="i">1</imag>
                      </apply>
                    </apply>
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="CONSTANT">e</id>
                      <apply>
                        <neg />
                        <parens>
                          <apply>
                            <mult />
                            <id xml:space="preserve" labels="*">x</id>
                            <imag symbol="i">1</imag>
                          </apply>
                        </parens>
                      </apply>
                    </apply>
                  </apply>
                </parens>
              </apply>
            </parens>
          </apply>
          <real>2</real>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

PTC Mathcad réécrit sin en termes de fonctions exponentielles.

• Utilisez le mot-clé rewrite avec d'autres modificateurs pour obtenir le type de résultat souhaité.

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <pow />
        <apply>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sin</id>
          <id xml:space="preserve">x</id>
        </apply>
        <real>2</real>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">cos</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <plus />
          <apply>
            <neg />
            <apply>
              <pow />
              <apply>
                <id xml:space="preserve" labels="FUNCTION">cos</id>
                <id xml:space="preserve" labels="*">x</id>
              </apply>
              <real>2</real>
            </apply>
          </apply>
          <real>1</real>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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        <id xml:space="preserve">x</id>
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      <command>
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          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">ln</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <id xml:space="preserve" labels="FUNCTION">ln</id>
          <apply>
            <plus />
            <apply>
              <nthRoot />
              <placeholder />
              <apply>
                <plus />
                <apply>
                  <pow />
                  <id xml:space="preserve" labels="*">x</id>
                  <real>2</real>
                </apply>
                <real>1</real>
              </apply>
            </apply>
            <id xml:space="preserve" labels="*">x</id>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">ln</id>
        <real>7</real>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">log</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <id xml:space="preserve" labels="FUNCTION">log</id>
            <real>7</real>
          </apply>
          <apply>
            <id xml:space="preserve" labels="FUNCTION">log</id>
            <id xml:space="preserve" labels="CONSTANT">e</id>
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        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <plus />
        <apply>
          <neg />
          <apply>
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            <apply>
              <mult />
              <apply>
                <pow />
                <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
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                  <mult />
                  <id xml:space="preserve">x</id>
                  <imag symbol="i">1</imag>
                </apply>
              </apply>
              <imag symbol="i">1</imag>
            </apply>
            <real>2</real>
          </apply>
        </apply>
        <apply>
          <div />
          <apply>
            <mult />
            <apply>
              <pow />
              <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
              <apply>
                <neg />
                <parens>
                  <apply>
                    <mult />
                    <id xml:space="preserve">x</id>
                    <imag symbol="i">1</imag>
                  </apply>
                </parens>
              </apply>
            </apply>
            <imag symbol="i">1</imag>
          </apply>
          <real>2</real>
        </apply>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve">sincos</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <id xml:space="preserve" labels="FUNCTION">sin</id>
          <id xml:space="preserve" labels="*">x</id>
        </apply>
      </symResult>
    </symEval>
  </math>
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          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sinh</id>
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      <symResult>
        <apply>
          <plus />
          <apply>
            <plus />
            <apply>
              <id xml:space="preserve" labels="FUNCTION">sinh</id>
              <id xml:space="preserve" labels="*">x</id>
            </apply>
            <apply>
              <mult />
              <real>2</real>
              <apply>
                <pow />
                <apply>
                  <id xml:space="preserve" labels="FUNCTION">sinh</id>
                  <apply>
                    <div />
                    <id xml:space="preserve" labels="*">x</id>
                    <real>2</real>
                  </apply>
                </apply>
                <real>2</real>
              </apply>
            </apply>
          </apply>
          <real>1</real>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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        <apply>
          <plus />
          <apply>
            <neg />
            <apply>
              <div />
              <real>2</real>
              <apply>
                <plus />
                <apply>
                  <pow />
                  <id xml:space="preserve" labels="CONSTANT">e</id>
                  <apply>
                    <mult />
                    <real>2</real>
                    <id xml:space="preserve" labels="*">x</id>
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                <real>1</real>
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          <real>1</real>
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  </math>
</region>

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            <id xml:space="preserve">rewrite</id>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">exp</id>
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            <plus />
            <apply>
              <neg />
              <apply>
                <div />
                <real>2</real>
                <apply>
                  <plus />
                  <apply>
                    <pow />
                    <id xml:space="preserve" labels="CONSTANT">e</id>
                    <apply>
                      <mult />
                      <real>2</real>
                      <id xml:space="preserve" labels="*">x</id>
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                  <real>1</real>
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            <real>1</real>
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          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">tanh</id>
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        <apply>
          <id xml:space="preserve" labels="FUNCTION">tanh</id>
          <id xml:space="preserve" labels="*">x</id>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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              <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">exp</id>
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            <id xml:space="preserve">brut</id>
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                <pow />
                <id xml:space="preserve" labels="CONSTANT">e</id>
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                  <real>2</real>
                  <id xml:space="preserve" labels="*">x</id>
                </apply>
              </apply>
              <real>1</real>
            </apply>
            <apply>
              <plus />
              <apply>
                <pow />
                <id xml:space="preserve" labels="CONSTANT">e</id>
                <apply>
                  <mult />
                  <real>2</real>
                  <id xml:space="preserve" labels="*">x</id>
                </apply>
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              <real>1</real>
            </apply>
          </apply>
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      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">rewrite</id>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">tanh</id>
          </sequence>
          <id xml:space="preserve">brut</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <minus />
            <apply>
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              <parens>
                <apply>
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                    <id xml:space="preserve" labels="FUNCTION">tanh</id>
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            <parens>
              <apply>
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                <apply>
                  <id xml:space="preserve" labels="FUNCTION">tanh</id>
                  <id xml:space="preserve" labels="*">x</id>
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          <apply>
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            <apply>
              <minus />
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                <id xml:space="preserve" labels="FUNCTION">tanh</id>
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                  <id xml:space="preserve" labels="FUNCTION">tanh</id>
                  <id xml:space="preserve" labels="*">x</id>
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        </apply>
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    </symEval>
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              <id xml:space="preserve" labels="FUNCTION">Γ</id>
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                <id xml:space="preserve" labels="*">q</id>
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Rubriques associées

A propos de la simplification et de la réécriture d'expressions

Combinaison d'expressions

Réécriture d'expressions

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