Esempio: semplificazione e riscrittura delle espressioni

Matematica simbolica > Utilizzo della matematica simbolica > Semplificazione e riscrittura di espressioni > Esempio: semplificazione e riscrittura delle espressioni

Utilizzare le parole chiave simboliche combine e rewrite per combinare e riscrivere espressioni.

Parola chiave: simplify

• Semplificare le seguenti espressioni:

• Inserire l'operatore di valutazione simbolica.

• Inserire la parola chiave simplify nel segnaposto.

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    <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>

Parola chiave: combine

• Utilizzare la parola chiave combine per combinare la seguente espressione:

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    <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>

La parola chiave combine non influisce sul risultato.

• Aggiungere il modificatore sincos per specificare la riscrittura del risultato in termini di seno o coseno.

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    <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>

• Utilizzare la parola chiave combine con altri modificatori per combinare più espressioni.

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        <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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      <apply>
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        <apply>
          <mult />
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          <apply>
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            <real>3</real>
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        <apply>
          <mult />
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          <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>

Fare clic per copiare questa espressione

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      <command>
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          <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>
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          <apply>
            <id xml:space="preserve" labels="FUNCTION">log</id>
            <id xml:space="preserve" labels="*">b</id>
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      </symResult>
    </symEval>
  </math>
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        <apply>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sinh</id>
          <id xml:space="preserve">y</id>
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      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">combine</id>
          <id xml:space="preserve">sinhcosh</id>
        </sequence>
      </command>
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        <apply>
          <div />
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            <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>
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              <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>

Parola chiave: rewrite

• Utilizzare la parola chiave rewrite per riscrivere l'espressione seguente utilizzando tipi specifici di identità:

PTC Mathcad restituisce un errore perché rewrite richiede un modificatore.

• Aggiungere il modificatore exp.

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      <apply>
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          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">exp</id>
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            <neg />
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                <imag symbol="i">1</imag>
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                    <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 />
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                            <mult />
                            <id xml:space="preserve" labels="*">x</id>
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                    </apply>
                  </apply>
                </parens>
              </apply>
            </parens>
          </apply>
          <real>2</real>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

PTC Mathcad riscrive sin secondo le funzioni esponenziali.

• Utilizzare la parola chiave rewrite con altri modificatori per ottenere il tipo di risultato desiderato.

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      <symResult>
        <apply>
          <plus />
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            <apply>
              <pow />
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                <id xml:space="preserve" labels="FUNCTION">cos</id>
                <id xml:space="preserve" labels="*">x</id>
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              <real>2</real>
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          <real>1</real>
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  </math>
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            <plus />
            <apply>
              <nthRoot />
              <placeholder />
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                <plus />
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                  <id xml:space="preserve" labels="*">x</id>
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                <real>1</real>
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            <id xml:space="preserve" labels="*">x</id>
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  </math>
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          <id xml:space="preserve">rewrite</id>
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