Risoluzione delle equazioni mediante i modificatori generati ed eval

Matematica simbolica > Utilizzo della matematica simbolica > Risoluzione delle equazioni mediante i modificatori generati ed eval

1. Definire e risolvere due equazioni per le variabili utilizzando un operatore booleano e la parola chiave solve. La soluzione viene restituita in termini di z.

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  <math resultRef="5">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <matrix rows="2" cols="1">
        <apply>
          <equal />
          <apply>
            <plus />
            <apply>
              <mult />
              <real>2</real>
              <id xml:space="preserve">x</id>
            </apply>
            <apply>
              <mult />
              <real>3</real>
              <id xml:space="preserve">y</id>
            </apply>
          </apply>
          <real>4</real>
        </apply>
        <apply>
          <equal />
          <apply>
            <plus />
            <apply>
              <mult />
              <real>2</real>
              <id xml:space="preserve">x</id>
            </apply>
            <id xml:space="preserve">z</id>
          </apply>
          <real>8</real>
        </apply>
      </matrix>
      <command>
        <sequence>
          <sequence>
            <sequence>
              <sequence>
                <id xml:space="preserve">solve</id>
                <id xml:space="preserve">x</id>
              </sequence>
              <id xml:space="preserve">y</id>
            </sequence>
            <id xml:space="preserve">z</id>
          </sequence>
          <id xml:space="preserve">fully</id>
        </sequence>
      </command>
      <symResult>
        <program>
          <if>
            <test>
              <apply>
                <elementOf />
                <id xml:space="preserve" labels="*">_z</id>
                <id xml:space="preserve" labels="CONSTANT">ℂ</id>
              </apply>
            </test>
            <then>
              <program>
                <matrix rows="1" cols="3">
                  <apply>
                    <div />
                    <apply>
                      <plus />
                      <apply>
                        <neg />
                        <id xml:space="preserve" labels="*">_z</id>
                      </apply>
                      <real>8</real>
                    </apply>
                    <real>2</real>
                  </apply>
                  <apply>
                    <div />
                    <apply>
                      <minus />
                      <id xml:space="preserve" labels="*">_z</id>
                      <real>4</real>
                    </apply>
                    <real>3</real>
                  </apply>
                  <id xml:space="preserve" labels="*">_z</id>
                </matrix>
              </program>
            </then>
            <else>
              <program>
                <id xml:space="preserve" labels="*">undefined</id>
              </program>
            </else>
          </if>
        </program>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
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2. Valutare i valori delle variabili presupponendo che tutti i valori siano maggiori di 0.

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  <math resultRef="6">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <matrix rows="2" cols="1">
        <apply>
          <equal />
          <apply>
            <plus />
            <apply>
              <mult />
              <real>2</real>
              <id xml:space="preserve">x</id>
            </apply>
            <apply>
              <mult />
              <real>3</real>
              <id xml:space="preserve">y</id>
            </apply>
          </apply>
          <real>4</real>
        </apply>
        <apply>
          <equal />
          <apply>
            <plus />
            <apply>
              <mult />
              <real>2</real>
              <id xml:space="preserve">x</id>
            </apply>
            <id xml:space="preserve">z</id>
          </apply>
          <real>8</real>
        </apply>
      </matrix>
      <command>
        <sequence>
          <sequence>
            <sequence>
              <sequence>
                <sequence>
                  <sequence>
                    <id xml:space="preserve">solve</id>
                    <id xml:space="preserve">x</id>
                  </sequence>
                  <id xml:space="preserve">y</id>
                </sequence>
                <id xml:space="preserve">z</id>
              </sequence>
              <id xml:space="preserve">fully</id>
            </sequence>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <greaterThan />
            <id xml:space="preserve">ALL</id>
            <real>0</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <program>
          <if>
            <test>
              <apply>
                <lessThan />
                <apply>
                  <lessThan />
                  <real>4</real>
                  <id xml:space="preserve" labels="*">_z</id>
                </apply>
                <real>8</real>
              </apply>
            </test>
            <then>
              <program>
                <matrix rows="1" cols="3">
                  <apply>
                    <div />
                    <apply>
                      <plus />
                      <apply>
                        <neg />
                        <id xml:space="preserve" labels="*">_z</id>
                      </apply>
                      <real>8</real>
                    </apply>
                    <real>2</real>
                  </apply>
                  <apply>
                    <div />
                    <apply>
                      <minus />
                      <id xml:space="preserve" labels="*">_z</id>
                      <real>4</real>
                    </apply>
                    <real>3</real>
                  </apply>
                  <id xml:space="preserve" labels="*">_z</id>
                </matrix>
              </program>
            </then>
            <else>
              <program>
                <id xml:space="preserve" labels="*">undefined</id>
              </program>
            </else>
          </if>
        </program>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

Il risultato per z viene restituito con valore tra 4 e 8 oppure non definito.

3. Valutare i valori della variabile inferiori a 4 utilizzando generated. generated non esegue l'assegnazione o la sostituzione nei valori.

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
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        <apply>
          <equal />
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            <plus />
            <apply>
              <mult />
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              <id xml:space="preserve">x</id>
            </apply>
            <apply>
              <mult />
              <real>3</real>
              <id xml:space="preserve">y</id>
            </apply>
          </apply>
          <real>4</real>
        </apply>
        <apply>
          <equal />
          <apply>
            <plus />
            <apply>
              <mult />
              <real>2</real>
              <id xml:space="preserve">x</id>
            </apply>
            <id xml:space="preserve">z</id>
          </apply>
          <real>8</real>
        </apply>
      </matrix>
      <command>
        <sequence>
          <sequence>
            <sequence>
              <sequence>
                <sequence>
                  <sequence>
                    <sequence>
                      <id xml:space="preserve">solve</id>
                      <id xml:space="preserve">x</id>
                    </sequence>
                    <id xml:space="preserve">y</id>
                  </sequence>
                  <id xml:space="preserve">z</id>
                </sequence>
                <apply>
                  <lessThan />
                  <id xml:space="preserve">generated</id>
                  <real>4</real>
                </apply>
              </sequence>
              <id xml:space="preserve">fully</id>
            </sequence>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <greaterThan />
            <id xml:space="preserve">ALL</id>
            <real>0</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <id xml:space="preserve" labels="*">undefined</id>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

Il risultato non è definito poiché si presuppone che il valore generato sia inferiore a 4.

4. Successivamente, valutare le equazioni per il valore generato uguale a 6.

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
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        <apply>
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            <plus />
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            <apply>
              <mult />
              <real>3</real>
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            </apply>
          </apply>
          <real>4</real>
        </apply>
        <apply>
          <equal />
          <apply>
            <plus />
            <apply>
              <mult />
              <real>2</real>
              <id xml:space="preserve">x</id>
            </apply>
            <id xml:space="preserve">z</id>
          </apply>
          <real>8</real>
        </apply>
      </matrix>
      <command>
        <sequence>
          <sequence>
            <sequence>
              <sequence>
                <sequence>
                  <sequence>
                    <sequence>
                      <id xml:space="preserve">solve</id>
                      <id xml:space="preserve">x</id>
                    </sequence>
                    <id xml:space="preserve">y</id>
                  </sequence>
                  <id xml:space="preserve">z</id>
                </sequence>
                <apply>
                  <equal />
                  <id xml:space="preserve">generated</id>
                  <real>6</real>
                </apply>
              </sequence>
              <id xml:space="preserve">fully</id>
            </sequence>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <greaterThan />
            <id xml:space="preserve">ALL</id>
            <real>0</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <matrix rows="1" cols="3">
          <apply>
            <div />
            <apply>
              <plus />
              <apply>
                <neg />
                <id xml:space="preserve" labels="*">_z</id>
              </apply>
              <real>8</real>
            </apply>
            <real>2</real>
          </apply>
          <apply>
            <div />
            <apply>
              <minus />
              <id xml:space="preserve" labels="*">_z</id>
              <real>4</real>
            </apply>
            <real>3</real>
          </apply>
          <id xml:space="preserve" labels="*">_z</id>
        </matrix>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
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5. Valutare il valore generato utilizzando il valore eval 6.

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            <plus />
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              <mult />
              <real>2</real>
              <id xml:space="preserve">x</id>
            </apply>
            <apply>
              <mult />
              <real>3</real>
              <id xml:space="preserve">y</id>
            </apply>
          </apply>
          <real>4</real>
        </apply>
        <apply>
          <equal />
          <apply>
            <plus />
            <apply>
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              <real>2</real>
              <id xml:space="preserve">x</id>
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            <id xml:space="preserve">z</id>
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          <real>8</real>
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      <command>
        <sequence>
          <sequence>
            <sequence>
              <sequence>
                <sequence>
                  <sequence>
                    <sequence>
                      <id xml:space="preserve">solve</id>
                      <id xml:space="preserve">x</id>
                    </sequence>
                    <id xml:space="preserve">y</id>
                  </sequence>
                  <id xml:space="preserve">z</id>
                </sequence>
                <apply>
                  <equal />
                  <id xml:space="preserve">generated</id>
                  <apply>
                    <id xml:space="preserve">eval</id>
                    <real>6</real>
                  </apply>
                </apply>
              </sequence>
              <id xml:space="preserve">fully</id>
            </sequence>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <greaterThan />
            <id xml:space="preserve">ALL</id>
            <real>0</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <matrix rows="1" cols="3">
          <real>1</real>
          <apply>
            <div />
            <real>2</real>
            <real>3</real>
          </apply>
          <real>6</real>
        </matrix>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

In questo caso viene utilizzato eval per sostituire il valore della variabile generata.

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