Решение уравнений с помощью генерируемых и расчетных модификаторов

Символьные операции > Работа с символьными операциями > Решение уравнений с помощью генерируемых и расчетных модификаторов

1. Определите и решите два уравнения для переменных с помощью логического оператора и решения. Решение возвращается в терминах z.

Щелкните для копирования этого выражения

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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>
</region>

2. Вычислите значения переменных, предполагая, что все значения больше 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>

Результат возвращается для z между 4 и 8, иначе он является неопределенным.

3. Вычислите значения переменных меньше 4 с помощью generated. generated не делает присвоения или замены значений.

<region id="ID0EYMVLB" actualWidth="543.26666666666665" actualHeight="49.49" top="441.60000000000008" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="7">
    <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>
                    <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>

Результат не определен, поскольку предполагается, что сгенерированное значение меньше, чем 4.

4. Далее вычислите уравнения для сгенерированного значения, равного 6.

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  <math resultRef="8">
    <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>
                    <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>
</region>

5. Вычислите сгенерированное значение, используя значение eval, равное 6.

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  <math resultRef="9">
    <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>
                    <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>

Здесь мы используем eval для подстановки значения сгенерированной переменной.

Было ли это полезно?