예제: 식 단순화 및 다시 쓰기

기호 > 기호 작업 > 식 단순화 및 다시 쓰기 > 예제: 식 단순화 및 다시 쓰기

예제: 식 단순화 및 다시 쓰기

기호 키워드 combine 및 rewrite를 사용하여 식을 결합하고 다시 씁니다.

키워드: simplify

• 다음 식을 단순화합니다.

• 기호 연산 연산자를 삽입합니다.

• 자리 표시자에 simplify 키워드를 삽입합니다.

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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>

키워드: combine

• combine 키워드를 사용하여 다음 식을 결합합니다.

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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>

combine 키워드는 결과에 영향을 미치지 않습니다.

• sincos 수정자를 추가하여 싸인이나 코사인으로 결과를 다시 쓰도록 지정합니다.

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
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          <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>

• 다른 수정자와 함께 combine 키워드를 사용하여 식을 더 결합합니다.

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          <apply>
            <mult />
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            <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>
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          <id xml:space="preserve" labels="CONSTANT">e</id>
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            <plus />
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              <id xml:space="preserve" labels="*">y</id>
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            <id xml:space="preserve" labels="*">x</id>
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        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">ln</id>
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        </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>
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        <apply>
          <mult />
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              <id xml:space="preserve">b</id>
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      <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>
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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>
      <symResult>
        <apply>
          <div />
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            <minus />
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              <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>

키워드: rewrite

• rewrite 키워드를 사용하여 다음과 같은 식을 특정 항등식 유형으로 다시 씁니다.

rewrite에는 수정자가 필요하므로 PTC Mathcad가 오류를 반환합니다.

• exp 수정자를 추가합니다.

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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 Mathcad가 지수 함수로 sin을 다시 작성합니다.

• 원하는 결과 유형을 얻으려면 다른 수정자와 함께 rewrite 키워드를 사용합니다.

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          <real>1</real>
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              <nthRoot />
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                <real>1</real>
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