예제: 키워드 및 수정자 조합

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예제: 키워드 및 수정자 조합

수정자 real 및 complex가 포함된 키워드 assume

1. x가 실수 및 복소수라고 가정하고 rectangular를 사용하여 식을 작성하고 계산합니다.

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  <math resultRef="14">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">exp</id>
        <id xml:space="preserve">x</id>
      </apply>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">rectangular</id>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">x</id>
            <id xml:space="preserve">real</id>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <pow />
          <id labels="CONSTANT" xml:space="preserve">e</id>
          <id labels="*" xml:space="preserve">x</id>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

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  <math resultRef="15">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">exp</id>
        <id xml:space="preserve">x</id>
      </apply>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">rectangular</id>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">x</id>
            <id xml:space="preserve">complex</id>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <plus />
          <apply>
            <id labels="FUNCTION" xml:space="preserve">Re</id>
            <apply>
              <pow />
              <id labels="CONSTANT" xml:space="preserve">e</id>
              <id labels="*" xml:space="preserve">x</id>
            </apply>
          </apply>
          <apply>
            <mult />
            <apply>
              <id labels="FUNCTION" xml:space="preserve">Im</id>
              <apply>
                <pow />
                <id labels="CONSTANT" xml:space="preserve">e</id>
                <id labels="*" xml:space="preserve">x</id>
              </apply>
            </apply>
            <imag symbol="i">1</imag>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

결과는 가정 내용에 따라 달라집니다.

x: 기본적으로 실수

키워드: 0보다 큰 값의 경우 simplify

1. 값이 0 이하인 경우와 0보다 큰 경우를 각각 가정하여 식을 작성하고 단순화합니다.

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  <math resultRef="18">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
        <apply>
          <nthRoot />
          <placeholder />
          <apply>
            <minus />
            <id xml:space="preserve">a</id>
            <imag symbol="i">3</imag>
          </apply>
        </apply>
        <apply>
          <nthRoot />
          <placeholder />
          <apply>
            <plus />
            <id xml:space="preserve">a</id>
            <imag symbol="i">1</imag>
          </apply>
        </apply>
      </apply>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">simplify</id>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <lessOrEqual />
            <id xml:space="preserve">a</id>
            <real>0</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <mult />
          <apply>
            <nthRoot />
            <placeholder />
            <apply>
              <minus />
              <id labels="*" xml:space="preserve">a</id>
              <imag symbol="i">3</imag>
            </apply>
          </apply>
          <apply>
            <nthRoot />
            <placeholder />
            <apply>
              <plus />
              <id labels="*" xml:space="preserve">a</id>
              <imag symbol="i">1</imag>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

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  <math resultRef="19">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
        <apply>
          <nthRoot />
          <placeholder />
          <apply>
            <minus />
            <id xml:space="preserve">a</id>
            <imag symbol="i">3</imag>
          </apply>
        </apply>
        <apply>
          <nthRoot />
          <placeholder />
          <apply>
            <plus />
            <id xml:space="preserve">a</id>
            <imag symbol="i">1</imag>
          </apply>
        </apply>
      </apply>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">simplify</id>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <greaterThan />
            <id xml:space="preserve">a</id>
            <real>0</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <nthRoot />
          <placeholder />
          <apply>
            <plus />
            <apply>
              <minus />
              <apply>
                <pow />
                <id labels="*" xml:space="preserve">a</id>
                <real>2</real>
              </apply>
              <apply>
                <mult />
                <imag symbol="i">2</imag>
                <id labels="*" xml:space="preserve">a</id>
              </apply>
            </apply>
            <real>3</real>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
    <formattingOverride BackgroundColor="#FFC3D9A5" />
  </math>
</region>

결과는 가정 내용에 따라 달라집니다.

키워드: solve 및 수정자 real

1. 방정식을 작성하여 풉니다.

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      <apply>
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            <id xml:space="preserve">x</id>
            <real>5</real>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>2</real>
          </apply>
        </apply>
        <real>1</real>
      </apply>
      <command>
        <id xml:space="preserve">solve</id>
      </command>
      <symResult>
        <matrix rows="5" cols="1">
          <real>-0.80873060047939201374</real>
          <apply>
            <plus />
            <real>-0.46491220160289785433</real>
            <imag symbol="i">1.0714738402702694092</imag>
          </apply>
          <apply>
            <minus />
            <real>-0.46491220160289785433</real>
            <imag symbol="i">1.0714738402702694092</imag>
          </apply>
          <apply>
            <minus />
            <real>0.8692775018425938612</real>
            <imag symbol="i">0.38826940659974035536</imag>
          </apply>
          <apply>
            <plus />
            <real>0.8692775018425938612</real>
            <imag symbol="i">0.38826940659974035536</imag>
          </apply>
        </matrix>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

2. x가 실수라고 가정하여 방정식을 다시 풉니다.

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  <math resultRef="21">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <plus />
        <apply>
          <minus />
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>5</real>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>2</real>
          </apply>
        </apply>
        <real>1</real>
      </apply>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">solve</id>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">x</id>
            <id xml:space="preserve">real</id>
          </apply>
        </sequence>
      </command>
      <symResult>
        <real>-0.80873060047939201374</real>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

결과가 필터링되어 해의 실수 값만 표시됩니다.

키워드: assume, 수정자 even 및 odd

1. 방정식을 작성한 후 solve를 사용하여 풉니다.

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              <real>5</real>
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            <apply>
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              <real>4</real>
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                <id xml:space="preserve">x</id>
                <real>3</real>
              </apply>
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          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>2</real>
          </apply>
        </apply>
        <real>4</real>
      </apply>
      <command>
        <id xml:space="preserve">solve</id>
      </command>
      <symResult>
        <matrix rows="5" cols="1">
          <real>2</real>
          <real>1</real>
          <real>-2</real>
          <apply>
            <div />
            <apply>
              <minus />
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                  <real>3</real>
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                <imag symbol="i">1</imag>
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              <real>1</real>
            </apply>
            <real>2</real>
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          <apply>
            <div />
            <apply>
              <minus />
              <apply>
                <neg />
                <parens>
                  <apply>
                    <mult />
                    <apply>
                      <nthRoot />
                      <placeholder />
                      <real>3</real>
                    </apply>
                    <imag symbol="i">1</imag>
                  </apply>
                </parens>
              </apply>
              <real>1</real>
            </apply>
            <real>2</real>
          </apply>
        </matrix>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

2. x가 정수라고 가정하여 방정식을 계산합니다.

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              <id xml:space="preserve">x</id>
              <real>5</real>
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            <apply>
              <mult />
              <real>4</real>
              <apply>
                <pow />
                <id xml:space="preserve">x</id>
                <real>3</real>
              </apply>
            </apply>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>2</real>
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        </apply>
        <real>4</real>
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            <id xml:space="preserve">assume</id>
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          <apply>
            <equal />
            <id xml:space="preserve">x</id>
            <id xml:space="preserve">integer</id>
          </apply>
        </sequence>
      </command>
      <symResult>
        <matrix rows="3" cols="1">
          <real>2</real>
          <real>1</real>
          <real>-2</real>
        </matrix>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

3. x가 짝수라고 가정하여 방정식을 계산합니다.

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <plus />
        <apply>
          <minus />
          <apply>
            <minus />
            <apply>
              <pow />
              <id xml:space="preserve">x</id>
              <real>5</real>
            </apply>
            <apply>
              <mult />
              <real>4</real>
              <apply>
                <pow />
                <id xml:space="preserve">x</id>
                <real>3</real>
              </apply>
            </apply>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>2</real>
          </apply>
        </apply>
        <real>4</real>
      </apply>
      <command>
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            <id xml:space="preserve">solve</id>
            <id xml:space="preserve">assume</id>
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          <apply>
            <equal />
            <id xml:space="preserve">x</id>
            <id xml:space="preserve">even</id>
          </apply>
        </sequence>
      </command>
      <symResult>
        <matrix rows="2" cols="1">
          <real>2</real>
          <real>-2</real>
        </matrix>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

4. x가 홀수라고 가정하여 방정식을 계산합니다.

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  <math resultRef="25">
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      <apply>
        <plus />
        <apply>
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          <apply>
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            <apply>
              <pow />
              <id xml:space="preserve">x</id>
              <real>5</real>
            </apply>
            <apply>
              <mult />
              <real>4</real>
              <apply>
                <pow />
                <id xml:space="preserve">x</id>
                <real>3</real>
              </apply>
            </apply>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>2</real>
          </apply>
        </apply>
        <real>4</real>
      </apply>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">solve</id>
            <id xml:space="preserve">assume</id>
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          <apply>
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            <id xml:space="preserve">x</id>
            <id xml:space="preserve">odd</id>
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        </sequence>
      </command>
      <symResult>
        <real>1</real>
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    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

결과는 가정 내용에 따라 달라집니다. even 및 odd의 결과를 조합하면 integer의 결과가 되는지 관찰합니다.

이게 도움이 되었습니까?