Gaussian elimination: Difference between revisions
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=={{header|Phix}}== |
=={{header|Phix}}== |
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{{trans|PHP}} |
{{trans|PHP}} |
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<lang Phix> |
<!--<lang Phix>(phixonline)--> |
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
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integer n = length(b) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">gauss_eliminate</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
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atom tmp |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">({</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">})</span> |
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for col=1 to n do |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
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integer m = col |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">tmp</span> |
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atom mx = a[m][m] |
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<span style="color: #008080;">for</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span> |
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for i=col+1 to n do |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">col</span> |
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tmp = abs(a[i][col]) |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">mx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">][</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]</span> |
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if tmp>mx then |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">col</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span> |
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{m,mx} = {i,tmp} |
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<span style="color: #000000;">tmp</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">col</span><span style="color: #0000FF;">])</span> |
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end if |
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<span style="color: #008080;">if</span> <span style="color: #000000;">tmp</span><span style="color: #0000FF;">></span><span style="color: #000000;">mx</span> <span style="color: #008080;">then</span> |
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end for |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mx</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmp</span><span style="color: #0000FF;">}</span> |
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if col!=m then |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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{a[col],a[m]} = {a[m],a[col]} |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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{b[col],b[m]} = {b[m],b[col]} |
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<span style="color: #008080;">if</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">m</span> <span style="color: #008080;">then</span> |
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end if |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">],</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">],</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]}</span> |
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for i=col+1 to n do |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">],</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">],</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]}</span> |
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tmp = a[i][col]/a[col][col] |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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for j=col+1 to n do |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">col</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span> |
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a[i][j] -= tmp*a[col][j] |
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<span style="color: #000000;">tmp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]/</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">][</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]</span> |
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end for |
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">col</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span> |
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a[i][col] = 0 |
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<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">tmp</span><span style="color: #0000FF;">*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> |
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b[i] -= tmp*b[col] |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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end for |
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<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> |
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end for |
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<span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">tmp</span><span style="color: #0000FF;">*</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]</span> |
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sequence x = repeat(0,n) |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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for col=n to 1 by -1 do |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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tmp = b[col] |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> |
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for j=n to col+1 by -1 do |
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<span style="color: #008080;">for</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">=</span><span style="color: #000000;">n</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span> |
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tmp -= x[j]*a[col][j] |
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<span style="color: #000000;">tmp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]</span> |
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end for |
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">n</span> <span style="color: #008080;">to</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span> |
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x[col] = tmp/a[col][col] |
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<span style="color: #000000;">tmp</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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return x |
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<span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tmp</span><span style="color: #0000FF;">/</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">col</span><span style="color: #0000FF;">][</span><span style="color: #000000;">col</span><span style="color: #0000FF;">]</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<span style="color: #008080;">return</span> <span style="color: #000000;">x</span> |
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constant a = {{1.00, 0.00, 0.00, 0.00, 0.00, 0.00}, |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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{1.00, 0.63, 0.39, 0.25, 0.16, 0.10}, |
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{1.00, 1.26, 1.58, 1.98, 2.49, 3.13}, |
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<span style="color: #008080;">constant</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">1.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.00</span><span style="color: #0000FF;">},</span> |
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{1.00, 1.88, 3.55, 6.70, 12.62, 23.80}, |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">1.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.63</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.39</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.25</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.16</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.10</span><span style="color: #0000FF;">},</span> |
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{1.00, 2.51, 6.32, 15.88, 39.90, 100.28}, |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">1.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.26</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.58</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.98</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.49</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.13</span><span style="color: #0000FF;">},</span> |
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{1.00, 3.14, 9.87, 31.01, 97.41, 306.02}}, |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">1.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.88</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.55</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.70</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">12.62</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.80</span><span style="color: #0000FF;">},</span> |
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b = {-0.01, 0.61, 0.91, 0.99, 0.60, 0.02} |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">1.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.51</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6.32</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">15.88</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">39.90</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">100.28</span><span style="color: #0000FF;">},</span> |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">1.00</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.14</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9.87</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">31.01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">97.41</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">306.02</span><span style="color: #0000FF;">}},</span> |
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pp(gauss_eliminate(a, b))</lang> |
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<span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">0.01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.61</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.91</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.99</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.60</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.02</span><span style="color: #0000FF;">}</span> |
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<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">gauss_eliminate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">))</span> |
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<!--</lang>--> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |