lagrange_basis.svg

<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<!-- Created with matplotlib (http://matplotlib.org/) -->
<svg height="120pt" version="1.1" viewBox="0 0 468 120" width="468pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
 <defs>
  <style type="text/css">
*{stroke-linecap:square;stroke-linejoin:round;}
  </style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="
M0 120.071
L468 120.071
L468 -1.42109e-14
L0 -1.42109e-14
z
" style="fill:none;opacity:0.0;"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="
M10.8 92.8588
L142.094 92.8588
L142.094 10.8
L10.8 10.8
z
" style="fill:none;opacity:0.0;"/>
   </g>
   <g id="patch_3">
    <path d="
M10.8 60.0353
L142.094 60.0353" style="fill:none;stroke:#808080;"/>
   </g>
   <g id="patch_4">
    <path d="
M60.0353 92.8588
L60.0353 10.8" style="fill:none;stroke:#808080;"/>
   </g>
   <g id="line2d_1">
    <path clip-path="url(#p24fba10013)" d="
M-38.4353 -104.082
M8.69027 -1
L9.7952 0.909195
L13.8144 7.52585
L17.8336 13.8144
L21.8528 19.7749
L25.872 25.4072
L29.8912 30.7115
L33.9104 35.6876
L37.9297 40.3357
L41.9489 44.6557
L45.9681 48.6475
L49.9873 52.3113
L54.0065 55.647
L58.0257 58.6545
L62.0449 61.334
L66.0641 63.6854
L70.0833 65.7087
L74.1025 67.4038
L78.1217 68.7709
L82.1409 69.8099
L86.1601 70.5208
L90.1794 70.9036
L94.1986 70.9582
L98.2178 70.6848
L102.237 70.0833
L106.256 69.1537
L110.275 67.896
L114.295 66.3102
L118.314 64.3963
L122.333 62.1543
L126.352 59.5842
L130.371 56.686
L134.391 53.4597
L138.41 49.9053
L142.429 46.0228
L146.448 41.8122
L150.467 37.2735
L154.487 32.4067
L158.506 27.2118" style="fill:none;stroke:#000000;"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_2">
      <defs>
       <path d="
M0 0
L0 -4" id="mcb557df647" style="stroke:#000000;stroke-linecap:butt;stroke-width:0.5;"/>
      </defs>
      <g>
       <use style="stroke:#000000;stroke-linecap:butt;stroke-width:0.5;" x="27.2117647059" xlink:href="#mcb557df647" y="60.0352941176"/>
      </g>
     </g>
     <g id="text_1">
      <!-- $-1$ -->
      <defs>
       <path d="
M9.28125 0
L9.28125 3.51562
Q21.7812 3.51562 21.7812 6.6875
L21.7812 59.1875
Q16.6094 56.6875 8.6875 56.6875
L8.6875 60.2031
Q20.9531 60.2031 27.2031 66.6094
L28.6094 66.6094
Q28.9531 66.6094 29.2656 66.3281
Q29.5938 66.0625 29.5938 65.7188
L29.5938 6.6875
Q29.5938 3.51562 42.0938 3.51562
L42.0938 0
z
" id="Cmr10-31"/>
       <path d="
M10.2031 23
Q9.375 23 8.82812 23.625
Q8.29688 24.2656 8.29688 25
Q8.29688 25.7344 8.82812 26.3594
Q9.375 27 10.2031 27
L67.5781 27
Q68.3594 27 68.875 26.3594
Q69.3906 25.7344 69.3906 25
Q69.3906 24.2656 68.875 23.625
Q68.3594 23 67.5781 23
z
" id="Cmsy10-a1"/>
      </defs>
      <g transform="translate(19.5317647059 72.0752941176)scale(0.12 -0.12)">
       <use transform="translate(0.0 0.390625)" xlink:href="#Cmsy10-a1"/>
       <use transform="translate(77.685546875 0.390625)" xlink:href="#Cmr10-31"/>
      </g>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_3">
      <g>
       <use style="stroke:#000000;stroke-linecap:butt;stroke-width:0.5;" x="125.682352941" xlink:href="#mcb557df647" y="60.0352941176"/>
      </g>
     </g>
     <g id="text_2">
      <!-- $2$ -->
      <defs>
       <path d="
M4.98438 0
L4.98438 2.6875
Q4.98438 2.9375 5.17188 3.21875
L20.7031 20.4062
Q24.2188 24.2188 26.4062 26.7969
Q28.6094 29.3906 30.75 32.7656
Q32.9062 36.1406 34.1562 39.625
Q35.4062 43.1094 35.4062 47.0156
Q35.4062 51.125 33.8906 54.8594
Q32.375 58.5938 29.375 60.8438
Q26.375 63.0938 22.125 63.0938
Q17.7812 63.0938 14.3125 60.4688
Q10.8438 57.8594 9.42188 53.7188
Q9.8125 53.8125 10.5 53.8125
Q12.75 53.8125 14.3281 52.2969
Q15.9219 50.7812 15.9219 48.3906
Q15.9219 46.0938 14.3281 44.5
Q12.75 42.9219 10.5 42.9219
Q8.15625 42.9219 6.5625 44.5469
Q4.98438 46.1875 4.98438 48.3906
Q4.98438 52.1562 6.39062 55.4375
Q7.8125 58.7344 10.4688 61.2969
Q13.1406 63.875 16.4844 65.2344
Q19.8281 66.6094 23.5781 66.6094
Q29.2969 66.6094 34.2188 64.1875
Q39.1562 61.7656 42.0312 57.3438
Q44.9219 52.9375 44.9219 47.0156
Q44.9219 42.6719 43.0156 38.7656
Q41.1094 34.8594 38.125 31.6562
Q35.1562 28.4688 30.5156 24.4062
Q25.875 20.3594 24.4219 19
L13.0938 8.10938
L22.7031 8.10938
Q29.7812 8.10938 34.5469 8.21875
Q39.3125 8.34375 39.5938 8.59375
Q40.7656 9.85938 42 17.8281
L44.9219 17.8281
L42.0938 0
z
" id="Cmr10-32"/>
      </defs>
      <g transform="translate(122.682352941 72.0752941176)scale(0.12 -0.12)">
       <use transform="translate(0.0 0.390625)" xlink:href="#Cmr10-32"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_4">
      <defs>
       <path d="
M0 0
L4 0" id="mc8fcea1516" style="stroke:#000000;stroke-linecap:butt;stroke-width:0.5;"/>
      </defs>
      <g>
       <use style="stroke:#000000;stroke-linecap:butt;stroke-width:0.5;" x="60.0352941176" xlink:href="#mc8fcea1516" y="92.8588235294"/>
      </g>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_5">
      <g>
       <use style="stroke:#000000;stroke-linecap:butt;stroke-width:0.5;" x="60.0352941176" xlink:href="#mc8fcea1516" y="27.2117647059"/>
      </g>
     </g>
    </g>
   </g>
   <g id="patch_5">
    <path d="
M10.8 10.8
L142.094 10.8" style="fill:none;opacity:0.0;"/>
   </g>
   <g id="patch_6">
    <path d="
M142.094 92.8588
L142.094 10.8" style="fill:none;opacity:0.0;"/>
   </g>
   <g id="text_3">
    <!-- $x(x-2)/3$ -->
    <defs>
     <path d="
M31 -24.8125
Q25.4375 -20.4062 21.4062 -14.7188
Q17.3906 -9.03125 14.8125 -2.57812
Q12.25 3.85938 10.9844 10.8906
Q9.71875 17.9219 9.71875 25
Q9.71875 32.1719 10.9844 39.2031
Q12.25 46.2344 14.8594 52.7344
Q17.4844 59.2344 21.5312 64.8906
Q25.5938 70.5625 31 74.8125
Q31 75 31.5 75
L32.4219 75
Q32.7188 75 32.9531 74.7344
Q33.2031 74.4688 33.2031 74.125
Q33.2031 73.6875 33.0156 73.4844
Q28.125 68.7031 24.875 63.2344
Q21.625 57.7656 19.6406 51.5781
Q17.6719 45.4062 16.7969 38.7812
Q15.9219 32.1719 15.9219 25
Q15.9219 -6.78125 32.9062 -23.2969
Q33.2031 -23.5781 33.2031 -24.125
Q33.2031 -24.3594 32.9375 -24.6719
Q32.6719 -25 32.4219 -25
L31.5 -25
Q31 -25 31 -24.8125" id="Cmr10-28"/>
     <path d="
M6.5 -25
Q5.60938 -25 5.60938 -24.125
Q5.60938 -23.6875 5.8125 -23.4844
Q22.9062 -6.78125 22.9062 25
Q22.9062 56.7812 6 73.2969
Q5.60938 73.5312 5.60938 74.125
Q5.60938 74.4688 5.875 74.7344
Q6.15625 75 6.5 75
L7.42188 75
Q7.71875 75 7.90625 74.8125
Q15.0938 69.1406 19.875 61.0312
Q24.6562 52.9375 26.875 43.75
Q29.1094 34.5781 29.1094 25
Q29.1094 17.9219 27.9062 11.0625
Q26.7031 4.20312 24.0938 -2.45312
Q21.4844 -9.125 17.4844 -14.7656
Q13.4844 -20.4062 7.90625 -24.8125
Q7.71875 -25 7.42188 -25
z
" id="Cmr10-29"/>
     <path d="
M7.8125 2.875
Q9.57812 1.51562 12.7969 1.51562
Q15.9219 1.51562 18.3125 4.51562
Q20.7031 7.51562 21.5781 11.0781
L26.125 28.8125
Q27.2031 33.6406 27.2031 35.4062
Q27.2031 37.8906 25.8125 39.75
Q24.4219 41.6094 21.9219 41.6094
Q18.75 41.6094 15.9688 39.625
Q13.1875 37.6406 11.2812 34.5938
Q9.375 31.5469 8.59375 28.4219
Q8.40625 27.7812 7.8125 27.7812
L6.59375 27.7812
Q5.8125 27.7812 5.8125 28.7188
L5.8125 29
Q6.78125 32.7188 9.125 36.25
Q11.4688 39.7969 14.8594 41.9844
Q18.2656 44.1875 22.125 44.1875
Q25.7812 44.1875 28.7344 42.2344
Q31.6875 40.2812 32.9062 36.9219
Q34.625 39.9844 37.2812 42.0781
Q39.9375 44.1875 43.1094 44.1875
Q45.2656 44.1875 47.5 43.4219
Q49.75 42.6719 51.1719 41.1094
Q52.5938 39.5469 52.5938 37.2031
Q52.5938 34.6719 50.9531 32.8281
Q49.3125 31 46.7812 31
Q45.1719 31 44.0938 32.0312
Q43.0156 33.0625 43.0156 34.625
Q43.0156 36.7188 44.4531 38.2969
Q45.9062 39.8906 47.9062 40.1875
Q46.0938 41.6094 42.9219 41.6094
Q39.7031 41.6094 37.3281 38.625
Q34.9688 35.6406 33.9844 31.9844
L29.5938 14.3125
Q28.5156 10.2969 28.5156 7.71875
Q28.5156 5.17188 29.9531 3.34375
Q31.3906 1.51562 33.7969 1.51562
Q38.4844 1.51562 42.1562 5.64062
Q45.8438 9.76562 47.0156 14.7031
Q47.2188 15.2812 47.7969 15.2812
L49.0312 15.2812
Q49.4219 15.2812 49.6562 15.0156
Q49.9062 14.75 49.9062 14.4062
Q49.9062 14.3125 49.8125 14.1094
Q48.3906 8.15625 43.8438 3.51562
Q39.3125 -1.125 33.5938 -1.125
Q29.9375 -1.125 26.9844 0.84375
Q24.0312 2.82812 22.7969 6.20312
Q21.2344 3.26562 18.4688 1.0625
Q15.7188 -1.125 12.5938 -1.125
Q10.4531 -1.125 8.17188 -0.359375
Q5.90625 0.390625 4.48438 1.95312
Q3.07812 3.51562 3.07812 5.90625
Q3.07812 8.25 4.70312 10.1719
Q6.34375 12.1094 8.79688 12.1094
Q10.4531 12.1094 11.5781 11.1094
Q12.7031 10.1094 12.7031 8.5
Q12.7031 6.39062 11.2969 4.82812
Q9.90625 3.26562 7.8125 2.875" id="Cmmi10-78"/>
     <path d="
M9.51562 7.71875
Q11.8594 4.29688 15.8125 2.64062
Q19.7812 0.984375 24.3125 0.984375
Q30.125 0.984375 32.5625 5.9375
Q35.0156 10.8906 35.0156 17.1875
Q35.0156 20.0156 34.5 22.8438
Q33.9844 25.6875 32.7656 28.125
Q31.5469 30.5625 29.4219 32.0312
Q27.2969 33.5 24.2188 33.5
L17.5781 33.5
Q16.7031 33.5 16.7031 34.4219
L16.7031 35.2969
Q16.7031 36.0781 17.5781 36.0781
L23.0938 36.5312
Q26.6094 36.5312 28.9219 39.1562
Q31.25 41.7969 32.3281 45.5781
Q33.4062 49.3594 33.4062 52.7812
Q33.4062 57.5625 31.1562 60.6406
Q28.9062 63.7188 24.3125 63.7188
Q20.5156 63.7188 17.0469 62.2812
Q13.5781 60.8438 11.5312 57.9062
Q11.7188 57.9531 11.8594 57.9844
Q12.0156 58.0156 12.2031 58.0156
Q14.4531 58.0156 15.9688 56.4531
Q17.4844 54.8906 17.4844 52.6875
Q17.4844 50.5312 15.9688 48.9688
Q14.4531 47.4062 12.2031 47.4062
Q10.0156 47.4062 8.45312 48.9688
Q6.89062 50.5312 6.89062 52.6875
Q6.89062 56.9844 9.46875 60.1562
Q12.0625 63.3281 16.1406 64.9688
Q20.2188 66.6094 24.3125 66.6094
Q27.3438 66.6094 30.7031 65.7031
Q34.0781 64.7969 36.8125 63.1094
Q39.5469 61.4219 41.2812 58.7812
Q43.0156 56.1562 43.0156 52.7812
Q43.0156 48.5781 41.1406 45.0156
Q39.2656 41.4531 35.9844 38.8594
Q32.7188 36.2812 28.8125 35.0156
Q33.1562 34.1875 37.0625 31.7344
Q40.9688 29.2969 43.3281 25.4844
Q45.7031 21.6875 45.7031 17.2812
Q45.7031 11.7656 42.6719 7.29688
Q39.6562 2.82812 34.7188 0.3125
Q29.7812 -2.20312 24.3125 -2.20312
Q19.625 -2.20312 14.9062 -0.40625
Q10.2031 1.375 7.20312 4.9375
Q4.20312 8.5 4.20312 13.4844
Q4.20312 15.9688 5.85938 17.625
Q7.51562 19.2812 10.0156 19.2812
Q11.625 19.2812 12.9688 18.5312
Q14.3125 17.7812 15.0625 16.4062
Q15.8281 15.0469 15.8281 13.4844
Q15.8281 11.0312 14.1094 9.375
Q12.4062 7.71875 10.0156 7.71875
z
" id="Cmr10-33"/>
     <path d="
M5.60938 -23
Q5.60938 -22.7031 5.71875 -22.6094
L40.4844 73.7812
Q40.6719 74.3594 41.1562 74.6719
Q41.6562 75 42.2812 75
Q43.1719 75 43.7188 74.4531
Q44.2812 73.9219 44.2812 73
L44.2812 72.6094
L9.51562 -23.7812
Q8.9375 -25 7.625 -25
Q6.78125 -25 6.1875 -24.4062
Q5.60938 -23.8281 5.60938 -23" id="Cmmi10-3d"/>
    </defs>
    <g style="fill:#808080;" transform="translate(33.9176470588 109.270588235)scale(0.14 -0.14)">
     <use transform="translate(0.0 25.0)" xlink:href="#Cmmi10-78"/>
     <use transform="translate(57.080078125 25.0)" xlink:href="#Cmr10-28"/>
     <use transform="translate(95.8984375 25.0)" xlink:href="#Cmmi10-78"/>
     <use transform="translate(152.978515625 25.0)" xlink:href="#Cmsy10-a1"/>
     <use transform="translate(230.6640625 25.0)" xlink:href="#Cmr10-32"/>
     <use transform="translate(280.6640625 25.0)" xlink:href="#Cmr10-29"/>
     <use transform="translate(319.482421875 25.0)" xlink:href="#Cmmi10-3d"/>
     <use transform="translate(369.482421875 25.0)" xlink:href="#Cmr10-33"/>
    </g>
   </g>
  </g>
  <g id="axes_2">
   <g id="patch_7">
    <path d="
M168.353 92.8588
L299.647 92.8588
L299.647 10.8
L168.353 10.8
z
" style="fill:none;opacity:0.0;"/>
   </g>
   <g id="patch_8">
    <path d="
M168.353 60.0353
L299.647 60.0353" style="fill:none;stroke:#808080;"/>
   </g>
   <g id="patch_9">
    <path d="
M217.588 92.8588
L217.588 10.8" style="fill:none;stroke:#808080;"/>
   </g>
   <g id="line2d_6">
    <path clip-path="url(#p9c6b2962f1)" d="
M119.118 224.153
M153.83 121.071
L155.291 117.48
L159.31 108.088
L163.329 99.1884
L167.348 90.7809
L171.367 82.8655
L175.387 75.4423
L179.406 68.5112
L183.425 62.0722
L187.444 56.1255
L191.463 50.6708
L195.483 45.7083
L199.502 41.238
L203.521 37.2598
L207.54 33.7737
L211.559 30.7798
L215.579 28.2781
L219.598 26.2685
L223.617 24.751
L227.636 23.7257
L231.655 23.1926
L235.675 23.1515
L239.694 23.6027
L243.713 24.546
L247.732 25.9814
L251.752 27.909
L255.771 30.3287
L259.79 33.2406
L263.809 36.6446
L267.828 40.5408
L271.848 44.9291
L275.867 49.8096
L279.886 55.1822
L283.905 61.0469
L287.924 67.4038
L291.944 74.2529
L295.963 81.5941
L299.982 89.4275
L304.001 97.753
L308.02 106.571
L312.04 115.88
L314.168 121.071" style="fill:none;stroke:#000000;"/>
   </g>
   <g id="matplotlib.axis_3">
    <g id="xtick_3">
     <g id="line2d_7">
      <g>
       <use style="stroke:#000000;stroke-linecap:butt;stroke-width:0.5;" x="184.764705882" xlink:href="#mcb557df647" y="60.0352941176"/>
      </g>
     </g>
     <g id="text_4">
      <!-- $-1$ -->
      <g transform="translate(177.084705882 72.0752941176)scale(0.12 -0.12)">
       <use transform="translate(0.0 0.390625)" xlink:href="#Cmsy10-a1"/>
       <use transform="translate(77.685546875 0.390625)" xlink:href="#Cmr10-31"/>
      </g>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_8">
      <g>
       <use style="stroke:#000000;stroke-linecap:butt;stroke-width:0.5;" x="283.235294118" xlink:href="#mcb557df647" y="60.0352941176"/>
      </g>
     </g>
     <g id="text_5">
      <!-- $2$ -->
      <g transform="translate(280.235294118 72.0752941176)scale(0.12 -0.12)">
       <use transform="translate(0.0 0.390625)" xlink:href="#Cmr10-32"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_4">
    <g id="ytick_3">
     <g id="line2d_9">
      <g>
       <use style="stroke:#000000;stroke-linecap:butt;stroke-width:0.5;" x="217.588235294" xlink:href="#mc8fcea1516" y="92.8588235294"/>
      </g>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_10">
      <g>
       <use style="stroke:#000000;stroke-linecap:butt;stroke-width:0.5;" x="217.588235294" xlink:href="#mc8fcea1516" y="27.2117647059"/>
      </g>
     </g>
    </g>
   </g>
   <g id="patch_10">
    <path d="
M168.353 10.8
L299.647 10.8" style="fill:none;opacity:0.0;"/>
   </g>
   <g id="patch_11">
    <path d="
M299.647 92.8588
L299.647 10.8" style="fill:none;opacity:0.0;"/>
   </g>
   <g id="text_6">
    <!-- $-(x+1)(x-2)/2$ -->
    <defs>
     <path d="
M7.51562 23
Q6.6875 23 6.14062 23.625
Q5.60938 24.2656 5.60938 25
Q5.60938 25.7344 6.14062 26.3594
Q6.6875 27 7.51562 27
L36.9219 27
L36.9219 56.5
Q36.9219 57.2812 37.5 57.7812
Q38.0938 58.2969 38.9219 58.2969
Q39.6562 58.2969 40.2812 57.7812
Q40.9219 57.2812 40.9219 56.5
L40.9219 27
L70.3125 27
Q71.0469 27 71.5781 26.3594
Q72.125 25.7344 72.125 25
Q72.125 24.2656 71.5781 23.625
Q71.0469 23 70.3125 23
L40.9219 23
L40.9219 -6.5
Q40.9219 -7.28125 40.2812 -7.78125
Q39.6562 -8.29688 38.9219 -8.29688
Q38.0938 -8.29688 37.5 -7.78125
Q36.9219 -7.28125 36.9219 -6.5
L36.9219 23
z
" id="Cmr10-2b"/>
    </defs>
    <g style="fill:#808080;" transform="translate(169.980588235 109.270588235)scale(0.14 -0.14)">
     <use transform="translate(0.0 25.0)" xlink:href="#Cmsy10-a1"/>
     <use transform="translate(77.685546875 25.0)" xlink:href="#Cmr10-28"/>
     <use transform="translate(116.50390625 25.0)" xlink:href="#Cmmi10-78"/>
     <use transform="translate(191.142578125 25.0)" xlink:href="#Cmr10-2b"/>
     <use transform="translate(275.201171875 25.0)" xlink:href="#Cmr10-31"/>
     <use transform="translate(325.201171875 25.0)" xlink:href="#Cmr10-29"/>
     <use transform="translate(364.01953125 25.0)" xlink:href="#Cmr10-28"/>
     <use transform="translate(402.837890625 25.0)" xlink:href="#Cmmi10-78"/>
     <use transform="translate(459.91796875 25.0)" xlink:href="#Cmsy10-a1"/>
     <use transform="translate(537.603515625 25.0)" xlink:href="#Cmr10-32"/>
     <use transform="translate(587.603515625 25.0)" xlink:href="#Cmr10-29"/>
     <use transform="translate(626.421875 25.0)" xlink:href="#Cmmi10-3d"/>
     <use transform="translate(676.421875 25.0)" xlink:href="#Cmr10-32"/>
    </g>
   </g>
  </g>
  <g id="axes_3">
   <g id="patch_12">
    <path d="
M325.906 92.8588
L457.2 92.8588
L457.2 10.8
L325.906 10.8
z
" style="fill:none;opacity:0.0;"/>
   </g>
   <g id="patch_13">
    <path d="
M325.906 60.0353
L457.2 60.0353" style="fill:none;stroke:#808080;"/>
   </g>
   <g id="patch_14">
    <path d="
M375.141 92.8588
L375.141 10.8" style="fill:none;stroke:#808080;"/>
   </g>
   <g id="line2d_11">
    <path clip-path="url(#p741d0f4f9b)" d="
M276.671 27.2118
L280.69 30.4791
L284.709 33.5823
L288.728 36.5216
L292.747 39.2967
L296.767 41.9078
L300.786 44.3549
L304.805 46.6379
L308.824 48.7569
L312.843 50.7118
L316.863 52.5027
L320.882 54.1295
L324.901 55.5923
L328.92 56.891
L332.939 58.0257
L336.959 58.9963
L340.978 59.8029
L344.997 60.4454
L349.016 60.9239
L353.036 61.2383
L357.055 61.3887
L361.074 61.375
L365.093 61.1973
L369.112 60.8555
L373.132 60.3497
L377.151 59.6799
L381.17 58.8459
L385.189 57.848
L389.208 56.686
L393.228 55.3599
L397.247 53.8698
L401.266 52.2156
L405.285 50.3974
L409.304 48.4151
L413.324 46.2688
L417.343 43.9585
L421.362 41.4841
L425.381 38.8456
L429.4 36.0431
L433.42 33.0765
L437.439 29.9459
L441.458 26.6513
L445.477 23.1926
L449.497 19.5698
L453.516 15.783
L457.535 11.8321
L461.554 7.71724
L465.573 3.43829
L469 -0.349676" style="fill:none;stroke:#000000;"/>
   </g>
   <g id="matplotlib.axis_5">
    <g id="xtick_5">
     <g id="line2d_12">
      <g>
       <use style="stroke:#000000;stroke-linecap:butt;stroke-width:0.5;" x="342.317647059" xlink:href="#mcb557df647" y="60.0352941176"/>
      </g>
     </g>
     <g id="text_7">
      <!-- $-1$ -->
      <g transform="translate(334.637647059 72.0752941176)scale(0.12 -0.12)">
       <use transform="translate(0.0 0.390625)" xlink:href="#Cmsy10-a1"/>
       <use transform="translate(77.685546875 0.390625)" xlink:href="#Cmr10-31"/>
      </g>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_13">
      <g>
       <use style="stroke:#000000;stroke-linecap:butt;stroke-width:0.5;" x="440.788235294" xlink:href="#mcb557df647" y="60.0352941176"/>
      </g>
     </g>
     <g id="text_8">
      <!-- $2$ -->
      <g transform="translate(437.788235294 72.0752941176)scale(0.12 -0.12)">
       <use transform="translate(0.0 0.390625)" xlink:href="#Cmr10-32"/>
      </g>
     </g>
    </g>
   </g>
   <g id="matplotlib.axis_6">
    <g id="ytick_5">
     <g id="line2d_14">
      <g>
       <use style="stroke:#000000;stroke-linecap:butt;stroke-width:0.5;" x="375.141176471" xlink:href="#mc8fcea1516" y="92.8588235294"/>
      </g>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_15">
      <g>
       <use style="stroke:#000000;stroke-linecap:butt;stroke-width:0.5;" x="375.141176471" xlink:href="#mc8fcea1516" y="27.2117647059"/>
      </g>
     </g>
    </g>
   </g>
   <g id="patch_15">
    <path d="
M325.906 10.8
L457.2 10.8" style="fill:none;opacity:0.0;"/>
   </g>
   <g id="patch_16">
    <path d="
M457.2 92.8588
L457.2 10.8" style="fill:none;opacity:0.0;"/>
   </g>
   <g id="text_9">
    <!-- $x(x+1)/6$ -->
    <defs>
     <path d="
M25 -2.20312
Q18.7969 -2.20312 14.6406 1.09375
Q10.5 4.39062 8.21875 9.64062
Q5.95312 14.8906 5.07812 20.6562
Q4.20312 26.4219 4.20312 32.3281
Q4.20312 40.2344 7.28125 48.1875
Q10.3594 56.1562 16.3281 61.375
Q22.3125 66.6094 30.5156 66.6094
Q33.9375 66.6094 36.8906 65.3125
Q39.8438 64.0156 41.5312 61.5
Q43.2188 58.9844 43.2188 55.4219
Q43.2188 53.375 41.8281 51.9844
Q40.4375 50.5938 38.375 50.5938
Q36.4219 50.5938 35 52
Q33.5938 53.4219 33.5938 55.4219
Q33.5938 57.375 35 58.7812
Q36.4219 60.2031 38.375 60.2031
L38.9219 60.2031
Q37.6406 62.0156 35.3281 62.8594
Q33.0156 63.7188 30.5156 63.7188
Q27.4844 63.7188 24.9219 62.3906
Q22.3594 61.0781 20.3125 58.8281
Q18.2656 56.5938 16.8906 53.875
Q15.5312 51.1719 14.7656 47.7031
Q14.0156 44.2344 13.8125 41.2031
Q13.625 38.1875 13.625 33.5938
Q15.375 37.7031 18.5938 40.3125
Q21.8281 42.9219 25.875 42.9219
Q30.3281 42.9219 33.9844 41.1094
Q37.6406 39.3125 40.2812 36.1094
Q42.9219 32.9062 44.3125 28.7969
Q45.7031 24.7031 45.7031 20.5156
Q45.7031 14.6562 43.0938 9.34375
Q40.4844 4.04688 35.7344 0.921875
Q31 -2.20312 25 -2.20312
M25 0.984375
Q28.8594 0.984375 31.2031 2.73438
Q33.5469 4.5 34.6406 7.39062
Q35.75 10.2969 36.0156 13.25
Q36.2812 16.2188 36.2812 20.5156
Q36.2812 26.1719 35.7344 30.1719
Q35.2031 34.1875 32.8125 37.2344
Q30.4219 40.2812 25.4844 40.2812
Q21.4375 40.2812 18.8281 37.5469
Q16.2188 34.8125 15.0156 30.6406
Q13.8125 26.4688 13.8125 22.6094
Q13.8125 21.2969 13.9219 20.6094
Q13.9219 20.4531 13.8906 20.3594
Q13.875 20.2656 13.8125 20.125
Q13.8125 15.8281 14.6875 11.4219
Q15.5781 7.03125 18.0625 4
Q20.5625 0.984375 25 0.984375" id="Cmr10-36"/>
    </defs>
    <g style="fill:#808080;" transform="translate(347.343529412 109.270588235)scale(0.14 -0.14)">
     <use transform="translate(0.0 25.0)" xlink:href="#Cmmi10-78"/>
     <use transform="translate(57.080078125 25.0)" xlink:href="#Cmr10-28"/>
     <use transform="translate(95.8984375 25.0)" xlink:href="#Cmmi10-78"/>
     <use transform="translate(170.537109375 25.0)" xlink:href="#Cmr10-2b"/>
     <use transform="translate(254.595703125 25.0)" xlink:href="#Cmr10-31"/>
     <use transform="translate(304.595703125 25.0)" xlink:href="#Cmr10-29"/>
     <use transform="translate(343.4140625 25.0)" xlink:href="#Cmmi10-3d"/>
     <use transform="translate(393.4140625 25.0)" xlink:href="#Cmr10-36"/>
    </g>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="p9c6b2962f1">
   <rect height="82.0588235294" width="131.294117647" x="168.352941176" y="10.8"/>
  </clipPath>
  <clipPath id="p24fba10013">
   <rect height="82.0588235294" width="131.294117647" x="10.8" y="10.8"/>
  </clipPath>
  <clipPath id="p741d0f4f9b">
   <rect height="82.0588235294" width="131.294117647" x="325.905882353" y="10.8"/>
  </clipPath>
 </defs>
</svg>