1 |
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2 |
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3 | mini_test = ->
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4 |
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5 | run_test [
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6 |
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7 |
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8 | "clearall",
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9 | "",
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10 |
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11 | "gdd=[[-exp(2*Phi(r)),0,0,0],[0,exp(2*Lambda(r)),0,0],[0,0,r^2,0],[0,0,0,r^2*sin(theta)^2]]",
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12 | "",
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13 |
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14 | "X=[t,r,theta,phi]",
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15 | "",
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16 |
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17 | "guu=inv(gdd)",
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18 | "",
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19 |
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20 | "gddd=d(gdd,X)",
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21 | "",
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22 |
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23 | "GAMDDD=1/2*(gddd+transpose(gddd,2,3)-transpose(transpose(gddd,2,3),1,2))",
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24 | "",
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25 |
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26 | "GAMUDD=contract(outer(guu,GAMDDD),2,3)",
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27 | "",
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28 |
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29 | "T1=d(GAMUDD,X)",
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30 | "",
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31 |
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32 | "T2=contract(outer(GAMUDD,GAMUDD),2,4)",
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33 | "",
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34 |
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35 | "RUDDD=transpose(T1,3,4)-T1+transpose(T2,2,3)-transpose(transpose(T2,2,3),3,4)",
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36 | "",
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37 |
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38 | "RDD=contract(RUDDD,1,3)",
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39 | "",
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40 |
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41 | "R=contract(contract(outer(guu,RDD),2,3),1,2)",
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42 | "",
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43 |
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44 | "GDD=RDD-1/2*gdd*R",
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45 | "",
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46 |
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47 | "Gtt=1/r^2*exp(2 Phi(r)) d(r*(1 - exp(-2 Lambda(r))),r)",
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48 | "",
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49 |
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50 | "Grr=-1/r^2*exp(2*Lambda(r))*(1-exp(-2*Lambda(r)))+2/r*d(Phi(r),r)",
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51 | "",
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52 |
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53 | "Gthetatheta=r^2*exp(-2*Lambda(r))*(d(d(Phi(r),r),r)+d(Phi(r),r)^2+d(Phi(r),r)/r-d(Phi(r),r)*d(Lambda(r),r)-d(Lambda(r),r)/r)",
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54 | "",
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55 |
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56 | "Gphiphi=sin(theta)^2*Gthetatheta",
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57 | "",
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58 |
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59 | "T=[[Gtt,0,0,0],[0,Grr,0,0],[0,0,Gthetatheta,0],[0,0,0,Gphiphi]]",
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60 | "",
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61 |
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62 | "GDD-T",
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63 | "[[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]]",
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64 |
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65 |
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66 |
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67 | "clearall",
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68 | "",
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69 |
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70 | "z=1-x^2-y^2",
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71 | "",
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72 |
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73 | "F=[x*y^2*z,-2*x^3,y*z^2]",
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74 | "",
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75 |
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76 | "S=[x,y,z]",
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77 | "",
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78 |
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79 | "s=dot(F,cross(d(S,x),d(S,y)))",
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80 | "",
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81 |
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82 | "defint(s,y,-sqrt(1-x^2),sqrt(1-x^2),x,-1,1)",
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83 | "1/48*pi",
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84 |
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85 |
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86 |
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87 | "clearall",
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88 | "",
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89 |
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90 | "laplacian(f)=1/r^2*d(r^2*d(f,r),r)+1/(r^2*sin(theta))*d(sin(theta)*d(f,theta),theta)+1/(r*sin(theta))^2*d(f,phi,phi)",
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91 | "",
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92 |
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93 | "n=7",
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94 | "",
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95 |
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96 | "l=3",
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97 | "",
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98 |
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99 | "m=1",
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100 | "",
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101 |
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102 | "R=r^l*exp(-r/n)*laguerre(2*r/n,n-l-1,2*l+1)",
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103 | "",
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104 |
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105 | "Y=legendre(cos(theta),l,abs(m))*exp(i*m*phi)",
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106 | "",
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107 |
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108 | "psi=R*Y",
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109 | "",
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110 |
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111 | "E=psi/n^2",
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112 | "",
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113 |
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114 | "K=laplacian(psi)",
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115 | "",
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116 |
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117 | "V=2*psi/r",
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118 | "",
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119 |
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120 |
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121 |
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122 |
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123 |
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124 |
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125 |
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126 |
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127 |
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128 |
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129 |
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130 |
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131 | "clearall",
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132 | "",
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133 |
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134 | "P=2x^3-y^3",
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135 | "",
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136 |
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137 | "Q=x^3+y^3",
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138 | "",
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139 |
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140 | "f=d(Q,x)-d(P,y)",
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141 | "",
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142 |
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143 | "x=r*cos(theta)",
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144 | "",
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145 |
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146 | "y=r*sin(theta)",
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147 | "",
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148 |
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149 | "defint(f*r,r,0,1,theta,0,2pi)",
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150 | "3/2*pi",
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151 |
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152 |
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153 |
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154 | "clearall",
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155 | "",
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156 |
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157 | "x=cos(t)",
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158 | "",
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159 |
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160 | "y=sin(t)",
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161 | "",
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162 |
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163 | "P=2x^3-y^3",
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164 | "",
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165 |
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166 | "Q=x^3+y^3",
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167 | "",
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168 |
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169 | "f=P*d(x,t)+Q*d(y,t)",
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170 | "",
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171 |
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172 | "f=circexp(f)",
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173 | "",
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174 |
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175 | "defint(f,t,0,2pi)",
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176 | "3/2*pi",
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177 |
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178 |
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179 |
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180 | "clearall",
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181 | "",
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182 |
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183 | "z=9-x^2-y^2",
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184 | "",
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185 |
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186 | "F=[3y,4z,-6x]",
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187 | "",
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188 |
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189 | "S=[x,y,z]",
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190 | "",
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191 |
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192 | "f=dot(curl(F),cross(d(S,x),d(S,y)))",
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193 | "",
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194 |
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195 | "x=r*cos(theta)",
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196 | "",
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197 |
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198 | "y=r*sin(theta)",
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199 | "",
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200 |
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201 | "defint(f*r,r,0,3,theta,0,2pi)",
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202 | "-27*pi",
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203 |
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204 |
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205 |
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206 | "clearall",
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207 | "",
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208 |
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209 | "x=3*cos(t)",
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210 | "",
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211 |
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212 | "y=3*sin(t)",
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213 | "",
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214 |
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215 | "z=9-x^2-y^2",
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216 | "",
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217 |
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218 | "P=3y",
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219 | "",
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220 |
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221 | "Q=4z",
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222 | "",
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223 |
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224 | "R=-6x",
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225 | "",
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226 |
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227 | "f=P*d(x,t)+Q*d(y,t)+R*d(z,t)",
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228 | "",
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229 |
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230 | "f=circexp(f)",
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231 | "",
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232 |
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233 | "defint(f,t,0,2pi)",
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234 | "-27*pi",
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235 | ]
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236 |
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