1# LaTeX2HTML 2018.3 (Released July 19, 2018) 2# Associate images original text with physical files. 3 4 5$key = q/(ell,m);MSF=1.2;LFS=12;AAT/; 6$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img19.png" 7 ALT="$(\ell, m)$">|; 8 9$key = q/(ell,m)le100;MSF=1.2;LFS=12;AAT/; 10$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img13.png" 11 ALT="$(\ell,m) \le 100$">|; 12 13$key = q/(theta,phi);MSF=1.2;LFS=12;AAT/; 14$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img23.png" 15 ALT="$(\theta,\phi)$">|; 16 17$key = q/(x,y,z)=(1,1,1)slashsqrt{3};MSF=1.2;LFS=12;AAT/; 18$cached_env_img{$key} = q|<IMG STYLE="height: 2.56ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img34.png" 19 ALT="$(x,y,z) = (1,1,1)/\sqrt{3}$">|; 20 21$key = q/0leellleell_{mathrm{max}};MSF=1.2;LFS=12;AAT/; 22$cached_env_img{$key} = q|<IMG STYLE="height: 2.04ex; vertical-align: -0.45ex; " SRC="|."$dir".q|idl_img11.png" 23 ALT="$0 \le \ell \le \ell_{\mathrm{max}}$">|; 24 25$key = q/0lemlem_{mathrm{max}};MSF=1.2;LFS=12;AAT/; 26$cached_env_img{$key} = q|<IMG STYLE="height: 1.98ex; vertical-align: -0.45ex; " SRC="|."$dir".q|idl_img12.png" 27 ALT="$0 \le m \le m_{\mathrm{max}}$">|; 28 29$key = q/0le|m|leell;MSF=1.2;LFS=12;AAT/; 30$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img75.png" 31 ALT="$0 \le \vert m\vert\le \ell$">|; 32 33$key = q/1lenle3;MSF=1.2;LFS=12;AAT/; 34$cached_env_img{$key} = q|<IMG STYLE="height: 1.92ex; vertical-align: -0.41ex; " SRC="|."$dir".q|idl_img52.png" 35 ALT="$1\le n \le 3$">|; 36 37$key = q/2le;MSF=1.2;LFS=12;AAT/; 38$cached_env_img{$key} = q|<IMG STYLE="height: 1.92ex; vertical-align: -0.41ex; " SRC="|."$dir".q|idl_img60.png" 39 ALT="$2 \le$">|; 40 41$key = q/2pi;MSF=1.2;LFS=12;AAT/; 42$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.10ex; " SRC="|."$dir".q|idl_img21.png" 43 ALT="$2\pi$">|; 44 45$key = q/2sin^{-1}left(||{ensuremath{textbf{V}}{-{ensuremath{textbf{W}}{||right)slash2;MSF=1.2;LFS=12;AAT/; 46$cached_env_img{$key} = q|<IMG STYLE="height: 2.45ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img28.png" 47 ALT="$2 \sin^{-1}\left(\vert\vert\ensuremath{\textbf{V}}-\ensuremath{\textbf{W}}\vert\vert\right)/2$">|; 48 49$key = q/3.4610^{18};MSF=1.2;LFS=12;AAT/; 50$cached_env_img{$key} = q|<IMG STYLE="height: 1.92ex; vertical-align: -0.10ex; " SRC="|."$dir".q|idl_img7.png" 51 ALT="$3.46 10^{18}$">|; 52 53$key = q/3pislash4;MSF=1.2;LFS=12;AAT/; 54$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img101.png" 55 ALT="$3\pi/4$">|; 56 57$key = q/9leq|mathrm{psym}|leq46;MSF=1.2;LFS=12;AAT/; 58$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img87.png" 59 ALT="$9\leq\vert\mathrm{psym}\vert\leq 46$">|; 60 61$key = q/=-1.6375,10^{30};MSF=1.2;LFS=12;AAT/; 62$cached_env_img{$key} = q|<IMG STYLE="height: 1.92ex; vertical-align: -0.29ex; " SRC="|."$dir".q|idl_img85.png" 63 ALT="$=-1.6375 10^{30}$">|; 64 65$key = q/=ell^2+ell+m+1;MSF=1.2;LFS=12;AAT/; 66$cached_env_img{$key} = q|<IMG STYLE="height: 2.04ex; vertical-align: -0.28ex; " SRC="|."$dir".q|idl_img76.png" 67 ALT="$=\ell^2 + 68\ell + m + 1$">|; 69 70$key = q/B(ell);MSF=1.2;LFS=12;AAT/; 71$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img2.png" 72 ALT="$B(\ell)$">|; 73 74$key = q/B(ell)=1;MSF=1.2;LFS=12;AAT/; 75$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img73.png" 76 ALT="$B(\ell) = 1$">|; 77 78$key = q/B(theta);MSF=1.2;LFS=12;AAT/; 79$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img3.png" 80 ALT="$B(\theta)$">|; 81 82$key = q/C(b)sqrt{2slash((2l_b+1)Deltal_b)};MSF=1.2;LFS=12;AAT/; 83$cached_env_img{$key} = q|<IMG STYLE="height: 3.56ex; vertical-align: -1.17ex; " SRC="|."$dir".q|idl_img45.png" 84 ALT="$C(b) \sqrt{ 2 / ((2l_b+1) \Delta l_b)}$">|; 85 86$key = q/C(ell);MSF=1.2;LFS=12;AAT/; 87$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img4.png" 88 ALT="$C(\ell)$">|; 89 90$key = q/C(ell)=sum_ma_{ellm}a^*_{ellm}slash(2ell+1);MSF=1.2;LFS=12;AAT/; 91$cached_env_img{$key} = q|<IMG STYLE="height: 2.39ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img56.png" 92 ALT="$C(\ell) = \sum_m a_{\ell m}a^*_{\ell m} / (2\ell+1)$">|; 93 94$key = q/C(ell)_{mathrm{meas}}=C(ell)B(ell)^2;MSF=1.2;LFS=12;AAT/; 95$cached_env_img{$key} = q|<IMG STYLE="height: 2.45ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img62.png" 96 ALT="$C(\ell)_{\mathrm{meas}} = C(\ell) 97B(\ell)^2$">|; 98 99$key = q/C(ell)_{mathrm{pix}}=C(ell)W(ell)^2;MSF=1.2;LFS=12;AAT/; 100$cached_env_img{$key} = q|<IMG STYLE="height: 2.56ex; vertical-align: -0.75ex; " SRC="|."$dir".q|idl_img68.png" 101 ALT="$C(\ell)_{\mathrm{pix}} = C(\ell) 102W(\ell)^2$">|; 103 104$key = q/C_ell;MSF=1.2;LFS=12;AAT/; 105$cached_env_img{$key} = q|<IMG STYLE="height: 2.04ex; vertical-align: -0.45ex; " SRC="|."$dir".q|idl_img57.png" 106 ALT="$C_\ell$">|; 107 108$key = q/Deltal(b);MSF=1.2;LFS=12;AAT/; 109$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img46.png" 110 ALT="$\Delta l(b)$">|; 111 112$key = q/Deltapsi;MSF=1.2;LFS=12;AAT/; 113$cached_env_img{$key} = q|<IMG STYLE="height: 2.16ex; vertical-align: -0.55ex; " SRC="|."$dir".q|idl_img106.png" 114 ALT="$\Delta\psi$">|; 115 116$key = q/Lambda;MSF=1.2;LFS=12;AAT/; 117$cached_env_img{$key} = q|<IMG STYLE="height: 1.69ex; vertical-align: -0.10ex; " SRC="|."$dir".q|idl_img5.png" 118 ALT="$\Lambda$">|; 119 120$key = q/N_wsimeq0.75N_{mathrm{side}}^2simeqN_{mathrm{pix}}slash16;MSF=1.2;LFS=12;AAT/; 121$cached_env_img{$key} = q|<IMG STYLE="height: 2.56ex; vertical-align: -0.75ex; " SRC="|."$dir".q|idl_img118.png" 122 ALT="$N_w \simeq 0.75 N_{\mathrm{side}}^2 \simeq N_{\mathrm{pix}}/16$">|; 123 124$key = q/N_wsimeqN_{mathrm{pix}}slash16;MSF=1.2;LFS=12;AAT/; 125$cached_env_img{$key} = q|<IMG STYLE="height: 2.45ex; vertical-align: -0.75ex; " SRC="|."$dir".q|idl_img95.png" 126 ALT="$N_w \simeq N_{\mathrm{pix}}/16$">|; 127 128$key = q/P(ell);MSF=1.2;LFS=12;AAT/; 129$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img71.png" 130 ALT="$P(\ell)$">|; 131 132$key = q/P(ell)=1;MSF=1.2;LFS=12;AAT/; 133$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img72.png" 134 ALT="$P(\ell) = 1351$">|; 136 137$key = q/P=sqrt{U^2+Q^2};MSF=1.2;LFS=12;AAT/; 138$cached_env_img{$key} = q|<IMG STYLE="height: 2.39ex; vertical-align: -0.55ex; " SRC="|."$dir".q|idl_img90.png" 139 ALT="$P = \sqrt{U^2 + Q^2}$">|; 140 141$key = q/P_ell;MSF=1.2;LFS=12;AAT/; 142$cached_env_img{$key} = q|<IMG STYLE="height: 2.04ex; vertical-align: -0.45ex; " SRC="|."$dir".q|idl_img43.png" 143 ALT="$P_\ell$">|; 144 145$key = q/Q'=Qcos(sDeltapsi)-Usin(sDeltapsi),;MSF=1.2;LFS=12;AAT/; 146$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img107.png" 147 ALT="$Q' = Q \cos (s\Delta\psi) - U \sin (s\Delta\psi), $">|; 148 149$key = q/U'=Ucos(sDeltapsi)+Qsin(sDeltapsi),;MSF=1.2;LFS=12;AAT/; 150$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img108.png" 151 ALT="$U' = U \cos (s\Delta\psi) + Q \sin (s\Delta\psi), $">|; 152 153$key = q/W(ell);MSF=1.2;LFS=12;AAT/; 154$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img8.png" 155 ALT="$W(\ell)$">|; 156 157$key = q/a^s_{ellm};MSF=1.2;LFS=12;AAT/; 158$cached_env_img{$key} = q|<IMG STYLE="height: 2.16ex; vertical-align: -0.67ex; " SRC="|."$dir".q|idl_img14.png" 159 ALT="$a^s_{\ell m}$">|; 160 161$key = q/a_{ellm};MSF=1.2;LFS=12;AAT/; 162$cached_env_img{$key} = q|<IMG STYLE="height: 1.46ex; vertical-align: -0.45ex; " SRC="|."$dir".q|idl_img1.png" 163 ALT="$a_{\ell m}$">|; 164 165$key = q/b(ell);MSF=1.2;LFS=12;AAT/; 166$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img35.png" 167 ALT="$b(\ell)$">|; 168 169$key = q/b(theta);MSF=1.2;LFS=12;AAT/; 170$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img36.png" 171 ALT="$b(\theta)$">|; 172 173$key = q/backslash;MSF=1.2;LFS=12;AAT/; 174$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img74.png" 175 ALT="$\backslash$">|; 176 177$key = q/cos^{-1}({ensuremath{textbf{V}}{.{ensuremath{textbf{W}}{);MSF=1.2;LFS=12;AAT/; 178$cached_env_img{$key} = q|<IMG STYLE="height: 2.45ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img27.png" 179 ALT="$\cos^{-1}(\ensuremath{\textbf{V}}.\ensuremath{\textbf{W}})$">|; 180 181$key = q/d_i=mathrm{dist}({ensuremath{textbf{V}}{,{{ensuremath{textbf{W}}{}_i);MSF=1.2;LFS=12;AAT/; 182$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img31.png" 183 ALT="$d_i = \mathrm{dist}(\ensuremath{\textbf{V}},{\ensuremath{\textbf{W}}}_i)$">|; 184 185$key = q/d_i=mathrm{dist}({{ensuremath{textbf{V}}{}_i,{{ensuremath{textbf{W}}{});MSF=1.2;LFS=12;AAT/; 186$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img32.png" 187 ALT="$d_i = \mathrm{dist}({\ensuremath{\textbf{V}}}_i,{\ensuremath{\textbf{W}}})$">|; 188 189$key = q/d_i=mathrm{dist}({{ensuremath{textbf{V}}{}_i,{{ensuremath{textbf{W}}{}_i);MSF=1.2;LFS=12;AAT/; 190$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img33.png" 191 ALT="$d_i = \mathrm{dist}({\ensuremath{\textbf{V}}}_i,{\ensuremath{\textbf{W}}}_i)$">|; 192 193$key = q/displaystyle0<phileqpislash2,;MSF=1.2;LFS=12;AAT/; 194$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img111.png" 195 ALT="$\displaystyle 0< \phi \leq \pi/2,$">|; 196 197$key = q/displaystyle<comment_mark>19272slash3>zgeq0,;MSF=1.2;LFS=12;AAT/; 198$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img112.png" 199 ALT="$\displaystyle %[Nside*(Nside+2)/4] 2002/3 > z \geq 0,$">|; 201 202$key = q/displaystyle<comment_mark>19512slash3>zgeq0,;MSF=1.2;LFS=12;AAT/; 203$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img115.png" 204 ALT="$\displaystyle %[Nside*(Nside+2)/4] 2052/3 > z \geq 0,$">|; 206 207$key = q/displaystylea_{ellm}^mathrm{OUT}=a_{ellm}^mathrm{IN}frac{B^mathrm{OUT}(ell)P^mathrm{OUT}(ell)}{B^mathrm{IN}(ell)P^mathrm{IN}(ell)},;MSF=1.2;LFS=12;AAT/; 208$cached_env_img{$key} = q|<IMG STYLE="height: 5.65ex; vertical-align: -2.27ex; " SRC="|."$dir".q|idl_img70.png" 209 ALT="$\displaystyle a_{\ell m}^\mathrm{OUT} = a_{\ell m}^\mathrm{IN} 210\frac{B^\mathrm{OUT}(\ell) P^\mathrm{OUT}(\ell)}{B^\mathrm{IN}(\ell) 211P^\mathrm{IN}(\ell)},$">|; 212 213$key = q/displaystyleb(ell);MSF=1.2;LFS=12;AAT/; 214$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img40.png" 215 ALT="$\displaystyle b(\ell)$">|; 216 217$key = q/displaystyleb(ell)=b_{ell0}sqrt{frac{4pi}{2ell+1}};MSF=1.2;LFS=12;AAT/; 218$cached_env_img{$key} = q|<IMG STYLE="height: 5.83ex; vertical-align: -2.17ex; " SRC="|."$dir".q|idl_img51.png" 219 ALT="$\displaystyle b(\ell)=b_{\ell 0} \sqrt{\frac{4 \pi}{2\ell+1}}$">|; 220 221$key = q/displaystyleb(theta)=sum_ellb(ell)P_ell(theta)frac{2ell+1}{4pi},;MSF=1.2;LFS=12;AAT/; 222$cached_env_img{$key} = q|<IMG STYLE="height: 5.65ex; vertical-align: -2.66ex; " SRC="|."$dir".q|idl_img50.png" 223 ALT="$\displaystyle b(\theta) = \sum_\ell b(\ell) P_\ell(\theta) \frac{2\ell+1}{4 \pi},$">|; 224 225$key = q/displaystyleb({textbf{r}})=sum_{ellm}b_{ellm}Y_{ellm}({textbf{r}}),;MSF=1.2;LFS=12;AAT/; 226$cached_env_img{$key} = q|<IMG STYLE="height: 4.37ex; vertical-align: -2.66ex; " SRC="|."$dir".q|idl_img49.png" 227 ALT="$\displaystyle b({\textbf{r}}) = \sum_{\ell m} b_{\ell m} Y_{\ell m}({\textbf{r}}),$">|; 228 229$key = q/displaystyleb_{ell0}sqrt{frac{4pi}{2ell+1}};MSF=1.2;LFS=12;AAT/; 230$cached_env_img{$key} = q|<IMG STYLE="height: 5.83ex; vertical-align: -2.17ex; " SRC="|."$dir".q|idl_img41.png" 231 ALT="$\displaystyle b_{\ell 0} \sqrt{\frac{4 \pi}{2\ell+1}}$">|; 232 233$key = q/displaystyleb_{ellm};MSF=1.2;LFS=12;AAT/; 234$cached_env_img{$key} = q|<IMG STYLE="height: 2.04ex; vertical-align: -0.45ex; " SRC="|."$dir".q|idl_img38.png" 235 ALT="$\displaystyle b_{\ell m}$">|; 236 237$key = q/displaystyleintb(theta)P_ell(theta)sin(theta)dtheta2pi;MSF=1.2;LFS=12;AAT/; 238$cached_env_img{$key} = q|<IMG STYLE="height: 4.31ex; vertical-align: -1.67ex; " SRC="|."$dir".q|idl_img42.png" 239 ALT="$\displaystyle \int b(\theta) P_\ell(\theta) \sin(\theta) d\theta 2\pi$">|; 240 241$key = q/displaystyleintd{textbf{r}}b({textbf{r}})Y_{ellm}^*({textbf{r}});MSF=1.2;LFS=12;AAT/; 242$cached_env_img{$key} = q|<IMG STYLE="height: 4.31ex; vertical-align: -1.67ex; " SRC="|."$dir".q|idl_img39.png" 243 ALT="$\displaystyle \int d{\textbf{r}} b({\textbf{r}}) Y_{\ell m}^*({\textbf{r}})$">|; 244 245$key = q/displaystylephi=0,quad{{rm{or}quadphi=frac{pi}{4N_{mathrm{side}}}.<comment_mark>1928;MSF=1.2;LFS=12;AAT/; 246$cached_env_img{$key} = q|<IMG STYLE="height: 4.60ex; vertical-align: -2.04ex; " SRC="|."$dir".q|idl_img113.png" 247 ALT="$\displaystyle \phi=0, \quad{\rm or}\quad \phi=\frac{\pi}{4N_{\mathrm{side}}}. % \nonumber %[Nside] 248$">|; 249 250$key = q/displaystylephi=0,quad{{rm{or}quadphi=frac{pi}{4N_{mathrm{side}}}.<comment_mark>1952;MSF=1.2;LFS=12;AAT/; 251$cached_env_img{$key} = q|<IMG STYLE="height: 4.60ex; vertical-align: -2.04ex; " SRC="|."$dir".q|idl_img116.png" 252 ALT="$\displaystyle \phi=0, \quad{\rm or}\quad \phi=\frac{\pi}{4N_{\mathrm{side}}}.% \nonumber %[Nside] 253$">|; 254 255$key = q/displaystylez=cos(theta)ge2slash3,;MSF=1.2;LFS=12;AAT/; 256$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img109.png" 257 ALT="$\displaystyle z=\cos(\theta)\ge 2/3,$">|; 258 259$key = q/ell(ell+1)C(ell)slash2pi;MSF=1.2;LFS=12;AAT/; 260$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img59.png" 261 ALT="$\ell(\ell+1)C(\ell)/2\pi$">|; 262 263$key = q/ell(ell+1)slash2pi;MSF=1.2;LFS=12;AAT/; 264$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img58.png" 265 ALT="$\ell(\ell+1)/2\pi$">|; 266 267$key = q/ell,m;MSF=1.2;LFS=12;AAT/; 268$cached_env_img{$key} = q|<IMG STYLE="height: 2.10ex; vertical-align: -0.55ex; " SRC="|."$dir".q|idl_img18.png" 269 ALT="$\ell,m$">|; 270 271$key = q/ell;MSF=1.2;LFS=12;AAT/; 272$cached_env_img{$key} = q|<IMG STYLE="height: 1.69ex; vertical-align: -0.10ex; " SRC="|."$dir".q|idl_img15.png" 273 ALT="$\ell$">|; 274 275$key = q/ell^2+ell+m+1;MSF=1.2;LFS=12;AAT/; 276$cached_env_img{$key} = q|<IMG STYLE="height: 2.04ex; vertical-align: -0.28ex; " SRC="|."$dir".q|idl_img55.png" 277 ALT="$\ell^2 + \ell + m + 1$">|; 278 279$key = q/ell_{mathrm{max}};MSF=1.2;LFS=12;AAT/; 280$cached_env_img{$key} = q|<IMG STYLE="height: 2.04ex; vertical-align: -0.45ex; " SRC="|."$dir".q|idl_img16.png" 281 ALT="$\ell_{\mathrm{max}}$">|; 282 283$key = q/equiv-1.637510^{30};MSF=1.2;LFS=12;AAT/; 284$cached_env_img{$key} = q|<IMG STYLE="height: 1.92ex; vertical-align: -0.29ex; " SRC="|."$dir".q|idl_img105.png" 285 ALT="$\equiv -1.6375 10^{30}$">|; 286 287$key = q/ge4;MSF=1.2;LFS=12;AAT/; 288$cached_env_img{$key} = q|<IMG STYLE="height: 1.92ex; vertical-align: -0.41ex; " SRC="|."$dir".q|idl_img119.png" 289 ALT="$\ge 4$">|; 290 291$key = q/ge;MSF=1.2;LFS=12;AAT/; 292$cached_env_img{$key} = q|<IMG STYLE="height: 1.87ex; vertical-align: -0.41ex; " SRC="|."$dir".q|idl_img103.png" 293 ALT="$\ge$">|; 294 295$key = q/i=ell^2+ell+m+1.;MSF=1.2;LFS=12;AAT/; 296$cached_env_img{$key} = q|<IMG STYLE="height: 2.04ex; vertical-align: -0.28ex; " SRC="|."$dir".q|idl_img54.png" 297 ALT="$i = \ell^2 + \ell + m + 1.$">|; 298 299$key = q/i=ell^2+ell+m+1;MSF=1.2;LFS=12;AAT/; 300$cached_env_img{$key} = q|<IMG STYLE="height: 2.04ex; vertical-align: -0.28ex; " SRC="|."$dir".q|idl_img10.png" 301 ALT="$i = \ell^2 + \ell + m + 1$">|; 302 303$key = q/l(l+1)slash2pi;MSF=1.2;LFS=12;AAT/; 304$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img47.png" 305 ALT="$l(l+1)/2\pi$">|; 306 307$key = q/ldots;MSF=1.2;LFS=12;AAT/; 308$cached_env_img{$key} = q|<IMG STYLE="height: 0.23ex; vertical-align: -0.10ex; " SRC="|."$dir".q|idl_img6.png" 309 ALT="$\ldots$">|; 310 311$key = q/le12N_{mathrm{side}}^2;MSF=1.2;LFS=12;AAT/; 312$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.67ex; " SRC="|."$dir".q|idl_img63.png" 313 ALT="$\le 12N_{\mathrm{side}}^2$">|; 314 315$key = q/le2^{29};MSF=1.2;LFS=12;AAT/; 316$cached_env_img{$key} = q|<IMG STYLE="height: 2.27ex; vertical-align: -0.41ex; " SRC="|."$dir".q|idl_img94.png" 317 ALT="$\le 2^{29}$">|; 318 319$key = q/le4;MSF=1.2;LFS=12;AAT/; 320$cached_env_img{$key} = q|<IMG STYLE="height: 1.92ex; vertical-align: -0.41ex; " SRC="|."$dir".q|idl_img61.png" 321 ALT="$\le 4$">|; 322 323$key = q/le;MSF=1.2;LFS=12;AAT/; 324$cached_env_img{$key} = q|<IMG STYLE="height: 1.87ex; vertical-align: -0.41ex; " SRC="|."$dir".q|idl_img104.png" 325 ALT="$\le$">|; 326 327$key = q/leq0;MSF=1.2;LFS=12;AAT/; 328$cached_env_img{$key} = q|<IMG STYLE="height: 1.92ex; vertical-align: -0.41ex; " SRC="|."$dir".q|idl_img88.png" 329 ALT="$\leq 0$">|; 330 331$key = q/m>ell;MSF=1.2;LFS=12;AAT/; 332$cached_env_img{$key} = q|<IMG STYLE="height: 1.69ex; vertical-align: -0.16ex; " SRC="|."$dir".q|idl_img17.png" 333 ALT="$m>\ell$">|; 334 335$key = q/mu;MSF=1.2;LFS=12;AAT/; 336$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.55ex; " SRC="|."$dir".q|idl_img66.png" 337 ALT="$\mu$">|; 338 339$key = q/ne0;MSF=1.2;LFS=12;AAT/; 340$cached_env_img{$key} = q|<IMG STYLE="height: 2.21ex; vertical-align: -0.55ex; " SRC="|."$dir".q|idl_img92.png" 341 ALT="$\ne 0$">|; 342 343$key = q/phi;MSF=1.2;LFS=12;AAT/; 344$cached_env_img{$key} = q|<IMG STYLE="height: 2.10ex; vertical-align: -0.55ex; " SRC="|."$dir".q|idl_img114.png" 345 ALT="$\phi$">|; 346 347$key = q/phi=tan^{-1}(UslashQ)slash2;MSF=1.2;LFS=12;AAT/; 348$cached_env_img{$key} = q|<IMG STYLE="height: 2.45ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img91.png" 349 ALT="$\phi = \tan^{-1}(U/Q) /2$">|; 350 351$key = q/pi;MSF=1.2;LFS=12;AAT/; 352$cached_env_img{$key} = q|<IMG STYLE="height: 1.11ex; vertical-align: -0.10ex; " SRC="|."$dir".q|idl_img20.png" 353 ALT="$\pi$">|; 354 355$key = q/pislash5;MSF=1.2;LFS=12;AAT/; 356$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img100.png" 357 ALT="$\pi/5$">|; 358 359$key = q/pm;MSF=1.2;LFS=12;AAT/; 360$cached_env_img{$key} = q|<IMG STYLE="height: 1.46ex; vertical-align: -0.29ex; " SRC="|."$dir".q|idl_img65.png" 361 ALT="$\pm$">|; 362 363$key = q/propto1slashsqrt{{{rm{n_obs}};MSF=1.2;LFS=12;AAT/; 364$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img102.png" 365 ALT="$\propto 1/\sqrt{{\rm n\_obs}}$">|; 366 367$key = q/propto2l+1;MSF=1.2;LFS=12;AAT/; 368$cached_env_img{$key} = q|<IMG STYLE="height: 1.81ex; vertical-align: -0.28ex; " SRC="|."$dir".q|idl_img48.png" 369 ALT="$\propto 2l+1$">|; 370 371$key = q/simeq;MSF=1.2;LFS=12;AAT/; 372$cached_env_img{$key} = q|<IMG STYLE="height: 1.05ex; vertical-align: -0.10ex; " SRC="|."$dir".q|idl_img86.png" 373 ALT="$\simeq$">|; 374 375$key = q/sqrt{3slashpi}3600slashN_{mathrm{side}};MSF=1.2;LFS=12;AAT/; 376$cached_env_img{$key} = q|<IMG STYLE="height: 3.56ex; vertical-align: -1.17ex; " SRC="|."$dir".q|idl_img67.png" 377 ALT="$\sqrt{3/\pi} 3600/N_{\mathrm{side}}$">|; 378 379$key = q/textstyle;MSF=1.2;LFS=12;AAT/; 380$cached_env_img{$key} = q|<IMG STYLE="vertical-align: 20px" 381 SRC="|."$dir".q|idl_img110.png" 382 ALT="$\textstyle $">|; 383 384$key = q/textstyleparbox{0.5hsize}{ifset,during{bfdegradation}eachbigpixelcontainingonebaonegoodpixelisconsideredasgood(optimistic)default=0(:notset)};MSF=1.2;LFS=12;AAT/; 385$cached_env_img{$key} = q|<IMG STYLE="height: 21.86ex; vertical-align: -10.43ex; " SRC="|."$dir".q|idl_img117.png" 386 ALT="$\textstyle \parbox{0.5\hsize}{if set, during {\bf degradation} each big pixel c... 387...ast one good pixel 388is considered as good (optimistic) 389default = 0 (:not set)}$">|; 390 391$key = q/textstyleparbox{hsize}{facname{}writesouttheinformationcontainedin{tt{Prim_stc}}30}{.parIf{ttNothealpix}isset,therestrictionsonNsidearevoid.};MSF=1.2;LFS=12;AAT/; 392$cached_env_img{$key} = q|<IMG STYLE="height: 55.43ex; vertical-align: -27.24ex; " SRC="|."$dir".q|idl_img120.png" 393 ALT="$\textstyle \parbox{\hsize}{\facname {} writes out the information contained in ... 394...{30}$.\\\\ 395\par 396If {\tt Nothealpix} is set, the restrictions on Nside are void.}$">|; 397 398$key = q/textstyleparbox{hsize}{facname~allowsthegenerationofarotationEulermatrix.Theuserr_matrix_new(a,b,c,slashZ)=euler_matrix({-{a,b,{-{c,slashZ)}};MSF=1.2;LFS=12;AAT/; 399$cached_env_img{$key} = q|<IMG STYLE="height: 41.85ex; vertical-align: -20.44ex; " SRC="|."$dir".q|idl_img53.png" 400 ALT="$\textstyle \parbox{\hsize}{\facname allows the generation of a rotation Eu... 401...Y)) \ [.1cm] 402euler\_matrix\_new(a,b,c,/Z) = euler\_matrix($-$a, b,$-$c,/Z) 403} 404}$">|; 405 406$key = q/textstyleparbox{hsize}{shouldproducesomethinglike{em1966081282562}meaningthattheide=128,themaximummultipolewas256,andthisafullskymap(type2).};MSF=1.2;LFS=12;AAT/; 407$cached_env_img{$key} = q|<IMG STYLE="height: 13.40ex; vertical-align: -6.22ex; " SRC="|."$dir".q|idl_img64.png" 408 ALT="$\textstyle \parbox{\hsize}{ should produce something like \\\\ 409{\em 196608 ... 410...s 411nside=128, the maximum multipole was 256, and this a full sky map 412(type 2). 413}$">|; 414 415$key = q/textstyleparbox{hsize}{willprintout{scriptsize{texttt{<Expression>hspace{3em}INTem}=hspace{3em}1A+1hspace{3em}INThspace{3em}=hspace{3em}1}}}};MSF=1.2;LFS=12;AAT/; 416$cached_env_img{$key} = q|<IMG STYLE="height: 7.23ex; vertical-align: -3.12ex; " SRC="|."$dir".q|idl_img69.png" 417 ALT="$\textstyle \parbox{\hsize}{ 418will print out 419\\\\ 420{\scriptsize{\texttt{ 421<Expressi... 422...} = \hspace{3em} 1 \\\\ 423A+1 \hspace{3em} INT \hspace{3em} = \hspace{3em} 1 424}}} 425}$">|; 426 427$key = q/theta;MSF=1.2;LFS=12;AAT/; 428$cached_env_img{$key} = q|<IMG STYLE="height: 1.69ex; vertical-align: -0.10ex; " SRC="|."$dir".q|idl_img37.png" 429 ALT="$\theta$">|; 430 431$key = q/x(0),ldots,x(n-1),y(0),ldots,y(n-1),z(0),ldots,z(n-1);MSF=1.2;LFS=12;AAT/; 432$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img22.png" 433 ALT="$x(0),\ldots,x(n-1), y(0),\ldots,y(n-1), z(0),\ldots,z(n-1)$">|; 434 435$key = q/x=sinthetacosphi;MSF=1.2;LFS=12;AAT/; 436$cached_env_img{$key} = q|<IMG STYLE="height: 2.10ex; vertical-align: -0.55ex; " SRC="|."$dir".q|idl_img24.png" 437 ALT="$x = \sin\theta\cos\phi$">|; 438 439$key = q/x_N(0),ldots,x_N(n-1),y_N(0),ldots,y_N(n-1),z_N(0),ldots,z_N(n-1);MSF=1.2;LFS=12;AAT/; 440$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img98.png" 441 ALT="$x_N(0),\ldots,x_N(n-1), y_N(0),\ldots,y_N(n-1), z_N(0),\ldots,z_N(n-1)$">|; 442 443$key = q/x_W(0),ldots,x_W(n-1),y_W(0),ldots,y_W(n-1),z_W(0),ldots,z_W(n-1);MSF=1.2;LFS=12;AAT/; 444$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img99.png" 445 ALT="$x_W(0),\ldots,x_W(n-1), y_W(0),\ldots,y_W(n-1),\ 446z_W(0),\ldots,z_W(n-1)$">|; 447 448$key = q/xgg1;MSF=1.2;LFS=12;AAT/; 449$cached_env_img{$key} = q|<IMG STYLE="height: 1.75ex; vertical-align: -0.19ex; " SRC="|."$dir".q|idl_img81.png" 450 ALT="$x\gg 1$">|; 451 452$key = q/xll1;MSF=1.2;LFS=12;AAT/; 453$cached_env_img{$key} = q|<IMG STYLE="height: 1.75ex; vertical-align: -0.19ex; " SRC="|."$dir".q|idl_img79.png" 454 ALT="$x\ll 1$">|; 455 456$key = q/y=sinh^{-1}(x);MSF=1.2;LFS=12;AAT/; 457$cached_env_img{$key} = q|<IMG STYLE="height: 2.62ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img77.png" 458 ALT="$y=\sinh^{-1} (x)$">|; 459 460$key = q/y=sinh^{-1}(xslash2)slashln(10);MSF=1.2;LFS=12;AAT/; 461$cached_env_img{$key} = q|<IMG STYLE="height: 2.62ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img82.png" 462 ALT="$y=\sinh^{-1} (x/2)/\ln(10)$">|; 463 464$key = q/y=sinthetasinphi;MSF=1.2;LFS=12;AAT/; 465$cached_env_img{$key} = q|<IMG STYLE="height: 2.10ex; vertical-align: -0.55ex; " SRC="|."$dir".q|idl_img25.png" 466 ALT="$y=\sin\theta\sin\phi$">|; 467 468$key = q/yapprox0.21x;MSF=1.2;LFS=12;AAT/; 469$cached_env_img{$key} = q|<IMG STYLE="height: 2.04ex; vertical-align: -0.55ex; " SRC="|."$dir".q|idl_img83.png" 470 ALT="$y \approx 0.21 x$">|; 471 472$key = q/yapproxln(2x);MSF=1.2;LFS=12;AAT/; 473$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img80.png" 474 ALT="$y\approx \ln(2x)$">|; 475 476$key = q/yapproxlog(x);MSF=1.2;LFS=12;AAT/; 477$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img84.png" 478 ALT="$y\approx \log(x)$">|; 479 480$key = q/yapproxx;MSF=1.2;LFS=12;AAT/; 481$cached_env_img{$key} = q|<IMG STYLE="height: 1.63ex; vertical-align: -0.55ex; " SRC="|."$dir".q|idl_img78.png" 482 ALT="$y \approx x$">|; 483 484$key = q/z=costheta;MSF=1.2;LFS=12;AAT/; 485$cached_env_img{$key} = q|<IMG STYLE="height: 1.69ex; vertical-align: -0.10ex; " SRC="|."$dir".q|idl_img26.png" 486 ALT="$z=\cos\theta$">|; 487 488$key = q/{0,ldots,4000};MSF=1.2;LFS=12;AAT/; 489$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img44.png" 490 ALT="$\{0,\ldots,4000\}$">|; 491 492$key = q/{1,ldots,2^{29}};MSF=1.2;LFS=12;AAT/; 493$cached_env_img{$key} = q|<IMG STYLE="height: 2.45ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img93.png" 494 ALT="$\{1,\ldots,2^{29}\}$">|; 495 496$key = q/{2,ldots,20};MSF=1.2;LFS=12;AAT/; 497$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img89.png" 498 ALT="$\{2,\ldots,20\}$">|; 499 500$key = q/{displaymath}N_w=frac{(N_{mathrm{side}}+1)(3N_{mathrm{side}}+1)}{4}.{displaymath};MSF=1.2;LFS=12;AAT/; 501$cached_env_img{$key} = q|<IMG STYLE="" 502 SRC="|."$dir".q|idl_img96.png" 503 ALT="\begin{displaymath}N_w=\frac{(N_{\mathrm{side}}+1)(3N_{\mathrm{side}}+1)}{4}.\end{displaymath}">|; 504 505$key = q/{displaymath}N_{mathrm{template}}=frac{1+N_{mathrm{side}}(N_{mathrm{side}}+6)}{4}.{displaymath};MSF=1.2;LFS=12;AAT/; 506$cached_env_img{$key} = q|<IMG STYLE="" 507 SRC="|."$dir".q|idl_img97.png" 508 ALT="\begin{displaymath}N_{\mathrm{template}}=\frac{1+N_{\mathrm{side}}(N_{\mathrm{side}}+6)}{4}.\end{displaymath}">|; 509 510$key = q/{ell,m};MSF=1.2;LFS=12;AAT/; 511$cached_env_img{$key} = q|<IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="|."$dir".q|idl_img9.png" 512 ALT="$\{\ell,m\}$">|; 513 514$key = q/{ensuremath{textbf{V}}{;MSF=1.2;LFS=12;AAT/; 515$cached_env_img{$key} = q|<IMG STYLE="height: 1.69ex; vertical-align: -0.10ex; " SRC="|."$dir".q|idl_img29.png" 516 ALT="$\ensuremath{\textbf{V}}$">|; 517 518$key = q/{ensuremath{textbf{W}}{;MSF=1.2;LFS=12;AAT/; 519$cached_env_img{$key} = q|<IMG STYLE="height: 1.69ex; vertical-align: -0.10ex; " SRC="|."$dir".q|idl_img30.png" 520 ALT="$\ensuremath{\textbf{W}}$">|; 521 5221; 523 524